Higher Dimensional Rotating Black Hole Solutions in Quadratic f(R) Gravitational Theory and the Conserved Quantities
Abstract
:1. Introduction
2. Basics of Gravitational Theory
3. Rotating Black Hole Solutions
4. Total Conserved Charge
5. Regularization with Relocalization for the Conserved Charge
6. Thermodynamics for Black Holes
7. Summary and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Symbols Used in the Calculations of Conserved Quantities
Appendix B. Non-Zero Components for the Christoffel Symbols of the Second Kind and Ricci Curvature Tensor
References
- Riess, A.G.; Filippenko, A.V.; Challis, P.; Clocchiatti, A.; Diercks, A.; Garnavich, P.M.; Gillil, R.L.; Hogan, C.J.; Jha, S.; Kirshner, R.P.; et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 1998, 116, 1009–1038. [Google Scholar] [CrossRef] [Green Version]
- Perlmutter, S.; Aldering, G.; Goldhaber, G.; Knop, R.A.; Nugent, P.; Castro, P.G.; Deustua, S.; Fabbro, S.; Goobar, A.; Groom, D.E.; et al. Measurements of Omega and Lambda from 42 high redshift supernovae. Astrophys. J. 1999, 517, 565–586. [Google Scholar] [CrossRef]
- Ade, P.A.R.; Aghanim, N.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; et al. Planck 2013 results. XVI. Cosmological parameters. Astron. Astrophys. 2014, 571, A16. [Google Scholar] [CrossRef] [Green Version]
- Spergel, D.N.; Bean, R.; Doré, O.; Nolta, M.R.; Bennett, C.L.; Dunkley, J.; Hinshaw, G.; Jarosik, N.E.; Komatsu, E.; Page, L.; et al. Wilkinson Microwave Anisotropy Probe (WMAP) three year results: Implications for cosmology. Astrophys. J. Suppl. 2007, 170, 377. [Google Scholar] [CrossRef] [Green Version]
- Jain, B.; Taylor, A. Cross-correlation tomography: Measuring dark energy evolution with weak lensing. Phys. Rev. Lett. 2003, 91, 141302. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Cole, S.; Percival, W.J.; Peacock, J.A.; Norberg, P.; Baugh, C.M.; Frenk, C.S.; Baldry, I.; Bland-Hawthorn, J.; Bridges, T.; Cannon, R.; et al. The 2dF Galaxy Redshift Survey: Power-spectrum analysis of the final dataset and cosmological implications. Mon. Not. Roy. Astron. Soc. 2005, 362, 505–534. [Google Scholar] [CrossRef]
- Eisenstein, D.J.; Zehavi, I.; Hogg, D.W.; Scoccimarro, R.; Blanton, M.R.; Nichol, R.C.; Scranton, R.; Seo, H.J.; Tegmark, M.; Zheng, Z.; et al. Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies. Astrophys. J. 2005, 633, 560–574. [Google Scholar] [CrossRef]
- Percival, W.J.; Reid, B.A.; Eisenstein, D.J.; Bahcall, N.A.; Budavari, T.; Frieman, J.A.; Fukugita, M.; Gunn, J.E.; Ivezić, Ž.; Knapp, G.R.; et al. Baryon acoustic oscillations in the Sloan Digital Sky Survey Data Release 7 galaxy sample. Mon. Not. Roy. Astron. Soc. 2010, 401, 2148–2168. [Google Scholar] [CrossRef] [Green Version]
- Padmanabhan, N.; Xu, X.; Eisenstein, D.J.; Scalzo, R.; Cuesta, A.J.; Mehta, K.T.; Kazin, E. A 2 per cent distance to z=0.35 by reconstructing baryon acoustic oscillations - I. Methods and application to the Sloan Digital Sky Survey. Mon. Not. Roy. Astron. Soc. 2012, 427, 2132–2145. [Google Scholar] [CrossRef] [Green Version]
- Blake, C.; Kazin, E.A.; Beutler, F.; Davis, T.M.; Parkinson, D.; Brough, S.; Colless, M.; Contreras, C.; Couch, W.; Croom, S.; et al. The WiggleZ Dark Energy Survey: Mapping the distance-redshift relation with baryon acoustic oscillations. Mon. Not. Roy. Astron. Soc. 2011, 418, 1707–1724. [Google Scholar] [CrossRef]
- Manera, M.; Scoccimarro, R.; Percival, W.J.; Samushia, L.; McBride, C.K.; Ross, A.J.; Sheth, R.K.; White, M.; Reid, B.A.; Sánchez, A.G.; et al. The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: A large sample of mock galaxy catalogues. Mon. Not. Roy. Astron. Soc. 2013, 428, 1036–1054. [Google Scholar] [CrossRef] [Green Version]
- Simon, J.; Verde, L.; Jimenez, R. Constraints on the redshift dependence of the dark energy potential. Phys. Rev. D 2005, 71, 123001. [Google Scholar] [CrossRef] [Green Version]
- Stern, D.; Jimenez, R.; Verde, L.; Kamionkowski, M.; Stanford, S.A. Cosmic Chronometers: Constraining the Equation of State of Dark Energy. I: H(z) Measurements. JCAP 2010, 1002, 8. [Google Scholar] [CrossRef] [Green Version]
- Zhang, C.; Zhang, H.; Yuan, S.; Zhang, T.J.; Sun, Y.C. Four new observational H(z) data from luminous red galaxies in the Sloan Digital Sky Survey data release seven. Res. Astron. Astrophys. 2014, 14, 1221–1233. [Google Scholar] [CrossRef] [Green Version]
- Blake, C.; Glazebrook, K.; Davis, T.M.; Brough, S.; Colless, M.; Contreras, C.; Couch, W.; Croom, S.; Drinkwater, M.J.; Forster, K.; et al. The WiggleZ Dark Energy Survey: Measuring the cosmic expansion history using the Alcock-Paczynski test and distant supernovae. Mon. Not. Roy. Astron. Soc. 2011, 418, 1725–1735. [Google Scholar] [CrossRef]
- Chuang, C.H.; Wang, Y. Modeling the Anisotropic Two-Point Galaxy Correlation Function on Small Scales and Improved Measurements of H(z), DA(z), and β(z) from the Sloan Digital Sky Survey DR7 Luminous Red Galaxies. Mon. Not. Roy. Astron. Soc. 2013, 435, 255–262. [Google Scholar] [CrossRef] [Green Version]
- Moresco, M.; Cimatti, A.; Jimenez, R.; Pozzetti, L.; Zamorani, G.; Bolzonella, M.; Dunlop, J.; Lamareille, F.; Mignoli, M.; Pearce, H.; et al. Improved constraints on the expansion rate of the Universe up to z 1.1 from the spectroscopic evolution of cosmic chronometers. JCAP 2012, 1208, 6. [Google Scholar] [CrossRef] [Green Version]
- Hawkins, E.; Maddox, S.; Cole, S.; Lahav, O.; Madgwick, D.S.; Norberg, P.; Peacock, J.A.; Baldry, I.K.; Baugh, C.M.; Bland-Hawthorn, J.; et al. The 2dF Galaxy Redshift Survey: Correlation functions, peculiar velocities and the matter density of the Universe. Mon. Not. R. Astron. Soc. 2003, 346, 78–96. [Google Scholar] [CrossRef]
- Tegmark, M.; Strauss, M.A.; Blanton, M.R.; Abazajian, K.; Dodelson, S.; Sandvik, H.; Wang, X.; Weinberg, D.H.; Zehavi, I.; Bahcall, N.A.; et al. Cosmological parameters from SDSS and WMAP. Phys. Rev. D 2004, 69, 103501. [Google Scholar] [CrossRef] [Green Version]
- Weinberg, S. The cosmological constant problem. Rev. Mod. Phys. 1989, 61, 1–23. [Google Scholar] [CrossRef]
- Nashed, G.G.L.; Bamba, K. Spherically symmetric charged black hole in conformal teleparallel equivalent of general relativity. JCAP 2018, 1809, 20. [Google Scholar] [CrossRef] [Green Version]
- Ferraro, R.; Fiorini, F. Modified teleparallel gravity: Inflation without an inflaton. Phys. Rev. D 2007, 75, 084031. [Google Scholar] [CrossRef] [Green Version]
- Ferraro, R.; Fiorini, F. Born-Infeld gravity in Weitzenböck spacetime. Phys. Rev. D 2008, 78, 124019. [Google Scholar] [CrossRef] [Green Version]
- Bengochea, G.R.; Ferraro, R. Dark torsion as the cosmic speed-up. Phys. Rev. D 2009, 79, 124019. [Google Scholar] [CrossRef] [Green Version]
- Li, B.; Sotiriou, T.P.; Barrow, J.D. Large-scale structure in f(T) gravity. Phys. Rev. D 2011, 83, 104017. [Google Scholar] [CrossRef] [Green Version]
- Nashed, G.L. FRW in quadratic form of f(T) gravitational theories. Gen. Rel. Grav. 2015, 47, 75. [Google Scholar] [CrossRef] [Green Version]
- Li, B.; Sotiriou, T.P.; Barrow, J.D. f(T) gravity and local Lorentz invariance. Phys. Rev. D 2011, 83, 064035. [Google Scholar] [CrossRef] [Green Version]
- Nashed, G.G.L. A special exact spherically symmetric solution in f(T) gravity theories. Gen. Rel. Grav. 2013, 45, 1887–1899. [Google Scholar] [CrossRef] [Green Version]
- Awad, A.; Nashed, G. Generalized teleparallel cosmology and initial singularity crossing. JCAP 2017, 1702, 46. [Google Scholar] [CrossRef]
- Nashed, G.G.L. Spherically symmetric charged-dS solution in f(T) gravity theories. Phys. Rev. 2013, D88, 104034. [Google Scholar] [CrossRef] [Green Version]
- Awad, A.M.; Capozziello, S.; Nashed, G.G.L. D-dimensional charged Anti-de-Sitter black holes in f(T) gravity. JHEP 2017, 7, 136. [Google Scholar] [CrossRef] [Green Version]
- Nashed, G.G.L.; El Hanafy, W. Analytic rotating black hole solutions in N-dimensional f(T) gravity. Eur. Phys. J. 2017, 77, 90. [Google Scholar] [CrossRef] [Green Version]
- Capozziello, S.; Gonzalez, P.A.; Saridakis, E.N.; Vasquez, Y. Exact charged black-hole solutions in D-dimensional f(T) gravity: Torsion vs. curvature analysis. J. High Energy Phys. 2013, 2, 39. [Google Scholar] [CrossRef] [Green Version]
- Kallosh, R.; Quevedo, F.; Uranga, A.M. String Theory Realizations of the Nilpotent Goldstino. J. High Energy Phys. 2015, 12, 39. [Google Scholar] [CrossRef] [Green Version]
- Hendi, S.H.; Dehghani, A. Thermodynamics of third-order Lovelock-AdS black holes in the presence of Born-Infeld type nonlinear electrodynamics. Phys. Rev. D 2015, 91, 064045. [Google Scholar] [CrossRef] [Green Version]
- Kofinas, G.; Papantonopoulos, E.; Saridakis, E.N. Modified Brans–Dicke cosmology with matter-scalar field interaction. Class. Quant. Grav. 2016, 33, 155004. [Google Scholar] [CrossRef] [Green Version]
- Guth, A.H. Inflationary universe: A possible solution to the horizon and flatness problems. Phys. Rev. D 1981, 23, 347–356. [Google Scholar] [CrossRef] [Green Version]
- Pogosian, L.; Silvestri, A. Pattern of growth in viable f(R) cosmologies. Phys. Rev. D 2008, 77, 23503. [Google Scholar] [CrossRef] [Green Version]
- Nojiri, S.; Odintsov, S.D. Unified cosmic history in modified gravity: From f(R) theory to Lorentz non-invariant models. Phys. Rept. 2011, 505, 59–144. [Google Scholar] [CrossRef] [Green Version]
- Capozziello, S.; De Laurentis, M. Extended Theories of Gravity. Phys. Rept. 2011, 509, 167–321. [Google Scholar] [CrossRef] [Green Version]
- Faraoni, V.; Capozziello, S. Beyond Einstein Gravity; Springer: Dordrecht, The Netherlands, 2011; Volume 170. [Google Scholar] [CrossRef] [Green Version]
- Bamba, K.; Odintsov, S.D. Inflationary cosmology in modified gravity theories. Symmetry 2015, 7, 220–240. [Google Scholar] [CrossRef] [Green Version]
- Cai, Y.F.; Capozziello, S.; De Laurentis, M.; Saridakis, E.N. f(T) teleparallel gravity and cosmology. Rept. Prog. Phys. 2016, 79, 106901. [Google Scholar] [CrossRef] [Green Version]
- Nojiri, S.; Odintsov, S.D.; Oikonomou, V.K. Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution. Phys. Rept. 2017, 692, 1–104. [Google Scholar] [CrossRef] [Green Version]
- Bamba, K.; Capozziello, S.; Nojiri, S.; Odintsov, S.D. Dark energy cosmology: The equivalent description via different theoretical models and cosmography tests. Astrophys. Space Sci. 2012, 342, 155–228. [Google Scholar] [CrossRef] [Green Version]
- Artymowski, M.; Lalak, Z. Inflation and dark energy from f(R) gravity. J. Cosmol. Astropart. Phys. 2014, 1409, 36. [Google Scholar] [CrossRef]
- Odintsov, S.D.; Oikonomou, V.K. Singular inflationary universe from F(R) gravity. Phys. Rev. D 2015, 92, 124024. [Google Scholar] [CrossRef] [Green Version]
- Motohashi, H.; Starobinsky, A.A. Constant-roll inflation: Confrontation with recent observational data. EPL 2017, 117, 39001. [Google Scholar] [CrossRef] [Green Version]
- Huang, Q.G. A polynomial f(R) inflation model. J. Cosmol. Astropart. Phys. 2014, 1402, 35. [Google Scholar] [CrossRef] [Green Version]
- Addazi, A.; Khlopov, M.Y. Dark matter and inflation in R + ζR2 supergravity. Phys. Lett. 2017, B766, 17–22. [Google Scholar] [CrossRef]
- Koyama, K. Cosmological Tests of Modified Gravity. Rept. Prog. Phys. 2016, 79, 46902. [Google Scholar] [CrossRef] [Green Version]
- Utiyama, R.; DeWitt, B.S. Renormalization of a classical gravitational field interacting with quantized matter fields. J. Math. Phys. 1962, 3, 608–618. [Google Scholar] [CrossRef]
- Barrow, J.D.; Cotsakis, S. Chaotic Behaviour in higher-order gravity theories. Phys. Lett. B 1989, 232, 172–176. [Google Scholar] [CrossRef]
- Clifton, T.; Barrow, J.D. Further exact cosmological solutions to higher-order gravity theories. Class. Quant. Grav. 2006, 23, 2951. [Google Scholar] [CrossRef]
- Middleton, J.; Barrow, J.D. Stability of an isotropic cosmological singularity in higher-order gravity. Phys. Rev. D 2008, 77, 103523. [Google Scholar] [CrossRef] [Green Version]
- Sk, N.; Sanyal, A.K. On the equivalence between different canonical forms of F(R) theory of gravity. Int. J. Mod. Phys. 2018, D27, 1850085. [Google Scholar] [CrossRef] [Green Version]
- Starobinsky, A.A. A New Type of Isotropic Cosmological Models without Singularity. Adv. Ser. Astrophys. Cosmol. 1987, 3, 130–133. [Google Scholar] [CrossRef]
- Starobinskii, A.A. The Perturbation Spectrum Evolving from a Nonsingular Initially De-Sitter Cosmology and the Microwave Background Anisotropy. Sov. Astron. Lett. 1983, 9, 302–304. [Google Scholar]
- Sotiriou, T.P.; Faraoni, V. f(R) theories of gravity. Rev. Mod. Phys. 2010, 82, 451–497. [Google Scholar] [CrossRef] [Green Version]
- De Felice, A.; Tsujikawa, S. f(R) theories. Living Rev. Rel. 2010, 13, 3. [Google Scholar] [CrossRef] [Green Version]
- Guo, J.Q.; Wang, D.; Frolov, A.V. Spherical collapse in f(R) gravity and the Belinskii-Khalatnikov-Lifshitz conjecture. Phys. Rev. D 2014, 90, 024017. [Google Scholar] [CrossRef] [Green Version]
- Clifton, T. Spherically Symmetric Solutions to Fourth-Order Theories of Gravity. Class. Quant. Grav. 2006, 23, 7445. [Google Scholar] [CrossRef] [Green Version]
- Sebastiani, L.; Zerbini, S. Static Spherically Symmetric Solutions in F(R) Gravity. Eur. Phys. J. 2011, C71, 1591. [Google Scholar] [CrossRef] [Green Version]
- Nashed, G.G.L.; Capozziello, S. Charged spherically symmetric black holes in f(R) gravity and their stability analysis. Phys. Rev. 2019, D99, 104018. [Google Scholar] [CrossRef] [Green Version]
- Chakrabarti, S.; Banerjee, N. Gravitational collapse in f (R) gravity for a spherically symmetric spacetime admitting a homothetic Killing vector. Eur. Phys. J. Plus 2016, 131, 144. [Google Scholar] [CrossRef] [Green Version]
- Zhang, C.Y.; Tang, Z.Y.; Wang, B. Gravitational collapse of massless scalar field in f(R) gravity. Phys. Rev. D 2016, 94, 104013. [Google Scholar] [CrossRef] [Green Version]
- De la Cruz-Dombriz, A.; Dobado, A.; Maroto, A.L. Black holes in f(R) theories. Phys. Rev. D 2009, 80, 124011. [Google Scholar] [CrossRef] [Green Version]
- Nashed, G.G.L. Higher Dimensional Charged Black Hole Solutions in f(R) Gravitational Theories. Adv. High Energy Phys. 2018, 2018, 7323574. [Google Scholar] [CrossRef] [Green Version]
- Moon, T.; Myung, Y.S.; Son, E.J. f(R) black holes. Gen. Rel. Grav. 2011, 43, 3079–3098. [Google Scholar] [CrossRef] [Green Version]
- Nashed, G.G.L. Spherically symmetric charged black holes in f(R) gravitational theories. Eur. Phys. J. Plus 2018, 133, 18. [Google Scholar] [CrossRef]
- Rodrigues, M.E.; Junior, E.L.B.; Marques, G.T.; Zanchin, V.T. Regular black holes in f(R) gravity coupled to nonlinear electrodynamics. Phys. Rev. D 2016, 94, 024062. [Google Scholar] [CrossRef] [Green Version]
- Nashed, G.G.L. Rotating charged black hole spacetimes in quadratic f(R) gravitational theories. Int. J. Mod. Phys. D 2018, 27, 1850074. [Google Scholar] [CrossRef]
- Cañate, P.; Jaime, L.G.; Salgado, M. Spherically symmetric black holes in f(R) gravity: Is geometric scalar hair supported? Class. Quant. Grav. 2016, 33, 155005. [Google Scholar] [CrossRef] [Green Version]
- Moon, T.; Myung, Y.S. Stability of Schwarzschild black hole in f(R) gravity with the dynamical Chern-Simons term. Phys. Rev. 2011, D84, 104029. [Google Scholar] [CrossRef] [Green Version]
- Ayon-Beato, E.; Garbarz, A.; Giribet, G.; Hassaine, M. Analytic Lifshitz black holes in higher dimensions. J. High Energy Phys. 2010, 4, 30. [Google Scholar] [CrossRef] [Green Version]
- Hendi, S.H.; Eslam Panah, B.; Mousavi, S.M. Some exact solutions of F(R) gravity with charged (a)dS black hole interpretation. Gen. Rel. Grav. 2012, 44, 835–853. [Google Scholar] [CrossRef] [Green Version]
- Hendi, S.H.; Eslam Panah, B.; Saffari, R. Exact solutions of three-dimensional black holes: Einstein gravity versus F(R) gravity. Int. J. Mod. Phys. 2014, D23, 1450088. [Google Scholar] [CrossRef] [Green Version]
- Cao, Z.; Galaviz, P.; Li, L.F. Binary black hole mergers in f(R) theory. Phys. Rev. D 2013, 87, 104029. [Google Scholar] [CrossRef] [Green Version]
- Addazi, A. (Anti)evaporation of Dyonic Black Holes in string-inspired dilaton f(R)-gravity. Int. J. Mod. Phys. 2017, A32, 1750102. [Google Scholar] [CrossRef] [Green Version]
- Fan, Z.Y.; Lü, H. Thermodynamical first laws of black holes in quadratically-extended gravities. Phys. Rev. D 2015, 91, 064009. [Google Scholar] [CrossRef] [Green Version]
- Akbar, M.; Cai, R.G. Thermodynamic Behavior of Field Equations for f(R) Gravity. Phys. Lett. 2007, B648, 243–248. [Google Scholar] [CrossRef] [Green Version]
- Faraoni, V. Black hole entropy in scalar-tensor and f(R) gravity: An Overview. Entropy 2010, 12, 1246. [Google Scholar] [CrossRef] [Green Version]
- Ortaggio, M. Higher dimensional black holes in external magnetic fields. J. High Energy Phys. 2005, 5, 48. [Google Scholar] [CrossRef]
- Tangherlini, F.R. Schwarzschild field inn dimensions and the dimensionality of space problem. Il Nuovo C. (1955–1965) 1963, 27, 636–651. [Google Scholar] [CrossRef]
- Myers, R.C.; Perry, M.J. Black holes in higher dimensional space-times. Ann. Phys. 1986, 172, 304–347. [Google Scholar] [CrossRef]
- Emparan, R.; Reall, H.S. A Rotating black ring solution in five-dimensions. Phys. Rev. Lett. 2002, 88, 101101. [Google Scholar] [CrossRef] [Green Version]
- Emparan, R. Rotating circular strings, and infinite nonuniqueness of black rings. J. High Energy Phys. 2004, 3, 64. [Google Scholar] [CrossRef] [Green Version]
- Horne, J.H.; Horowitz, G.T. Exact black string solutions in three-dimensions. Nucl. Phys. 1992, B368, 444–462. [Google Scholar] [CrossRef] [Green Version]
- Cisterna, A.; Oliva, J. Exact black strings and p-branes in general relativity. Class. Quant. Grav. 2018, 35, 35012. [Google Scholar] [CrossRef] [Green Version]
- Sheykhi, A.; Salarpour, S.; Bahrampour, Y. Rotating black strings in f(R)-Maxwell theory. Phys. Scr. 2013, 87, 45004. [Google Scholar] [CrossRef] [Green Version]
- Sheykhi, A. Higher-dimensional charged f(R) black holes. Phys. Rev. D 2012, 86, 024013. [Google Scholar] [CrossRef] [Green Version]
- Hendi, S.H.; Sheykhi, A. Charged rotating black string in gravitating nonlinear electromagnetic fields. Phys. Rev. D 2013, 88, 044044. [Google Scholar] [CrossRef] [Green Version]
- Kobayashi, T.; Maeda, K.I. Relativistic stars in f(R) gravity, and absence thereof. Phys. Rev. D 2008, 78, 064019. [Google Scholar] [CrossRef] [Green Version]
- Kobayashi, T.; Maeda, K.I. Can higher curvature corrections cure the singularity problem in f(R) gravity? Phys. Rev. D 2009, 79, 24009. [Google Scholar] [CrossRef] [Green Version]
- Nashed, G.G.L.; El Hanafy, W.; Odintsov, S.D.; Oikonomou, V.K. Thermodynamical correspondence of f(R) gravity in the Jordan and Einstein frames. Int. J. Mod. Phys. D 2020, 29, 2050090. [Google Scholar] [CrossRef]
- Elizalde, E.; Nashed, G.G.L.; Nojiri, S.; Odintsov, S.D. Spherically symmetric black holes with electric and magnetic charge in extended gravity: Physical properties, causal structure, and stability analysis in Einstein’s and Jordan’s frames. Eur. Phys. J. C 2020, 80, 109. [Google Scholar] [CrossRef] [Green Version]
- Nashed, G.G.L.; Saridakis, E.N. New rotating black holes in nonlinear Maxwell f(R) gravity. Phys. Rev. D 2020, 102, 124072. [Google Scholar] [CrossRef]
- Cognola, G.; Elizalde, E.; Nojiri, S.; Odintsov, S.D.; Zerbini, S. One-loop f(R) gravity in de Sitter universe. J. Cosmol. Astropart. Phys. 2005, 5, 10. [Google Scholar] [CrossRef] [Green Version]
- Koivisto, T.; Kurki-Suonio, H. Cosmological perturbations in the palatini formulation of modified gravity. Class. Quant. Grav. 2006, 23, 2355–2369. [Google Scholar] [CrossRef]
- Nashed, G.G.L.; Saridakis, E.N. Rotating AdS black holes in Maxwell-f(T) gravity. Class. Quant. Grav. 2019, 36, 135005. [Google Scholar] [CrossRef] [Green Version]
- Bahamonde, S.; Odintsov, S.D.; Oikonomou, V.K.; Tretyakov, P.V. Deceleration versus acceleration universe in different frames of F(R) gravity. Phys. Lett. 2017, 766, 225–230. [Google Scholar] [CrossRef]
- Bahamonde, S.; Odintsov, S.D.; Oikonomou, V.K.; Wright, M. Correspondence of F(R) Gravity Singularities in Jordan and Einstein Frames. Ann. Phys. 2016, 373, 96–114. [Google Scholar] [CrossRef] [Green Version]
- Lemos, J.P.S. Cylindrical black hole in general relativity. Phys. Lett. 1995, B353, 46–51. [Google Scholar] [CrossRef] [Green Version]
- Awad, A.M. Higher dimensional charged rotating solutions in (A)dS space-times. Class. Quant. Grav. 2003, 20, 2827–2834. [Google Scholar] [CrossRef]
- Stachel, J. Globally stationary but locally static space-times: A gravitational analog of the Aharonov-Bohm effect. Phys. Rev. 1982, 26, 1281–1290. [Google Scholar] [CrossRef]
- Obukhov, Y.N.; Rubilar, G.F. Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry. Phys. Rev. D 2006, 74, 64002. [Google Scholar] [CrossRef] [Green Version]
- Kopczynski, W. Variational principles for gravity and fluids. Ann. Phys. 1990, 203, 308–338. [Google Scholar] [CrossRef]
- Komar, A. Asymptotic Covariant Conservation Laws for Gravitational Radiation. Phys. Rev. 1962, 127, 1411–1418. [Google Scholar] [CrossRef]
- Shirafuji, T.; Nashed, G.G.L.; Kobayashi, Y. Equivalence principle in the new general relativity. Prog. Theor. Phys. 1996, 96, 933–948. [Google Scholar] [CrossRef] [Green Version]
- Komar, A. Covariant Conservation Laws in General Relativity. Phys. Rev. 1959, 113, 934–936. [Google Scholar] [CrossRef]
- Ashtekar, A. Angular Momentum of Isolated Systems in General Relativity. In Cosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity; Bergmann, P.G., De Sabbata, V., Eds.; Springer: Boston, MA, USA, 1980; pp. 435–448. [Google Scholar] [CrossRef]
- Obukhov, Y.N.; Rubilar, G.F. Invariant conserved currents in gravity theories: Diffeomorphisms and local gauge symmetries. Phys. Rev. D 2007, 76, 124030. [Google Scholar] [CrossRef]
- Nashed, G.G.L. Energy and momentum of a spherically symmetric dilaton frame as regularized by teleparallel gravity. Ann. Phys. 2011, 523, 450–458. [Google Scholar] [CrossRef] [Green Version]
- Obukhov, Y.N.; Rubilar, G.F. Invariant conserved currents for gravity. Phys. Lett. 2008, B660, 240–246. [Google Scholar] [CrossRef]
- Awad, A.; Chamblin, A. A Bestiary of higher dimensional Taub—NUT AdS space-times. Class. Quant. Grav. 2002, 19, 2051–2062. [Google Scholar] [CrossRef]
- Sheykhi, A. Thermodynamics of apparent horizon and modified Friedmann equations. Eur. Phys. J. 2010, C69, 265–269. [Google Scholar] [CrossRef] [Green Version]
- Hendi, S.H.; Sheykhi, A.; Dehghani, M.H. Thermodynamics of higher dimensional topological charged AdS black branes in dilaton gravity. Eur. Phys. J. 2010, C70, 703–712. [Google Scholar] [CrossRef] [Green Version]
- Sheykhi, A.; Dehghani, M.H.; Hendi, S.H. Thermodynamic instability of charged dilaton black holes in AdS spaces. Phys. Rev. D 2010, 81, 84040. [Google Scholar] [CrossRef] [Green Version]
- Davies, P.C.W. Thermodynamics of Black Holes. Proc. Roy. Soc. Lond. 1977, 353, 499–521. [Google Scholar] [CrossRef]
- Babichev, E.O.; Dokuchaev, V.I.; Eroshenko, Y.N. Black holes in the presence of dark energy. Phys. Usp. 2013, 56, 1155–1175, Erratum in 2013, 189, 1257. [Google Scholar] [CrossRef] [Green Version]
- Saridakis, E.N.; Gonzalez-Diaz, P.F.; Siguenza, C.L. Unified dark energy thermodynamics: Varying w and the -1-crossing. Class. Quant. Grav. 2009, 26, 165003. [Google Scholar] [CrossRef] [Green Version]
- Brevik, I.; Nojiri, S.; Odintsov, S.D.; Vanzo, L. Entropy and universality of the Cardy-Verlinde formula in a dark energy universe. Phys. Rev. D 2004, 70, 043520. [Google Scholar] [CrossRef] [Green Version]
- Nunes, R.C.; Pan, S.; Saridakis, E.N.; Abreu, E.M.C. New observational constraints on f(R) gravity from cosmic chronometers. J. Cosmol. Astropart. Phys. 2017, 1701, 5. [Google Scholar] [CrossRef] [Green Version]
- Nashed, G.G.L. Stability of the vacuum nonsingular black hole. Chaos Solitons Fractals 2003, 15, 841. [Google Scholar] [CrossRef] [Green Version]
- Nouicer, K. Black holes thermodynamics to all order in the Planck length in extra dimensions. Class. Quant. Grav. 2007, 24, 5917–5934, Erratum in 2007, 24, 6435. [Google Scholar] [CrossRef]
- Dymnikova, I.; Korpusik, M. Thermodynamics of regular cosmological black holes with de Sitter interior. Gravit. Cosmol. 2011, 17, 35–37. [Google Scholar] [CrossRef]
- Chamblin, A.; Emparan, R.; Johnson, C.V.; Myers, R.C. Charged AdS black holes and catastrophic holography. Phys. Rev. 1999, D60, 64018. [Google Scholar] [CrossRef] [Green Version]
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Nashed, G.G.L.; Bamba, K. Higher Dimensional Rotating Black Hole Solutions in Quadratic f(R) Gravitational Theory and the Conserved Quantities. Entropy 2021, 23, 358. https://doi.org/10.3390/e23030358
Nashed GGL, Bamba K. Higher Dimensional Rotating Black Hole Solutions in Quadratic f(R) Gravitational Theory and the Conserved Quantities. Entropy. 2021; 23(3):358. https://doi.org/10.3390/e23030358
Chicago/Turabian StyleNashed, Gamal G. L., and Kazuharu Bamba. 2021. "Higher Dimensional Rotating Black Hole Solutions in Quadratic f(R) Gravitational Theory and the Conserved Quantities" Entropy 23, no. 3: 358. https://doi.org/10.3390/e23030358