Thermal stability of d-dimensional Lifshitz like topological black holes in special class of F(R) gravity

Document Type : Full length research Paper

Authors

1 Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz 71454, Iran

2 Department of Elementary Particles, Faculty of Physics, University of Kashan, Kashan, Iran

Abstract

In recent years, modified gravity models have played an important role in the cosmological structures. One of these models is F(R) gravity theory which opened a new insight in the context of black hole thermodynamics. Some of interesting consequences of the black hole thermodynamics resulted into investigation of thermal properties of different black holes. In this paper, first we investigate topological Lifshitz-like black hole solutions of F(R) gravity in d-dimensions and then study thermodynamic properties of such special class of F(R) gravity. Finally, we examine thermal stability and possible phase transition with respect to the heat capacity and Gibbs free energy.

Keywords

Main Subjects


[1] A. Codello, R. Percacci, C. Rahmede, Ultraviolet properties of f(R)-gravity, International Journal of Modern Physics A 23 (2008) 143.
[2] G. Cognola, E. Elizalde, S. Nojiri, S.D. Odintsov, S. Zerbini, One-loop f(R) gravity in de Sitter universe, Journal of Cosmology and Astroparticle Physics 05 (2005) 010.
[3] J.Q. GuoA.V. Frolov, Cosmological dynamics in f(R) gravity, Physical Review D 88 (2013) 124036.
https://doi.org/10.1103/PhysRevD.88.124036

[4] M. Zhang, Interior volume of Banados-Teitelboim-Zanelli black hole, General Relativity Gravitation 51 (2019) 13.

https://doi.org/10.1016/j.physletb.2019.01.032

[5] D.A. GomesR.V. MalufC.A.S. Almeida, Thermodynamics of Schwarzschild-like black holes in bumblebee gravity models, Annals of Physics (in press)[arXiv:1811.08503].
https://doi.org/10.1016/j.aop.2020.168198

[6] S.W. Hawking, Black hole explosions, Nature 248 (1974) 30.

https://doi.org/10.1038/248030a0

[7] V. Faraoni, Black hole entropy in scalar-tensor and f(R) gravity: an overview, Entropy 12 (2010) 1246.
[8] A. AddaziS. Capozziello, The fate of Schwarzschild-de Sitter black holes in f(R) gravity, Modern Physics Letters A 31 (2016) 1650054.
https://doi.org/10.1142/S0217732316500541

[9] S.H. Hendi, D. Momeni, Black-hole solutions in F(R) gravity with conformal anomaly, European Physical Journal C 71 (2011) 1823.

https://doi.org/10.1140/epjc/s10052-011-1823-y

[10] S.H. Hendi, B. Eslam Panah, R. Saffari, Exact solutions of three-dimensional black holes: Einstein gravity versus F(R) gravity, International Journal of Modern Physics D 23 (2014) 1450088.

https://doi.org/10.1142/S0218271814500886

[11] J.C.C. de SouzaV. Faraoni, The phase-space view of f (R) gravity, Classical and Quantum Gravity 24 (2007) 3637.

https://doi.org/10.1088/0264-9381/24/14/006

[12] S. NojiriS.D. OdintsovP.V. Tretyakov, Dark energy from modified F(R)-scalar-Gauss-Bonnet gravity, Physics Letters B 651 (2007) 224.
https://doi.org/10.1016/j.physletb.2007.06.029
[13] A. Guarnizo, L. Castaneda, J.M. Tejeiro, Geodesic Deviation Equation in f(R) Gravity, General Relativity Gravitation 43 (2011) 2713.
[14] P. Horava, Quantum gravity at a Lifshitz Point, Physical Review D 79 (2009) 084008.
[15] J.D. BekensteinBlack holes, entropy, Physical Review D 7 (1973) 2333.
[16] M. Calza, M. Rinaldi, L. Sebastiani, A special class of solutions in F(R)-gravity, European Physical Journal C 178 (2018) 78.
[17] H.J. Schmidt, Comparing selfinteracting scalar fields and R + R3 cosmological models, Astronomische Nachrichten (Astronomical Notes) 308 (1987) 183.
[18] A.D. Dolgov, M. Kawasaki, Can modified gravity explain accelerated cosmic expansion? Physics Letters B 573 (2003) 1.
[19] S. Nojiri, S.D. Odintsov, Modified gravity with negative and positive powers of curvature: Unification of inflation and cosmic acceleration, Physical Review D 68 (2003) 123512.
[20] V. Faraoni, Matter instability in modified gravity, Physical Review D 74 (2006) 104017.
[21] V. Faraoni, Viability criterion for modified gravity with an extra force, Physical Review D 76 (2007) 127501.
[22] O. Bertolami, M.C. Sequeira, Energy conditions and stability in f(R) theories of gravity with nonminimal coupling to matter, Physical Review D 79 (2009) 104010.
[23] S.H. Hendi, R.B. Mann, N. Riazi, B. Eslam Panah, Eguchi-Hanson-like space-times in F(R) gravity, Physical Review D 86 (2012) 104034.
[24] S.H. Hendi, The relation between F(R) gravity and Einstein-conformally invariant Maxwell source, Physics Letters B 690 (2010) 220.
[25] S.H. Hendi, A. Dehghani, Thermodynamics of third order Lovelock adS black holes in the presence of Born-Infeld type nonlinear electrodynamics, Physical Review D 91 (2015) 064045.
[26] S.H. Hendi, R. Ramezani-Arani, E. Rahimi, Thermal stability of a special class of black holes solutions in F(R) gravity, European Physical Journal C 79 (2019) 472.
[27] G. Gibbons, R. Kallosh, B. Kol, Moduli, scalar charges, and the first law of black hole thermodynamics, Physical Review Letters 77 (1996) 4992.
https://doi.org/10.1103/PhysRevLett.77.4992

[28] J.D. Brown, C. Teitelboim, Dynamical neutralization of the cosmological constant, Physics Letters B 195 (1987) 177.

https://doi.org/10.1016/0370-2693(87)91190-7

[29] M.M. Caldarelli, G. Cognola, D. Klemm, Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories, Classical and Quantum Gravity 17 (2000) 399.
[30] S.H. Hendi, S. Panahiyan, R. Mamasani, Thermodynamic stability of charged BTZ black holes: Ensemble dependency problem and its solution, General Relativity Gravitation 47 (2015) 91.
[31] D. Kubiznak, R.B. Mann, P-V criticality of charged AdS black holes, Journal of High Energy Physics 07 (2012) 033.