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Neutron Stars in the Context of f($\mathbb{T},\mathcal{T}$ ) Gravity

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## Abstract

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## 1. Introduction

## 2. Gravitational Field Equations of $\mathit{f}(\mathbb{T},\mathcal{T})$ Gravity

## 3. Stellar Structure Equations

## 4. Results

## 5. Final Remarks

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- 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] - Sotiriou, T.P.; Faraoni, V. f(R) Theories Of Gravity. Rev. Mod. Phys.
**2010**, 82, 451–497. [Google Scholar] [CrossRef] [Green Version] - Rubin, V.C.; Ford, W.K., Jr. Rotation of the Andromeda nebula from a spectroscopic survey of emission regions. Astrophys. J.
**1970**, 159, 379. [Google Scholar] [CrossRef] - Zwicky, F. Die rotverschiebung von extragalaktischen nebeln. Helv. Phys. Acta
**1933**, 6, 110–127. [Google Scholar] - 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 Ω and Λ from 42 high-redshift supernovae. Astrophys. J.
**1999**, 517, 565. [Google Scholar] [CrossRef] - Sahni, V. 5 dark matter and dark energy. Phys. Early Universe
**2004**, 653, 141–179. [Google Scholar] - Capozziello, S.; De Laurentis, M. Extended theories of gravity. Phys. Rep.
**2011**, 509, 167–321. [Google Scholar] [CrossRef] [Green Version] - De Felice, A.; Tsujikawa, S. f(R) theories. Living Rev. Relativ.
**2010**, 13, 1–161. [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. Rep.
**2011**, 505, 59–144. [Google Scholar] [CrossRef] [Green Version] - Lobo, F.S.N. The dark side of gravity: Modified theories of gravity. arXiv
**2008**, arXiv:0807.1640. [Google Scholar] - Harada, T. Neutron stars in scalar-tensor theories of gravity and catastrophe theory. Phys. Rev. D
**1998**, 57, 4802. [Google Scholar] [CrossRef] [Green Version] - Orellana, M.; García, F.; Pannia, F.A.T.; Romero, G.E. Structure of neutron stars in R-squared gravity. Gen. Relativ. Gravit.
**2013**, 45, 771–783. [Google Scholar] [CrossRef] [Green Version] - Momeni, D.; Myrzakulov, R. Tolman–Oppenheimer–Volkoff equations in modified Gauss–Bonnet gravity. Int. J. Geom. Methods Mod. Phys.
**2015**, 12, 1550014. [Google Scholar] [CrossRef] [Green Version] - Oliveira, A.; Velten, H.; Fabris, J.; Casarini, L. Neutron stars in Rastall gravity. Phys. Rev. D
**2015**, 92, 044020. [Google Scholar] [CrossRef] [Green Version] - Hendi, S.; Bordbar, G.; Panah, B.E.; Panahiyan, S. Modified TOV in gravity’s Rainbow: Properties of neutron stars and dynamical stability conditions. J. Cosmol. Astropart. Phys.
**2016**, 2016, 013. [Google Scholar] [CrossRef] [Green Version] - Singh, K.N.; Rahaman, F.; Banerjee, A. Einstein’s cluster mimicking compact star in the teleparallel equivalent of general relativity. Phys. Rev. D
**2019**, 100, 084023. [Google Scholar] [CrossRef] [Green Version] - Maurya, S.K.; Tello-Ortiz, F. Charged anisotropic compact star in f(R,T) gravity: A minimal geometric deformation gravitational decoupling approach. Phys. Dark Universe
**2020**, 27, 100442. [Google Scholar] [CrossRef] - Mota, C.E.; Santos, L.C.N.; Grams, G.; da Silva, F.M.; Menezes, D.P. Combined Rastall and Rainbow theories of gravity with applications to neutron stars. Phys. Rev. D
**2019**, 100, 024043. [Google Scholar] [CrossRef] [Green Version] - Mota, C.E.; Santos, L.C.N.; da Silva, F.M.; Flores, C.V.; da Silva, T.J.N.; Menezes, D.P. Anisotropic compact stars in Rastall–Rainbow gravity. Class. Quantum Gravity
**2022**, 39, 085008. [Google Scholar] [CrossRef] - da Silva, F.M.; Santos, L.C.N.; Barros, C.C. Rapidly rotating compact stars in Rastall’s gravity. Class. Quantum Gravity
**2021**, 38, 165011. [Google Scholar] [CrossRef] - Cooney, A.; DeDeo, S.; Psaltis, D. Neutron stars in f(R) gravity with perturbative constraints. Phys. Rev. D
**2010**, 82, 064033. [Google Scholar] [CrossRef] [Green Version] - Capozziello, S.; De Laurentis, M.; Farinelli, R.; Odintsov, S.D. Mass-radius relation for neutron stars in f(R) gravity. Phys. Rev. D
**2016**, 93, 023501. [Google Scholar] [CrossRef] [Green Version] - Arapoğlu, S.; Deliduman, C.; Ekşi, K.Y. Constraints on perturbative f(R) gravity via neutron stars. J. Cosmol. Astropart. Phys.
**2011**, 2011, 020. [Google Scholar] [CrossRef] [Green Version] - Moraes, P.H.R.S.; Arbañil, J.D.V.; Malheiro, M. Stellar equilibrium configurations of compact stars in f(R,T) theory of gravity. J. Cosmol. Astropart. Phys.
**2016**, 2016, 005. [Google Scholar] [CrossRef] [Green Version] - Pretel, J.M.Z.; Jorás, S.E.; Reis, R.R.R.; Arbañil, J.D.V. Neutron stars in f(R,T) gravity with conserved energy-momentum tensor: Hydrostatic equilibrium and asteroseismology. J. Cosmol. Astropart. Phys.
**2021**, 2021, 055. [Google Scholar] [CrossRef] - dos Santos, S.I.; Carvalho, G.A.; Moraes, P.H.R.S.; Lenzi, C.H.; Malheiro, M. A conservative energy-momentum tensor in the f(R,T) gravity and its implications for the phenomenology of neutron stars. Eur. Phys. J. Plus
**2019**, 134, 1–8. [Google Scholar] [CrossRef] [Green Version] - Sharif, M.; Waseem, A. Anisotropic quark stars in f(R,T) gravity. Eur. Phys. J. C
**2018**, 78, 1–10. [Google Scholar] [CrossRef] - Deb, D.; Ketov, S.V.; Khlopov, M.; Ray, S. Study on charged strange stars in f(R,T) gravity. J. Cosmol. Astropart. Phys.
**2019**, 2019, 070. [Google Scholar] [CrossRef] [Green Version] - Rastall, P. Generalization of the Einstein theory. Phys. Rev. D
**1972**, 6, 3357. [Google Scholar] [CrossRef] - Mota, C.E.; Santos, L.C.N.; da Silva, F.M.; Grams, G.; Lobo, I.P.; Menezes, D.P. Generalized Rastall’s gravity and its effects on compact objects. Int. J. Mod. Phys. D
**2022**, 31, 2250023. [Google Scholar] [CrossRef] - Velten, H.; Caramês, T.R.P. To conserve, or not to conserve: A review of nonconservative theories of gravity. Universe
**2021**, 7, 38. [Google Scholar] [CrossRef] - Harko, T.; Lobo, F.S.N.; Otalora, G.; Saridakis, E.N. f(T,$\mathcal{T}$) gravity and cosmology. J. Cosmol. Astropart. Phys.
**2014**, 2014, 021. [Google Scholar] [CrossRef] [Green Version] - Salako, I.G.; Khlopov, M.; Ray, S.; Arouko, M.; Saha, P.; Debnath, U. Study on anisotropic strange stars in f(T,T) gravity. Universe
**2020**, 6, 167. [Google Scholar] [CrossRef] - Singh, V.; Singh, C. Friedmann cosmology with matter creation in modified f (R, T) gravity. Int. J. Theor. Phys.
**2016**, 55, 1257–1273. [Google Scholar] [CrossRef] - Carroll, S. Spacetime and Geometry; Cambridge University Press: Cambridge, UK, 2019. [Google Scholar]
- Fattoyev, F.J.; Horowitz, C.J.; Piekarewicz, J.; Shen, G. Relativistic effective interaction for nuclei, giant resonances, and neutron stars. Phys. Rev. C
**2010**, 82, 055803. [Google Scholar] [CrossRef] [Green Version] - Lourenço, O.; Dutra, M.; Lenzi, C.H.; Flores, C.V.; Menezes, D.P. Consistent relativistic mean-field models constrained by GW170817. Phys. Rev. C
**2019**, 99, 045202. [Google Scholar] [CrossRef] [Green Version] - Dutra, M.; Lourenço, O.; Menezes, D.P. Stellar properties and nuclear matter constraints. Phys. Rev. C
**2016**, 93, 025806. [Google Scholar] [CrossRef] [Green Version] - Guichon, P.A.M. A possible quark mechanism for the saturation of nuclear matter. Phys. Lett. B
**1988**, 200, 235–240. [Google Scholar] [CrossRef] - Saito, K.; Thomas, A.W. A quark-meson coupling model for nuclear and neutron matter. Phys. Lett. B
**1994**, 327, 9–16. [Google Scholar] [CrossRef] [Green Version] - Saito, K.; Thomas, A.W. Composite nucleons in scalar and vector mean fields. Phys. Rev. C
**1995**, 52, 2789. [Google Scholar] [CrossRef] [Green Version] - Pal, S.; Hanauske, M.; Zakout, I.; Stöcker, H.; Greiner, W. Neutron star properties in the quark-meson coupling model. Phys. Rev. C
**1999**, 60, 015802. [Google Scholar] [CrossRef] [Green Version] - Grams, G.; Santos, A.M.; Menezes, D.P. Equation of State Grid with the Quark-Meson-Coupling Model. Braz. J. Phys.
**2016**, 46, 111–119. [Google Scholar] [CrossRef] - Baym, G.; Pethick, C.; Sutherland, P. The Ground state of matter at high densities: Equation of state and stellar models. Astrophys. J.
**1971**, 170, 299–317. [Google Scholar] [CrossRef] - Özel, F.; Freire, P. Masses, Radii, and the Equation of State of Neutron Stars. Annu. Rev. Astron. Astrophys.
**2016**, 54, 401–440. [Google Scholar] [CrossRef] [Green Version] - Steiner, A.W.; Heinke, C.O.; Bogdanov, S.; Li, C.K.; Ho, W.C.; Bahramian, A.; Han, S. Constraining the mass and radius of neutron stars in globular clusters. Mon. Not. R. Astron. Soc.
**2018**, 476, 421–435. [Google Scholar] [CrossRef] - Cromartie, H.T.; Fonseca, E.; Ransom, S.M.; Demorest, P.B.; Arzoumanian, Z.; Blumer, H.; Brook, P.R.; DeCesar, M.E.; Dolch, T.; Ellis, J.A.; et al. Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar. Nat. Astron.
**2020**, 4, 72–76. [Google Scholar] [CrossRef] [Green Version] - Reed, B.T.; Fattoyev, F.J.; Horowitz, C.J.; Piekarewicz, J. Implications of PREX-2 on the equation of state of neutron-rich matter. Phys. Rev. Lett.
**2021**, 126, 172503. [Google Scholar] [CrossRef] - Demorest, P.B.; Pennucci, T.; Ransom, S.M.; Roberts, M.S.E.; Hessels, J.W.T. A two-solar-mass neutron star measured using Shapiro delay. Nature
**2010**, 467, 1081–1083. [Google Scholar] [CrossRef] [Green Version] - Antoniadis, J.; Freire, P.C.C.; Wex, N.; Tauris, T.M.; Lynch, R.S.; Van Kerkwijk, M.H.; Kramer, M.; Bassa, C.; Dhillon, V.S.; Driebe, T.; et al. A massive pulsar in a compact relativistic binary. Science
**2013**, 340, 1233232. [Google Scholar] [CrossRef] [Green Version] - Abbott, B.P.; Abbott, R.; Abbott, T.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R.X.; Adya, V.B.; et al. GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral. Phys. Rev. Lett.
**2017**, 119, 161101. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Mass-radius relation for families of NS described by the IU-FSU EoS. We analyze the effect of varying the parameter $\overline{\omega}$ of the $f(\mathbb{T},\mathcal{T})$ theory. The red and green line segment represent the radius range of the 1.4 M${}_{\odot}$ NS for PSR J0030+0451 and PREX-2, respectively. The orange rectangular region corresponds to the range of radius estimates for 2.08 ± 0.07 M${}_{\odot}$ NS PSR J0740+6620. Similarly, the blue, pink, and golden horizontal lines stand, respectively, for the mass measurements of NS PSR J1614+2230, NS PSR J0348+0432, and GW170817 event [51]. The purple solid line curve is solution for the usual TOV equation from GR.

**Figure 2.**Mass-radius relation for families of NS described by the QMC EoS. We analyze the effect of varying the parameter $\overline{\omega}$ of the $f(\mathbb{T},\mathcal{T})$ theory. The red and green line segment represent the radius range of the 1.4 M${}_{\odot}$ NS for PSR J0030+0451 and PREX-2, respectively. The orange rectangular region corresponds to the range of radius estimates for 2.08 ± 0.07 M${}_{\odot}$ NS PSR J0740+6620. Similarly, the blue, pink, and golden horizontal lines stand, respectively, for the mass measurements of NS PSR J1614+2230, NS PSR J0348+0432 and GW170817 event [51]. The purple solid line curve is the solution for the usual TOV equation from GR.

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**MDPI and ACS Style**

Mota, C.E.; Santos, L.C.N.; da Silva, F.M.; Flores, C.V.; Lobo, I.P.; Bezerra, V.B.
Neutron Stars in the Context of *f*(*Universe* **2023**, *9*, 260.
https://doi.org/10.3390/universe9060260

**AMA Style**

Mota CE, Santos LCN, da Silva FM, Flores CV, Lobo IP, Bezerra VB.
Neutron Stars in the Context of *f*(*Universe*. 2023; 9(6):260.
https://doi.org/10.3390/universe9060260

**Chicago/Turabian Style**

Mota, Clésio E., Luis C. N. Santos, Franciele M. da Silva, César V. Flores, Iarley P. Lobo, and Valdir B. Bezerra.
2023. "Neutron Stars in the Context of *f*(*Universe* 9, no. 6: 260.
https://doi.org/10.3390/universe9060260