# Classical Collapse to Black Holes and Quantum Bounces: A Review

## Abstract

**:**

## 1. Introduction

## 2. Classical Collapse...

- Scale factor $a(r,t)$ given by: $R=ra$.
- Mass function $M(r,t)$ given by: $F={r}^{3}M$.
- Velocity profile $b(r,t)$ given by: $G=1+{r}^{2}b$.

#### 2.1. Dust, Homogeneous Fluids and Null Shells

#### 2.2. Toy Models vs. Realistic Models

#### 2.3. Numerical Simulations

## 3. ...And Quantum Bounces

#### 3.1. A Brief History of Collapse Models with Quantum Corrected Interiors

#### 3.2. The Exterior Geometry

## 4. Open Issues

#### 4.1. The Horizon in the Exterior

#### 4.2. The Black Hole to White Hole Transition

#### 4.3. Lifespan of the Black Hole

#### 4.4. Hawking Radiation and Time Symmetry

#### 4.5. Matter Models

#### 4.6. Other Possibilities

## 5. Remnants and Phenomenology

#### 5.1. Compact Objects

#### 5.2. A Toy Model of Collapse to a Dark Energy Star

#### 5.3. Future Observations

## 6. Discussion

## Conflicts of Interest

## References

- Penrose, R. Gravitational Collapse and Space-Time Singularities. Phys. Rev. Lett.
**1965**, 14, 57–59. [Google Scholar] [CrossRef] - Hawking, S.W.; Penrose, R. The Singularities of Gravitational Collapse and Cosmology. Proc. R. Soc. Lond. A
**1970**, 314, 529–548. [Google Scholar] [CrossRef] - Hawking, S.W.; Ellis, G.F.R. The Large Scale Structure of Space-Time; Cambridge University Press: Cambridge, UK, 1973. [Google Scholar]
- Hawking, S.W. Breakdown of predictability in gravitational collapse. Phys. Rev. D
**1976**, 14, 2460–2473. [Google Scholar] [CrossRef] - Misner, C.W.; Thorne, K.S.; Zurek, W.H. John Wheeler, relativity, and quantum information. Phys. Today
**2009**, 1638, 40–46. [Google Scholar] [CrossRef] - Oppenheimer, J.R.; Snyder, H. On continued gravitational contraction. Phys. Rev.
**1939**, 56, 455–459. [Google Scholar] [CrossRef] - Datt, S. Über eine Klasse von Lösungen der Gravitationsgleichungen der Relativität. Z. Phys.
**1938**, 108, 314–321. [Google Scholar] [CrossRef] - Bardeen, J.M. Non singular general relativistic gravitational collapse. In Proceedings of the International Conference GR5; USSR: Tiblisi, Georgia, 1968. [Google Scholar]
- Hayward, S.A. Formation and evaporation of regular black holes. Phys. Rev. Lett.
**2006**, 96, 031103. [Google Scholar] [CrossRef] [PubMed] - Frolov, V.P. Notes on non-singular models of black holes. Phys. Rev. D
**2016**, 94, 104056. [Google Scholar] [CrossRef] - Bojowald, M. Non-singular black holes and degrees of freedom in quantum gravity. Phys. Rev. Lett.
**2005**, 95, 061301. [Google Scholar] [CrossRef] [PubMed] - Bambi, C.; Modesto, L. Rotating regular black holes. Phys. Lett. B
**2013**, 721, 329–334. [Google Scholar] [CrossRef] - Toshmatov, B.; Ahmedov, B.; Abdujabbarov, A.; Stuchlik, Z. Rotating Regular Black Hole Solution. Phys. Rev. D
**2014**, 89, 104017. [Google Scholar] [CrossRef] - Abdujabbarov, A.; Amir, M.; Ahmedov, B.; Ghosh, S.G. Shadow of rotating regular black holes. Phys. Rev. D
**2016**, 93, 104004. [Google Scholar] [CrossRef] - Neves, J.C.S.; Saa, A. Regular rotating black holes and the weak energy condition. Phys. Lett. B
**2014**, 734, 44–48. [Google Scholar] [CrossRef] - Ashtekar, A.; Bojowald, M. Quantum geometry and the Schwarzschild singularity. Class. Quantum Gravity
**2006**, 23, 391–411. [Google Scholar] [CrossRef] - Bojowald, M. Quantum Geometry and its Implications for Black Holes. Int. J. Mod. Phys. D
**2006**, 15, 1545–1559. [Google Scholar] [CrossRef] - Gambini, R.; Pullin, J. Loop quantization of the Schwarzschild black hole. Phys. Rev. Lett.
**2013**, 110, 211301. [Google Scholar] [CrossRef] [PubMed] - Hossenfelder, S.; Modesto, L.; Premont-Schwarz, I. A Model for non-singular black hole collapse and evaporation. Phys. Rev. D
**2010**, 81, 044036. [Google Scholar] [CrossRef] - Bonanno, A.; Reuter, M. Renormalization group improved black hole spacetimes. Phys. Rev. D
**2000**, 62, 043008. [Google Scholar] [CrossRef] - Gegenberg, J.; Kunstatter, G.; Small, R.D. Quantum Structure of Space Near a Black Hole Horizon. Class. Quantum Gravity
**2006**, 23, 6087–6100. [Google Scholar] [CrossRef] - Casadio, R.; Giugno, A.; Micu, O. Horizon Quantum Mechanics: A hitchhiker’s guide to quantum black holes. Int. J. Mod. Phys. D
**2016**, 25, 1630006. [Google Scholar] [CrossRef] - Torres, R. On the interior of (Quantum) Black Holes. Phys. Lett. B
**2013**, 724, 338–345. [Google Scholar] [CrossRef] - Torres, R. Non-Singular Black Holes, the Cosmological Constant and Asymptotic Safety. arXiv, 2017; arXiv:1703.09997. [Google Scholar]
- Mazur, P.O.; Mottola, E. Gravitational Condensate Stars: An Alternative to Black Holes. arXiv, 2002; arXiv:gr-qc/0109035. [Google Scholar]
- Baccetti, V.; Mann, R.B.; Terno, D.R. Role of evaporation in gravitational collapse. arXiv, 2016; arXiv:1610.07839. [Google Scholar]
- Baccetti, V.; Mann, R.B.; Terno, D.R. Horizon avoidance in spherically-symmetric collapse. arXiv, 2017; arXiv:1703.09369. [Google Scholar]
- Mersini-Houghton, L. Backreaction of Hawking Radiation on a Gravitationally Collapsing Star I: Black Holes? Phys. Lett. B
**2014**, 738, 61–67. [Google Scholar] [CrossRef] - Kawai, H.; Yokokura, Y. Interior of black holes and information recovery. Phys. Rev. D
**2016**, 93, 044011. [Google Scholar] [CrossRef] - Kawai, H.; Yokokura, Y. A model of black hole evaporation and 4D Weyl anomaly. arXiv, 2017; arXiv:1701.03455. [Google Scholar]
- Barceló, C.; Carballo-Rubio, R.; Garay, L.J. Mutiny at the white-hole district. Int. J. Mod. Phys. D
**2014**, 23, 1442022. [Google Scholar] [CrossRef] - Haggard, H.M.; Rovelli, C. Black hole fireworks: Quantum-gravity effects outside the horizon spark black to white hole tunneling. Phys. Rev. D
**2015**, 92, 104020. [Google Scholar] [CrossRef] - Barceló, C.; Carballo-Rubio, R.; Garay, L.J.; Jannes, G. The lifetime problem of evaporating black holes: Mutiny or resignation. Class. Quantum Gravity
**2015**, 32, 035012. [Google Scholar] [CrossRef] - Frolov, V.P.; Vilkovisky, G.A. Quantum Gravity removes classical singularities and shortens the life of a black hole. In Proceedings of the Second Marcel Grossmann Meeting on General Relativity, Trieste, Italy, 5–11 July 1979. [Google Scholar]
- Frolov, V.P.; Vilkovisky, G.A. Spherically Symmetric Collapse in Quantum Gravity. Phys. Lett. B
**1981**, 106, 307–313. [Google Scholar] [CrossRef] - Ashtekar, A.; Pawlowski, T.; Singh, P. Quantum nature of the big bang. Phys. Rev. Lett.
**2006**, 96, 141301. [Google Scholar] [CrossRef] [PubMed] - Ashtekar, A.; Pawlowski, T.; Singh, P.; Vandersloot, K. Loop quantum cosmology of k = 1 FRW models. Phys. Rev. D
**2007**, 75, 24035. [Google Scholar] [CrossRef] - Bojowald, M. Absence of Singularity in Loop Quantum Cosmology. Phys. Rev. Lett.
**2001**, 86, 5227–5230. [Google Scholar] [CrossRef] [PubMed] - Bojowald, M.; Goswami, R.; Maartens, R.; Singh, P. Black hole mass threshold from nonsingular quantum gravitational collapse. Phys. Rev. Lett.
**2005**, 95, 091302. [Google Scholar] [CrossRef] [PubMed] - Zhang, Y.; Zhu, Y.; Modesto, L.; Bambi, C. Can static regular black holes form from gravitational collapse? Eur. Phys. J. C
**2015**, 75, 96. [Google Scholar] [CrossRef] - Barrau, A.; Bolliet, B.; Vidotto, F.; Weimer, C. Phenomenology of bouncing black holes in quantum gravity: A closer look. J. Cosmol. Astropart. Phys.
**2016**, 2016, 022. [Google Scholar] [CrossRef] - Hawking, S.W. Gravitationally collapsed objects of very low mass. Mon. Not. R. Astron. Soc.
**1971**, 152, 75–78. [Google Scholar] [CrossRef] - Visser, M.; Wiltshire, D.L. Stable gravastars—An alternative to black holes? Class. Quantum Gravity
**2004**, 21, 1135–1152. [Google Scholar] [CrossRef] - Barceló, C.; Liberati, S.; Sonego, S.; Visser, M. Fate of gravitational collapse in semiclassical gravity. Phys. Rev. D
**2008**, 77, 044032. [Google Scholar] [CrossRef] - Itoh, N. Hydrostatic Equilibrium of Hypothetical Quark Stars. Prog. Theor. Phys.
**1970**, 44, 291–292. [Google Scholar] [CrossRef] - Witten, E. Cosmic separation of phases. Phys. Rev. D
**1984**, 30, 272–285. [Google Scholar] [CrossRef] - Ruffini, R.; Bonazzola, S. Systems of Self-Gravitating Particles in General Relativity and the Concept of an Equation of State. Phys. Rev.
**1969**, 187, 1767–1783. [Google Scholar] [CrossRef] - Schunck, F.E.; Mielke, E.W. General relativistic boson stars. Class. Quantum Gravity
**2003**, 20, R301–R356. [Google Scholar] [CrossRef] - Giddings, S.B. Black holes and massive remnants. Phys. Rev. D
**1992**, 46, 1347–1352. [Google Scholar] [CrossRef] - Chen, P.; Ong, Y.C.; Yeom, D. Black Hole Remnants and the Information Loss Paradox. Phys. Rep.
**2015**, 603, 1–45. [Google Scholar] [CrossRef] - Lochan, K.; Chakraborty, S.; Padmanabhan, T. Information retrieval from black holes. Phys. Rev. D
**2016**, 94, 044056. [Google Scholar] [CrossRef] - Israel, W. Singular hypersurfaces and thin shells in general relativity. Il Nuovo Cimento B (1965–1970)
**1966**, 44, 1–4. [Google Scholar] [CrossRef] - Fayos, F.; Jaen, X.; Llanta, E.; Senovilla, J.M.M. Matching of the Vaidya and Robertson-Walker metric. Class. Quantum Gravity
**1991**, 8, 2057–2068. [Google Scholar] [CrossRef] - Fayos, F.; Jaen, X.; Llanta, E.; Senovilla, J.M.M. Interiors of Vaidya’s radiating metric: Gravitational collapse. Phys. Rev. D
**1992**, 45, 2732–2738. [Google Scholar] [CrossRef] - Fayos, F.; Senovilla, J.M.M.; Torres, R. General matching of two spherically symmetric spacetimes. Phys. Rev. D
**1996**, 54, 4862–4872. [Google Scholar] [CrossRef] - Misner, C.; Sharp, D. Relativistic Equations for Adiabatic, Spherically Symmetric Gravitational Collapse. Phys. Rev.
**1964**, 136, B571–B576. [Google Scholar] [CrossRef] - Tooper, R.F. General Relativistic Polytropic Fluid Spheres. Astrophys. J.
**1964**, 140, 434–459. [Google Scholar] [CrossRef] - Joshi, P.S.; Malafarina, D. Recent developments in gravitational collapse and spacetime singularities. Int. J. Mod. Phys. D
**2011**, 20, 2641–2729. [Google Scholar] [CrossRef] - Martin-Moruno, P.; Visser, M. Semiclassical energy conditions for quantum vacuum states. J. High Energy Phys.
**2013**, 2013, 050. [Google Scholar] [CrossRef] - Senovilla, J.M.M.; Garfinkle, D. The 1965 Penrose singularity theorem. Class. Quantum Gravity
**2015**, 32, 124008. [Google Scholar] [CrossRef] - Roman, T.A.; Bergmann, P.G. Stellar collapse without singularities? Phys. Rev. D
**1983**, 28, 1265–1277. [Google Scholar] [CrossRef] - Vaidya, P. The Gravitational Field of a Radiating Star. Proc. Math. Sci.
**1951**, 33, 264–276. [Google Scholar] - Joshi, P.S. Gravitational Collapse and Spacetime Singularities; Cambridge University Press: Cambridge, UK, 2008. [Google Scholar]
- Barceló, C.; Carballo-Rubio, R.; Garay, L.J. Where does the physics of extreme gravitational collapse reside? Universe
**2016**, 2, 7. [Google Scholar] [CrossRef] - Ziprick, J.; Kunstatter, G. Spherically Symmetric Black Hole Formation in Painlevé-Gullstrand Coordinates. Phys. Rev. D
**2009**, 79, 101503. [Google Scholar] [CrossRef] - Silk, J.; Wright, J.P. The gravitational collapse of a slowly rotating relativistic star. Mon. Not. R. Astron. Soc.
**1969**, 143, 55–71. [Google Scholar] [CrossRef] - Chandrasekhar, S.; Miller, J.C. On slowly rotating homogeneous masses in general relativity. Mon. Not. R. Astron. Soc.
**1974**, 167, 63–80. [Google Scholar] [CrossRef] - Hartle, J.B.; Thorne, K.S. Slowly Rotating Relativistic Stars. II. Models for Neutron Stars and Supermassive Stars. Astrophys. J.
**1968**, 153, 807–834. [Google Scholar] [CrossRef] - Baumgarte, T.W.; Shapiro, S.L. Numerical Relativity: Solving Einstein’s Equations on the Computer; Cambridge University Press: Cambridge, UK, 2010. [Google Scholar]
- May, M.M.; White, R.H. Hydrodynamic Calculations of General-Relativistic Collapse. Phys. Rev.
**1966**, 141, 1232–1241. [Google Scholar] [CrossRef] - Stark, R.F.; Piran, T. Gravitational-wave emission from rotating gravitational collapse. Phys. Rev. Lett.
**1985**, 55, 891–894. [Google Scholar] [CrossRef] [PubMed] - Eardley, D.M.; Smarr, L. Time functions in numerical relativity: Marginally bound dust collapse. Phys. Rev. D
**1979**, 19, 2239–2259. [Google Scholar] [CrossRef] - Shapiro, S.L.; Teukolsky, S.A. Formation of naked singularities: The violation of cosmic censorship. Phys. Rev. Lett.
**1991**, 66, 994–997. [Google Scholar] [CrossRef] [PubMed] - Baiotti, L.; Hawke, I.; Montero, P.J.; Loffler, F.; Rezzolla, L.; Stergioulas, N.; Font, J.A.; Seidel, E. Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole. Phys. Rev. D
**2005**, 71, 024035. [Google Scholar] [CrossRef] - Giacomazzo, B.; Rezzolla, L.; Stergioulas, N. Collapse of differentially rotating neutron stars and cosmic censorship. Phys. Rev. D
**2011**, 84, 024022. [Google Scholar] [CrossRef] - Nathanail, A.; Most, E.R.; Rezzolla, L. Gravitational collapse to a Kerr–Newman black hole. Mon. Not. R. Astron. Soc. Lett.
**2017**, 469, L31–L35. [Google Scholar] [CrossRef] - Hajicek, P. Unitary dynamics of spherical null gravitating shells. Nucl. Phys. B
**2001**, 603, 555–577. [Google Scholar] [CrossRef] - Hajicek, P.; Kiefer, C. Singularity avoidance by collapsing shells in quantum gravity. Int. J. Mod. Phys. D
**2001**, 10, 775–779. [Google Scholar] [CrossRef] - Vaz, C.; Witten, L.; Singh, T.P. Towards a quantization of null dust collapse. Phys. Rev. D
**2002**, 65, 104016. [Google Scholar] [CrossRef] - Vaz, C. Quantum gravitational collapse does not result in a black hole. Nucl. Phys. B
**2015**, 891, 558–569. [Google Scholar] [CrossRef] - Kiefer, C.; Múller-Hill, J.; Vaz, C. Classical and quantum LTB model for the non-marginal case. Phys. Rev. D
**2006**, 73, 044025. [Google Scholar] [CrossRef] - Tippett, B.K.; Husain, V. Gravitational collapse of quantum matter. Phys. Rev. D
**2011**, 84, 104031. [Google Scholar] [CrossRef] - Husain, V.; Winkler, O. Quantum resolution of black hole singularities. Class. Quantum Gravity
**2005**, 22, L127–L134. [Google Scholar] [CrossRef] - Husain, V.; Winkler, O. Quantum black holes from null expansion operators. Class. Quantum Gravity
**2005**, 22, L135–L141. [Google Scholar] [CrossRef] - Husain, V.; Winkler, O. Flat slice Hamiltonian formalism for dynamical black holes. Phys. Rev. D
**2005**, 71, 104001. [Google Scholar] [CrossRef] - Husain, V.; Winkler, O. Quantum Hamiltonian for gravitational collapse. Phys. Rev. D
**2006**, 73, 124007. [Google Scholar] [CrossRef] - Husain, V.; Winkler, O. Semiclassical states for quantum cosmology. Phys. Rev. D
**2007**, 75, 024014. [Google Scholar] [CrossRef] - Husain, V.; Terno, D.R. Dynamics and entanglement in spherically symmetric quantum gravity. Phys. Rev. D
**2010**, 81, 044039. [Google Scholar] [CrossRef] - Ziprick, J.; Kunstatter, G. Dynamical Singularity Resolution in Spherically Symmetric Black Hole Formation. Phys. Rev. D
**2009**, 80, 024032. [Google Scholar] [CrossRef] - Ziprick, J.; Kunstatter, G. Quantum Corrected Spherical Collapse: A Phenomenological Framework. Phys. Rev. D
**2010**, 82, 044031. [Google Scholar] [CrossRef] - Abedi, J.; Arfaei, H. Obstruction of black hole singularity by quantum field theory effects. J. High Energy Phys.
**2016**, 2016, 135. [Google Scholar] [CrossRef] - Arfaei, H.; Noorikuhani, M. Quantum vacuum effects on the final fate of a collapsing ball of dust. J. High Energy Phys.
**2017**, 2017, 124. [Google Scholar] [CrossRef] - Koch, B.; Saueressig, F. Black holes within Asymptotic Safety. Int. J. Mod. Phys. A
**2014**, 29, 1430011. [Google Scholar] [CrossRef] - Saueressig, F.; Alkofer, N.; D’Odorico, G.; Vidotto, F. Black holes in Asymptotically Safe Gravity. arXiv, 2015; arXiv:1503.06472. [Google Scholar]
- Bonanno, A.; Reuter, M. Spacetime structure of an evaporating black hole in quantum gravity. Phys. Rev. D
**2006**, 73, 083005. [Google Scholar] [CrossRef] - Fayos, F.; Torres, R. A quantum improvement to the gravitational collapse of radiating stars. Class. Quantum Gravity
**2011**, 28, 105004. [Google Scholar] [CrossRef] - Casadio, R.; Hsu, S.D.H.; Mirza, B. Asymptotic Safety, Singularities, and Gravitational Collapse. Phys. Lett. B
**2011**, 695, 317–319. [Google Scholar] [CrossRef] - Bambi, C.; Malafarina, D.; Modesto, L. Terminating black holes in asymptotically free quantum gravity. Eur. Phys. J. C
**2014**, 74, 2767. [Google Scholar] [CrossRef] - Barcelò, C.; Garay, L.J.; Jannes, G. Quantum Non-Gravity and Stellar Collapse. Found. Phys.
**2011**, 41, 1532–1541. [Google Scholar] [CrossRef] - Ashtekar, A. Loop Quantum Cosmology: An Overview. Gen. Relativ. Gravit.
**2009**, 41, 707–741. [Google Scholar] [CrossRef] - Goswami, R.; Joshi, P.S.; Singh, P. Quantum evaporation of a naked singularity. Phys. Rev. Lett.
**2006**, 96, 031302. [Google Scholar] [CrossRef] [PubMed] - Bambi, C.; Malafarina, D.; Modesto, L. Non-singular quantum-inspired gravitational collapse. Phys. Rev. D
**2013**, 88, 044009. [Google Scholar] [CrossRef] - Torres, R.; Fayos, F. Singularity free gravitational collapse in an effective dynamical quantum spacetime. Phys. Lett. B
**2014**, 733, 169–175. [Google Scholar] [CrossRef] - Torres, R. Singularity-free gravitational collapse and asymptotic safety. Phys. Lett. B
**2014**, 733, 21–24. [Google Scholar] [CrossRef] - Bambi, C.; Malafarina, D.; Modesto, L. Black supernovae and black holes in non-local gravity. J. High Energy Phys.
**2016**, 2016, 147. [Google Scholar] [CrossRef] - Ziaie, A.H.; Moniz, P.V.; Ranjbar, A.; Sepangi, H.R. Einstein-Cartan gravitational collapse of a homogeneous Weyssenhoff fluid. Eur. Phys. J. C
**2014**, 74, 3154. [Google Scholar] [CrossRef] - Bambi, C.; Cardenas-Avendano, A.; Olmo, G.J.; Rubiera-Garcia, D. Wormholes and nonsingular space-times in Palatini f(R) gravity. Phys. Rev. D
**2016**, 93, 064016. [Google Scholar] [CrossRef] - Lobo, F.S.N.; Martinez-Asencio, J.; Olmo, G.J.; Rubiera-Garcia, D. Dynamical generation of wormholes with charged fluids in quadratic Palatini gravity. Phys. Rev. D
**2014**, 90, 024033. [Google Scholar] [CrossRef] - Kreienbuehl, A.; Husain, V.; Seahra, S.S. Modified general relativity as a model for quantum gravitational collapse. Class. Quantum Gravity
**2012**, 29, 095008. [Google Scholar] [CrossRef] - Choptuik, M.W. Universality and scaling in gravitational collapse of a massless scalar field. Phys. Rev. Lett.
**1993**, 70, 9–12. [Google Scholar] [CrossRef] [PubMed] - Casadio, R.; Micu, O.; Nicolini, P. Minimum length effects in black hole physics. In Quantum Aspects of Black Holes; Calmet, X., Ed.; Springer: Berlin/Heidelberg, Germany, 2014. [Google Scholar]
- Bambi, C.; Malafarina, D.; Marcianò, A.; Modesto, L. Singularity avoidance in classical gravity from four-fermion interaction. Phys. Lett. B
**2014**, 734, 27–30. [Google Scholar] [CrossRef] - Markov, M.A. Limiting density of matter as a universal law of nature. J. Exp. Theor. Phys. Lett.
**1982**, 36, 265–267. [Google Scholar] - Markov, M.A. Problems of a perpetually oscillating universe. Ann. Phys.
**1984**, 155, 333–357. [Google Scholar] [CrossRef] - Hawking, S.W. Information Preservation and Weather Forecasting for Black Holes. arXiv, 2014; arXiv:1401.5761. [Google Scholar]
- Ambrus, M.; Hajicek, P. Quantum superposition principle and graviational collapse: Scattering times for spherical shells. Phys. Rev. D
**2005**, 72, 064025. [Google Scholar] [CrossRef] - Joshi, P.S.; Dwivedi, I.H. Naked singularities in spherically symmetric inhomogeneous Tolman-Bondi dust cloud collapse. Phys. Rev. D
**1993**, 47, 5357–5369. [Google Scholar] [CrossRef] - Helou, A.; Musco, I.; Miller, J.C. Causal Nature and Dynamics of Trapping Horizons in Black Hole Collapse. arXiv, 2016; arXiv:1601.05109. [Google Scholar]
- Barceló, C.; Carballo-Rubio, R.; Garay, L.J. Black holes turn white fast, otherwise stay black: No half measures. J. High Energy Phys.
**2016**, 2016, 157. [Google Scholar] [CrossRef] - Visser, M. Physical observability of horizons. Phys. Rev. D
**2014**, 90, 127502. [Google Scholar] [CrossRef] - Misner, C.W.; Thorne, K.S.; Wheeler, J.A. Gravitation; W. H. Freeman: San Francisco, CA, USA, 1973. [Google Scholar]
- Barceló, C.; Carballo-Rubio, R.; Garay, L.J. Exponential fading to white of black holes in quantum gravity. Class. Quantum Gravity
**2017**, 34, 105007. [Google Scholar] [CrossRef] - Christodoulou, M.; Rovelli, C.; Speziale, S.; Vilensky, I. Realistic Observable in Background-Free Quantum Gravity: The Planck-Star Tunnelling-Time. Phys. Rev. D
**2016**, 94, 084035. [Google Scholar] [CrossRef] - Eardley, D.M. Death of white holes in the early universe. Phys. Rev. Lett.
**1974**, 33, 442–444. [Google Scholar] [CrossRef] - Barrabès, C.; Brady, P.R.; Poisson, E. Death of white holes. Phys. Rev. D
**1993**, 47, 2383–2387. [Google Scholar] [CrossRef] - Hawking, S.W. Particle creation by black holes. Commun. Math. Phys.
**1975**, 43, 199–220. [Google Scholar] [CrossRef] - Ashtekar, A.; Bojowald, M. Black hole evaporation: A paradigm. Class. Quantum Gravity
**2005**, 22, 3349–3362. [Google Scholar] [CrossRef] - Gerlach, U.H. The mechanism of blackbody radiation from an incipient black hole. Phys. Rev. D
**1976**, 14, 1479–1508. [Google Scholar] [CrossRef] - Torres, R.; Fayos, F. On the quantum corrected gravitational collapse. arXiv, 2015. [Google Scholar] [CrossRef]
- Giddings, S.B. Hawking radiation, the Stefan-Boltzmann law, and unitarization. Phys. Lett. B
**2016**, 754, 39–42. [Google Scholar] [CrossRef] - Dey, R.; Liberati, S.; Pranzetti, D. The black hole quantum atmosphere. arXiv, 2017; arXiv:1701.06161. [Google Scholar]
- Bardeen, J.M.; Carter, B.; Hawking, S.W. The four laws of black hole mechanics. Commun. Math. Phys.
**1973**, 31, 161–170. [Google Scholar] [CrossRef] - De Lorenzo, T.; Perez, A. Improved Black Hole Fireworks: Asymmetric Black-Hole-to-White-Hole Tunneling Scenario. Phys. Rev. D
**2016**, 93, 124018. [Google Scholar] [CrossRef] - Booth, I.; Brits, L.; Gonzalez, J.A.; van den Broeck, C. Marginally trapped tubes and dynamical horizons. Class. Quantum Gravity
**2006**, 23, 413–440. [Google Scholar] [CrossRef] - Brizuela, D.; Marugán, G.A.M.; Pawlowski, T. Effective dynamics of the hybrid quantization of the Gowdy T
^{3}universe. Phys. Rev. D**2011**, 84, 124017. [Google Scholar] [CrossRef] - Fernandez-Mendez, M.; Marugán, G.A.M. Effective dynamics of scalar perturbations in a flat Friedmann-Robertson-Walker spacetime in loop quantum cosmology. Phys. Rev. D
**2014**, 89, 044041. [Google Scholar] [CrossRef] - Liu, Y.; Malafarina, D.; Modesto, L.; Bambi, C. Singularity avoidance in quantum-inspired inhomogeneous dust collapse. Phys. Rev. D
**2014**, 90, 044040. [Google Scholar] [CrossRef] - Bojowald, M.; Harada, T.; Tibrewala, R. Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity. Phys. Rev. D
**2008**, 78, 064057. [Google Scholar] [CrossRef] - Ford, L.H.; Roman, T.A. Averaged Energy Conditions and Quantum Inequalities. Phys. Rev. D
**1995**, 51, 4277–4286. [Google Scholar] [CrossRef] - Abreu, G.; Barceló, C.; Visser, M. Entropy bounds in terms of the w parameter. J. High Energy Phys.
**2011**, 2011, 092. [Google Scholar] [CrossRef] - Martin-Moruno, P.; Visser, M. Classical and quantum flux energy conditions for vacuum quantum states. Phys. Rev. D
**2013**, 88, 061701. [Google Scholar] [CrossRef] - Barceló, C.; Visser, M. Twilight for the energy conditions? Int. J. Mod. Phys. D
**2002**, 11, 1553–1560. [Google Scholar] [CrossRef] - Weber, F. Strange Quark Matter and Compact Stars. Prog. Part. Nucl. Phys.
**2005**, 54, 193–288. [Google Scholar] [CrossRef] - Zel’dovich, Y.B. The Equation of State at Ultrahigh Densities and Its Relativistic Limitations. J. Exp. Theor. Phys.
**1962**, 14, 1143–1147. [Google Scholar] - Sakharov, A.D. The initial stage of an expanding universe and the appearance of a nonuniform distribution of matter. J. Exp. Theor. Phys.
**1966**, 22, 241–249. [Google Scholar] - Hagedorn, R. Thermodynamics of strong interactions at high energy and its consequences for astrophysics. Astron. Astrophys.
**1970**, 5, 184–205. [Google Scholar] - Bahcall, J.N.; Frautschi, S. The hadron barrier in cosmology and gravitational collapse. Astrophys. J.
**1971**, 170, L81–L84. [Google Scholar] [CrossRef] - Malafarina, D. Gravitational collapse of Hagedorn fluids. Phys. Rev. D
**2016**, 93, 104042. [Google Scholar] [CrossRef] - Harko, T. Gravitational collapse of a Hagedorn fluid in Vaidya geometry. Phys. Rev. D
**2003**, 68, 064005. [Google Scholar] [CrossRef] - Frolov, V.P.; Markov, M.A.; Mukhanov, V.F. Black Holes as Possible Sources of Closed and Semiclosed Worlds. Phys. Rev. D
**1990**, 41, 383–394. [Google Scholar] [CrossRef] - Poplawski, N. Universe in a black hole in Einstein-Cartan gravity. Astrophys. J.
**2016**, 832, 96. [Google Scholar] [CrossRef] - Hsu, S.D.H. Spacetime topology change and black hole information. Phys. Lett. B
**2007**, 644, 67–71. [Google Scholar] [CrossRef] - Smolin, L. Did the univrese evolve? Class. Quantum Gravity
**1992**, 9, 173–191. [Google Scholar] [CrossRef] - Campiglia, M.; Gambini, R.; Olmedo, J.; Pullin, J. Quantum self-gravitating collapsing matter in a quantum geometry. Class. Quantum Gravity
**2016**, 33, 18LT01. [Google Scholar] [CrossRef] - Singh, P.; Vidotto, F. Exotic singularities and spatially curved Loop Quantum Cosmology. Phys. Rev. D
**2011**, 83, 064027. [Google Scholar] [CrossRef] - Hossenfelder, S.; Smolin, L. Conservative solutions to the black hole information problem. Phys. Rev. D
**2010**, 81, 064009. [Google Scholar] [CrossRef] - Hawking, S.W.; Laflamme, R. Baby Universes and the Non-renormalizability of Gravity. Phys. Lett. B
**1988**, 209, 39–41. [Google Scholar] [CrossRef] - Hawking, S.W. Wormholes in Space-Time. Phys. Rev. D
**1988**, 37, 904–910. [Google Scholar] [CrossRef] - Hellaby, C.; Dray, T. Failure of standard conservation laws at a classical change of signature. Phys. Rev. D
**1994**, 49, 5096–5104. [Google Scholar] [CrossRef] - Liberati, S.; Maccione, L. Quantum gravity phenomenology: Achievements and challenges. J. Phys. Conf. Ser.
**2011**, 314, 012007. [Google Scholar] [CrossRef] - Ashtekar, A.; Gupt, B. Quantum gravity in the sky: Interplay between fundamental theory and observations. Class. Quantum Gravity
**2017**, 34, 014002. [Google Scholar] [CrossRef] - Narlikar, J.V.; Rao, K.A.; Dadhich, N. High energy radiation from white holes. Nature
**1974**, 251, 590–591. [Google Scholar] [CrossRef] - Tolman, R.C. Static solutions of Einstein’s field equations for spheres of fluid. Phys. Rev.
**1939**, 55, 364–373. [Google Scholar] [CrossRef] - Oppenheimer, J.R.; Volkoff, G. On massive neutron cores. Phys. Rev.
**1939**, 55, 374–381. [Google Scholar] [CrossRef] - Chandrasekhar, S. The maximum mass of ideal white dwarfs. Astrophys. J.
**1931**, 74, 81–82. [Google Scholar] [CrossRef] - Visser, M.; Barcelo, C.; Liberati, S.; Sonego, S. Small, dark, and heavy: But is it a black hole? In Proceedings of the Black Holes in General Relativity and String Theory, Veli Losinj, Croatia, 24–30 August 2008. [Google Scholar]
- Mazur, P.O.; Mottola, E. Surface tension and negative pressure interior of a non-singular ’black hole’. Class. Quantum Gravity
**2015**, 32, 215024. [Google Scholar] [CrossRef] - Cattoen, C.; Faber, T.; Visser, M. Gravastars must have anisotropic pressures. Class. Quantum Gravity
**2005**, 22, 4189–4202. [Google Scholar] [CrossRef] - Chirenti, C.B.M.H.; Rezzolla, L. How to tell a gravastar from a black hole. Class. Quantum Gravity
**2007**, 24, 4191–4206. [Google Scholar] [CrossRef] - Cardoso, V.; Franzin, E.; Pani, P. Is the Gravitational-Wave Ringdown a Probe of the Event Horizon? Phys. Rev. Lett.
**2016**, 116, 171101. [Google Scholar] [CrossRef] [PubMed] - Sakai, N.; Saida, H.; Tamaki, T. Gravastar shadows. Phys. Rev. D
**2014**, 90, 104013. [Google Scholar] [CrossRef] - Barcelò, C.; Liberati, S.; Sonego, S.; Visser, M. Hawking-like radiation does not require a trapped region. Phys. Rev. Lett.
**2006**, 97, 171301. [Google Scholar] [CrossRef] [PubMed] - Husain, V.; Winkler, O. How red is a quantum black hole? Int. J. Mod. Phys. D
**2005**, 14, 2233–2238. [Google Scholar] [CrossRef] - Rovelli, C.; Vidotto, F. Planck stars. Int. J. Mod. Phys. D
**2014**, 23, 1442026. [Google Scholar] [CrossRef] - De Lorenzo, T.; Pacilio, C.; Rovelli, C.; Speziale, S. On the Effective Metric of a Planck Star. Gen. Relativ. Gravit.
**2015**, 47, 41. [Google Scholar] [CrossRef] - Barrau, A.; Rovelli, C. Planck star phenomenology. Phys. Lett. B
**2014**, 739, 405–409. [Google Scholar] [CrossRef] - Lobo, F.S.N. Stable dark energy stars. Class. Quantum Gravity
**2006**, 23, 1525–1541. [Google Scholar] [CrossRef] - DeBenedictis, A.; Garattini, R.; Lobo, F.S.N. Phantom stars and topology change. Phys. Rev. D
**2008**, 78, 104003. [Google Scholar] [CrossRef] - Rahaman, F.; Yadav, A.K.; Ray, S.; Maulick, R.; Sharma, R. Singularity-free dark energy star. Gen. Relativ. Gravit.
**2012**, 44, 107–124. [Google Scholar] [CrossRef] - Giddings, S.B. Possible observational windows for quantum effects from black holes. Phys. Rev. D
**2014**, 90, 124033. [Google Scholar] [CrossRef] - Stuchlík, Z.; Schee, J. Circular geodesic of Bardeen and Ayon–Beato–Garcia regular black-hole and no-horizon spacetimes. Int. J. Mod. Phys. D
**2015**, 24, 1550020. [Google Scholar] [CrossRef] - Eiroa, E.F.; Sendra, C.M. Gravitational lensing by a regular black hole. Class. Quantum Gravity
**2011**, 28, 085008. [Google Scholar] [CrossRef] - Chiba, T.; Kimura, M. A Note on Geodesics in the Hayward Metric. Prog. Theor. Exp. Phys.
**2017**, 2017, 043E01. [Google Scholar] [CrossRef] - Bambi, C.; Malafarina, D. Kα iron line profile from accretion disks around regular and singular exotic compact objects. Phys. Rev. D
**2013**, 88, 064022. [Google Scholar] [CrossRef] - Doeleman, S.; Agol, E.; Backer, D.; Baganoff, F.; Bower, G.C.; Broderick, A.; Fabian, A.; Fish, V.; Gammie, C.; Ho, P.; et al. Imaging an Event Horizon: Submm-VLBI of a Super Massive Black Hole. arXiv, 2009; arXiv:0906.3899. [Google Scholar]
- Goddi, C.; Falcke, H.; Kramer, M.; Rezzolla, L.; Brinkerink, C.; Bronzwaer, T.; Davelaar, J.R.; Deane, R.; de Laurentis, M.; Desvignes, G.; et al. BlackHoleCam: Fundamental physics of the Galactic center. Int. J. Mod. Phys. D
**2016**, 26, 1730001. [Google Scholar] [CrossRef] - Johannsen, T. Sgr A* and General Relativity. Class. Quantum Gravity
**2016**, 33, 113001. [Google Scholar] [CrossRef] - Bambi, C.; Jiang, J.; Steiner, J.F. Testing the no-hair theorem with the continuum-fitting and the iron line methods: A short review. Class. Quantum Gravity
**2016**, 33, 064001. [Google Scholar] [CrossRef] - Haggard, H.; Rovelli, C. Quantum gravity effects around Sagittarius A*. Int. J. Mod. Phys. D
**2016**, 25, 1644021. [Google Scholar] [CrossRef] - Barrau, A.; Rovelli, C.; Vidotto, F. Fast Radio Bursts and White Hole Signals. Phys. Rev. D
**2014**, 90, 127503. [Google Scholar] [CrossRef] - Abbott, B.P.; Abbott, R.; Abbott, T.D.; Abernathy, M.R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R.X.; et al. Observation of Gravitational Waves from a Binary Black Hole Merger. Phys. Rev. Lett.
**2016**, 116, 061102. [Google Scholar] [CrossRef] [PubMed] - Giddings, S.B. Gravitational wave tests of quantum modifications to black hole structure—With post-GW150914 update. Class. Quantum Gravity
**2016**, 33, 235010. [Google Scholar] [CrossRef] - Konoplya, R.A.; Zhidenko, A. Detection of gravitational waves from black holes: Is there a window for alternative theories? Phys. Lett. B
**2016**, 756, 350–353. [Google Scholar] [CrossRef] - Konoplya, R.A.; Zhidenko, A. Wormholes versus black holes: Quasinormal ringing at early and late times. J. Cosmol. Astropart. Phys.
**2016**, 2016, 043. [Google Scholar] [CrossRef] - Konoplya, R.A.; Zhidenko, A. Quasinormal modes of black holes: From astrophysics to string theory. Rev. Mod. Phys.
**2011**, 83, 793. [Google Scholar] [CrossRef] - Zel’dovich, Y.B. Generation of Waves by a Rotating Body. J. Exp. Theor. Phys. Lett.
**1971**, 14, 180–181. [Google Scholar] - Starobinsky, A. Amplification of waves during reection from a black hole. J. Exp. Theor. Phys.
**1973**, 37, 28. [Google Scholar] - Bekenstein, J.D.; Schiffer, M. The many faces of superradiance. Phys. Rev. D
**1998**, 58, 064014. [Google Scholar] [CrossRef] - Marolf, D. The Black Hole information problem: Past, present, and future. arXiv, 2017; arXiv:1703.02143. [Google Scholar]
- Unruh, W.G.; Wald, R.M. Information Loss. arXiv, 2017; arXiv:1703.02140. [Google Scholar]
- Chakraborty, S.; Lochan, K. Black Holes: Eliminating Information or Illuminating New Physics? arXiv, 2017. [Google Scholar]
- Cardoso, V.; Hopper, S.; Macedo, C.F.B.; Palenzuela, C.; Pani, P. Gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale. Phys. Rev. D
**2016**, 94, 084031. [Google Scholar] [CrossRef] - Abedi, J.; Dykaar, H.; Afshordi, N. Echoes from the Abyss: Evidence for Planck-scale structure at black hole horizons. arXiv, 2016; arXiv:1612.00266. [Google Scholar]
- Barceló, C.; Carballo-Rubio, R.; Garay, L.J. Gravitational echoes from macroscopic quantum gravity effects. arXiv, 2017; arXiv:1701.09156. [Google Scholar]
- Price, R.; Khanna, G. Gravitational wave sources: Reflections and echoes. arXiv, 2017; arXiv:1702.04833. [Google Scholar]
- Giddings, S.B.; Psaltis, D. Event Horizon Telescope Observations as Probes for Quantum Structure of Astrophysical Black Holes. arXiv, 2016; arXiv:1606.07814. [Google Scholar]

1. | The choice of Painlevé-Gullstrand coordinates is particularly well suited for describing collapse that starts from rest at a finite radius (see [65] for a detailed discussion). |

**Figure 1.**Penrose diagrams for collapse with the formation of a singularity (double solid line).

**Left panel**: Collapse of a spherical dust cloud. The solid curved line ${r}_{b}$ represents the boundary of the cloud. The interior region I, is described by pressureless particles (grey area), the exterior region II, is described by the Schwarzschild vacuum space-time. As the boundary passes the Schwarzschild radius the trapped region develops. In the exterior the event horizon (solid diagonal line) forms at $r=2M$, while in the interior the apparent horizon (dashed line) moves inwards from the boundary towards $r=0$.

**Right panel**: Collapse of a thin null shell (thick line) separating a Minkowski interior, region I, from a Schwarzschild exterior, region II. The event horizon (dashed line) meets the collapsing shell at the Schwarzschild radius. The null fluid focuses at the center forming a singularity at $r=0$.

**Figure 2.**Finkelstein diagram for the black hole to white hole transition. The grey area enclosed within dashed lines represents the region where quantum effects are important (QG). The grey area within solid lines represents the trapped region in the exterior space-time. The solid thick line ${r}_{b}$ represents the boundary of the cloud. The solid thin vertical line represents the horizon in the exterior region. In this case the transition is completely symmetric in time. The bounce occurs at the same time ${t}_{B}$ for all shells (as in the homogeneous case). An horizon grazing photon (thin curved line), stays in the vicinity of the horizon until right after ${t}_{B}$. The lifetime of the white hole is the same as the lifetime of the black hole.

**Figure 3.**Penrose diagrams for homogeneous collapse with semi-classical corrections. The thick solid line ${r}_{b}$ represents the boundary of the cloud. The grey areas represent the trapped regions enclosed by apparent horizons. The dashed lines represent the apparent horizon (curved) and the event horizon (straight) in the classical case. Collapse follows the classical behaviour until a certain time before the bounce. All shells bounce at the same co-moving time ${t}_{B}$.

**Left panel**: When quantum effects become important the apparent horizon in the interior (ah) starts moving outwards. At the same time the outer horizon (oh) in the exterior moves inward. The two horizons meet and annihilate before ${t}_{B}$. At the time of the bounce the cloud is not trapped. After the bounce the solution is described by a time reversal of the collapsing solution, therefore a new trapped region (this time with a white hole horizon) develops for a finite time. In this scenario the bounce affects the whole space time instantaneously.

**Right panel**: The darker grey area represents the region where quantum effects are non negligible. Outside the quantum gravity region (QG) the space-time is given by a classical collapse solution for $t<{t}_{B}$ and its time reversal for $t>{t}_{B}$. Quantum gravity effects reach a portion of the space-time outside the horizon. Dotted lines represent lines of constant t (note that due to homogeneity, in the interior, the quantum gravity region occurs at the same t).

**Figure 4.**Penrose diagrams of a collapsing Vaidya null shell with a massless mirror (

**left panel**) and a semi-reflective mirror (

**right panel**). The trajectory of the static mirror is given by the fixed value of the radius $r={r}_{\mathrm{m}}>2M$ (solid thin line). The dotted line represents a line of constant t.

**Left panel**: The ingoing wavepacket (thick solid line) reaches the mirror and bounces back to infinity.

**Right panel**: The ingoing wavepacket reaches the semi-reflective mirror. The wave function is split into two entangled parts, one ingoing and one outgoing (dashed lines). As a consequence, when the ingoing part crosses the Schwarzschild radius, an ‘entangled’ horizon (dot-dashed line) and eventually an ‘entangled’ singularity (double dotted line) form. If a detector is placed on the trajectory of the outgoing part of the wavepacket the whole system will collapse to either the diagram in the left panel of this figure (if there is detection) or to the diagram in the right panel of Figure 1 (if there is no detection).

**Figure 5.**Finkelstein diagrams for the black hole to white hole transition with asymmetry in time. The grey area enclosed within dashed lines represents the region where quantum effects are important (QG). The grey area within solid lines represents the trapped region in the exterior space-time. The solid thick line ${r}_{b}$ represents the boundary of the cloud. The solid thin vertical line represents the horizon in the exterior region. In the time asymmetric transition, the bounce curve ${t}_{B}\left(r\right)$ (dotted line) is not constant (see Figure 2 for comparison with the symmetric case). An horizon grazing photon (thin curved line) remains in the vicinity of the horizon for longer time with respect to the symmetric case. The lifetime of the white hole is short as compared with the lifetime of the black hole.

**Figure 6.**Two possible Penrose diagrams for the formation of a baby universe inside a black hole. Collapse of a matter cloud (grey region II within boundary ${r}_{\mathrm{b}}$) proceeds classically until after the formation of the event horizon (thick dashed line). The event horizon in not affected by quantum corrections close to the singularity. Far away observers (in region I) see the formation of a Schwarzschild black hole.

**Left panel**: The singularity at the end of collapse is removed and replaced by a junction surface (double solid line ${r}_{\mathrm{s}}$) to a DeSitter universe (region III). The thin dashed lines represent the Cauchy horizons (see [150]).

**Right panel**: When reaching the quantum gravity region (darker grey region) matter undergoes a phase transition and re-expands after the bounce (region III). However, as opposed to the white hole scenario, the expanding matter remains confined within the horizon and generates an expanding universe causally disconnected from the original one. The dynamics of horizons in the baby universe would depend on the properties of the expanding matter.

**Figure 7.**Penrose diagrams of the formation of exotic compact objects from collapse with semi-classical corrections. The thick solid line describes the boundary of the collapsing body ${r}_{b}$. Dashed lines describe apparent horizon (curved) and event horizon (straight) in the classical case.

**Left panel**: Quantum effects modify the geometry in the exterior and the outer horizon (oh) shrinks. The outer horizon eventually annihilates with the expanding inner horizon (ih) at the point P, the trapped region (grey area) lives for a finite time. The geometry tends towards the classical case at large distances, while for large t near the compact object (up to a radius greater than the Schwarzschild radius) there are no trapped regions.

**Right panel**: The outer horizon (oh) is well described by the black hole event horizon. Quantum effects result in the formation of an inner horizon (ih) and the system settles to a regular black hole geometry. The trapped region (grey area) is enclosed within the two horizons in the exterior and the apparent horizon (ah) in the interior (solid lines).

**Figure 8.**Comparison between classical homogeneous dust collapse (dashed lines) and semi-classical collapse leading to an almost static compact remnant (solid lines) for a fluid approaching a ‘dark energy’ equation of state.

**Left panel**: Comparison of the scale factors $a\left(t\right)$. In the classical case a goes to zero in a finite time. In the semi-classical case a goes to zero as t goes to infinity.

**Right panel**: Comparison of the apparent horizon curves ${r}_{\mathrm{ah}}\left(t\right)$. In the classical case ${r}_{\mathrm{ah}}$ goes to zero in a finite time. In the semi-classical case the apparent horizon reaches a minimum value and then tends to infinity as t grows, thus indicating that eventually it crosses the boundary of the collapsing object (indicated here by the dotted line of the co-moving radius ${r}_{b}$). The plots have values of the parameters chosen as follows: ${M}_{0}=10$, $\lambda =1/3$, ${\rho}_{\mathrm{cr}}=1000$, ${r}_{b}=0.25$. Note that in order to have the initial boundary surface not trapped one has to consider ${r}_{b}<{r}_{\mathrm{ah}}\left(0\right)$ so that if ${r}_{b}$ is smaller than the minimum value of ${r}_{\mathrm{ah}}$ no trapped surfaces form.

© 2017 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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Malafarina, D.
Classical Collapse to Black Holes and Quantum Bounces: A Review. *Universe* **2017**, *3*, 48.
https://doi.org/10.3390/universe3020048

**AMA Style**

Malafarina D.
Classical Collapse to Black Holes and Quantum Bounces: A Review. *Universe*. 2017; 3(2):48.
https://doi.org/10.3390/universe3020048

**Chicago/Turabian Style**

Malafarina, Daniele.
2017. "Classical Collapse to Black Holes and Quantum Bounces: A Review" *Universe* 3, no. 2: 48.
https://doi.org/10.3390/universe3020048