Black Hole Entropy for Two Higher Derivative Theories of Gravity

The dark energy issue is attracting the attention of an increasing number of physicists all over the world. Among the possible alternatives to explain what as been named the “Mystery of the Millennium” are the so-called Modified Theories of Gravity. A crucial test for such models is represented by the existence and (if this is the case) the properties of their black hole solutions. Nowadays, to our knowledge, only two non-trivial, static, spherically symmetric, solutions with vanishing cosmological constant are known by Barrow & Clifton (2005) and Deser, Sarioglu & Tekin (2008). The aim of the paper is to discuss some features of such solutions, with emphasis on their thermodynamic properties such as entropy and temperature.

[1]  H. Kodama.  Conserved Energy Flux for the Spherically Symmetric System and the Backreaction Problem in the Black Hole Evaporation , 1980 .

[2]  K. Stelle.  Renormalization of Higher Derivative Quantum Gravity , 1977 .

[3]  H. Maeda,et al.  Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity , 2007, 0709.1199.

[4]  Brown,et al.  Quasilocal energy and conserved charges derived from the gravitational action. , 1992, Physical review. D, Particles and fields.

[5]  T. Padmanabhan.  Dark energy: mystery of the millennium , 2006, astro-ph/0603114.

[6]  Reconciling dark energy models with f(R) theories , 2005, astro-ph/0501426.

[7]  John Archibald Wheeler,et al.  Black Hole , 2020 .

[8]  Hayward.  Gravitational energy in spherical symmetry. , 1994, Physical review. D, Particles and fields.

[9]  T. Sotiriou,et al.  f(R) Theories Of Gravity , 2008, 0805.1726.

[10]  E. Fradkin,et al.  Renormalizable asymptotically free quantum theory of gravity , 1982 .

[11]  D. Sharp,et al.  RELATIVISTIC EQUATIONS FOR ADIABATIC, SPHERICALLY SYMMETRIC GRAVITATIONAL COLLAPSE , 1964 .

[12]  Damien A. Easson,et al.  Black holes in an asymptotically safe gravity theory with higher derivatives , 2010, 1007.1317.

[13]  Dark energy in modified Gauss-Bonnet gravity: Late-time acceleration and the hierarchy problem , 2005, hep-th/0601008.

[14]  Quasilocal gravitational energy. , 1993, Physical review. D, Particles and fields.

[15]  Shinji Tsujikawa,et al.  Dynamics of dark energy , 2006 .

[16]  Charged dilaton black holes with unusual asymptotics , 1995, gr-qc/9502042.

[17]  J. Oliva,et al.  A new cubic theory of gravity in five dimensions: black hole, Birkhoff's theorem and C-function , 2010, 1003.4773.

[18]  A. G.,et al.  MEASUREMENTS OF AND FROM 42 HIGH-REDSHIFT SUPERNOVAE , 1998 .

[19]  The power of general relativity , 2005, gr-qc/0509059.

[20]  R. Brustein,et al.  Wald's entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling , 2007, 0712.3206.

[21]  L. A. King.  Theories of gravity , 1973 .

[22]  A. Barvinsky,et al.  Asymptotic freedom in higher-derivative quantum gravity , 1985 .

[23]  Unified first law of black hole dynamics and relativistic thermodynamics , 1997, gr-qc/9710089.

[24]  M. Visser,et al.  Tolman mass, generalized surface gravity, and entropy bounds. , 2010, Physical review letters.

[25]  R. Wald,et al.  Black hole entropy is Noether charge. , 1993, Physical review. D, Particles and fields.

[26]  Mark Trodden,et al.  Is Cosmic Speed-Up Due to New Gravitational Physics? , 2003, astro-ph/0306438.

[27]  E. Fradkin,et al.  S matrix for gravitational field. ii. local measure, general relations, elements of renormalization theory , 1973 .

[28]  S. Deser,et al.  New energy definition for higher curvature gravities , 2007, gr-qc/0701140.

[29]  J. Oliva,et al.  Classification of Six Derivative Lagrangians of Gravity and Static Spherically Symmetric Solutions , 2010, 1004.0737.

[30]  Valerio Faraoni,et al.  Black Hole Entropy in Scalar-Tensor and ƒ(R) Gravity: An Overview , 2010, Entropy.

[31]  G. Zoccatelli,et al.  On the Hawking radiation as tunneling for a class of dynamical black holes , 2007, 0707.4425.

[32]  One-loop f(R) gravity in de Sitter universe , 2005, hep-th/0501096.

[33]  S. Deser,et al.  Spherically symmetric solutions of Einstein + non-polynomial gravities , 2007, 0705.1669.

[34]  P. Binétruy.  The cosmological constant , 1999 .

[35]  A. Starobinsky,et al.  The Case for a positive cosmological Lambda term , 1999, astro-ph/9904398.

[36]  Z. Berezhiani,et al.  Exact Spherically Symmetric Solutions in Massive Gravity , 2008, 0803.1687.

[37]  M. Nadalini,et al.  Hamilton-Jacobi tunneling method for dynamical horizons in different coordinate gauges , 2009, 0906.1725.

[38]  S. D. Odintsov,et al.  INTRODUCTION TO MODIFIED GRAVITY AND GRAVITATIONAL ALTERNATIVE FOR DARK ENERGY , 2006, hep-th/0601213.

[39]  P. Peebles,et al.  The Cosmological Constant and Dark Energy , 2002, astro-ph/0207347.

[40]  A. Starobinsky,et al.  A new type of isotropic cosmological models without singularity , 1980 .

[41]  J. Isenberg.  Black Hole Physics: Basic Concepts and New Developments, by Valeri P. Frolov and Igor D. Novikov , 1998 .

[42]  B. Dewitt,et al.  Renormalization of a classical gravitational field interacting with quantized matter fields , 1962 .

[43]  R. Ellis,et al.  Measurements of $\Omega$ and $\Lambda$ from 42 high redshift supernovae , 1998, astro-ph/9812133.

[44]  S. Hayward,et al.  Local Hawking temperature for dynamical black holes , 2008, 0806.0014.

[45]  N. Ohta,et al.  Generalized Misner-Sharp Energy in f(R) Gravity , 2009, 0910.2387.

[46]  M. Phillips,et al.  Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant , 1998, astro-ph/9805201.

[47]  Quintessence without scalar fields , 2003, astro-ph/0303041.

[48]  Temperature, energy, and heat capacity of asymptotically anti-de Sitter black holes. , 1994, Physical review. D, Particles and fields.

[49]  T. Padmanabhan.  Cosmological constant—the weight of the vacuum , 2002, hep-th/0212290.