Violation of the first law of black hole thermodynamics in $f(T)$ gravity

Abstract

We prove that, in general, the first law of black hole thermodynamics, $\delta Q=T\delta S$, is violated in $f(T)$ gravity. As a result, it is possible that there exists entropy production, which implies that the black hole thermodynamics can be in non-equilibrium even in the static spacetime. This feature is very different from that of $f(R)$ or that of other higher derivative gravity theories. We find that the violation of first law results from the lack of local Lorentz invariance in $f(T)$ gravity. By investigating two examples, we note that $f"(0)$ should be negative in order to avoid the naked singularities and superluminal motion of light. When $f"(T)$ is small, the entropy of black holes in $f(T)$ gravity is approximatively equal to $\frac{f^{\prime }(T)}{4}A$.

18 pages, no figure, version accepted for publication in JCAP

References in corpus (20)

• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• On Born-Infeld Gravity in Weitzenbock spacetime
• Cosmological perturbations in f(T) gravity
• Observational constraints on $f(T)$ theory
• f(T) gravity mimicking dynamical dark energy. Background and perturbation analysis
• Atom Interferometry tests of the isotropy of post-Newtonian gravity
• Generalizations of teleparallel gravity and local Lorentz symmetry
• $f(T)$ models with phantom divide line crossing
• Degrees of freedom of $f(T)$ gravity
• Spherically symmetric static spacetimes in vacuum f(T) gravity
• Static Solutions with Spherical Symmetry in f(T) Theories
• Spontaneous breaking of Lorentz invariance, black holes and perpetuum mobile of the 2nd kind
• Cosmological evolution in exponential gravity
• $f(T)$ Theories and Varying Fine Structure Constant
• Translation of Einstein's Attempt of a Unified Field Theory with Teleparallelism
• Pure kinetic k-essence as the cosmic speed-up
• Comment on "Einstein's Other Gravity and the Acceleration of the Universe''
• f(R) Gravity and Maxwell Equations from the Holographic Principle

Cited by in corpus (97)

• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• f(T) teleparallel gravity and cosmology
• Reconstruction of $f(T)$ gravity: Rip cosmology, finite-time future singularities and thermodynamics
• $f(T,\mathcal{T})$ gravity and cosmology
• Teleparallel equivalent of Gauss-Bonnet gravity and its modifications
• Good and bad tetrads in f(T) gravity
• Solar system constraints on f(T) gravity
• Phase-Space analysis of Teleparallel Dark Energy
• Nonminimal torsion-matter coupling extension of f(T) gravity
• Viable f(T) models are practically indistinguishable from LCDM
• Thermodynamics of cosmological horizons in $f(T)$ gravity
• Generalized second law of thermodynamics in f(T) gravity
• New Schwarzschild-like solutions in f(T) gravity through Noether symmetries
• Observational Constraints on Teleparallel Dark Energy
• Static Anisotropic Solutions in f(T) Theory
• Exact charged black-hole solutions in D-dimensional f(T) gravity: torsion vs curvature analysis
• Anisotropic Universe Models in f(T) Gravity
• Noether symmetries and analytical solutions in f(T)-cosmology: A complete study
• Cosmological applications of $F(T,T_G)$ gravity
• Anisotropic Compact Stars in $f(G)$ Gravity
• Noether Symmetry in $f(T)$ Theory
• Energy conditions bounds on f(T) gravity
• Violation of First Law of Thermodynamics in f(R,T) Gravity
• New Static Solutions in f(T) Theory
• Dynamics of Teleparallel Dark Energy
• Attractor Solutions in f(T) Cosmology
• Strong gravitational lensing --- A probe for extra dimensions and Kalb-Ramond field
• Corrected form of the first law of thermodynamics for regular black holes
• Regular black holes in $f(T)$ Gravity through a nonlinear electrodynamics source
• Circularly symmetric solutions in three-dimensional Teleparallel, f(T) and Maxwell-f(T) gravity
• Stability of a non-minimally conformally coupled scalar field in F(T) cosmology
• Dynamical features of scalar-torsion theories
• A spherically-symmetric charged-dS solution in f(T) gravity theories
• Primordial Fluctuations within Teleparallelism
• $f(T)$ gravitational baryogenesis
• Thick Brane Split Caused by Spacetime Torsion
• Anisotropic fluid for a set of non-diagonal tetrads in f(T) gravity
• Stability of motion and thermodynamics in charged black holes in $f(T)$ gravity
• Generalized second law of thermodynamics in f(R,T) theory of gravity
• Updated constraints on $f(T)$ models using direct and indirect measurements of the Hubble parameter
• Phase Portraits of general f(T) Cosmology
• Energy conditions in generalized teleparallel gravity models
• Self-Gravitating Spherically Symmetric Solutions in Scalar-Torsion Theories
• Constraining $f(T)$ Theories with the Varying Gravitational Constant
• LCDM Model in f(T) Gravity: Reconstruction, Thermodynamics and Stability
• Traversable wormholes in the extended teleparallel theory of gravity with matter coupling
• Holographic f(T)-gravity model with power-law entropy correction
• Generalized teleparallel cosmology and initial singularity crossing
• Dynamical system analysis for nonminimal torsion-matter coupled gravity
• $D$-dimensional charged Anti-de-Sitter black holes in $f(T)$ gravity
• Statefinder Analysis of f(T) Cosmology
• Cosmic acceleration in non-flat $f(T)$ cosmology
• Matter Density Perturbations in Modified Teleparallel Theories
• Analytic rotating black hole solutions in $N$-dimensional $f(T)$ gravity
• Weak Gravity Conjecture, Black Branes and Violations of Universal Thermodynamic Relation
• Generalized second law of thermodynamics in scalar-tensor gravity
• Geodesic Deviation Equation in $f(T)$ gravity
• First Order Formalism for Thick Branes in Modified Teleparallel Gravity
• The generalized second law of gravitational thermodynamics on the apparent horizon in f(R)-gravity
• Power-law and intermediate inflationary models in f(T)-gravity
• QCD ghost f(T)-gravity model
• Noether charge and black hole entropy in teleparallel gravity
• Modified teleparallel gravity with higher-derivative torsion terms
• Logamediate Inflation in f(T) Teleparallel Gravity
• Thermodynamic properties of modified gravity theories
• Matter stability in modified teleparallel gravity
• Born-Infeld and Charged Black Holes with non-linear source in $f(T)$ Gravity
• Black-Bounce in $f(T)$ Gravity
• Non-minimal Coupling of Torsion-matter Satisfying Null Energy Condition for Wormhole Solutions
• Rotating and non-rotating AdS black holes in $f(\mathcal{T})$ gravity non-linear electrodynamics
• Planar Symmetry in f(T) gravity
• Anisotropic Quintessence Strange Stars in f(T) Gravity with Modified Chaplygin Gas
• Violation of causality in $f(T)$ gravity
• Spherical Accretion of Matter by Charged Black Holes on f(T) Gravity
• Black holes and regular black holes in coincident $f(\mathbb{Q},{\mathbb{B}}_Q)$ gravity coupled to nonlinear electrodynamics
• New black-to-white hole solutions with improved geometry and energy conditions
• The generalized second law of thermodynamics for interacting $f(R)$ gravity
• Charged Anti-de Sitter BTZ black holes in Maxwell-$f(T)$ gravity
• Hyperscaling violating black holes in scalar-torsion theories
• Regularization of $f(T)$ gravity theories and local Lorentz transformation
• Charged gravastar model in $f(T)$ gravity admitting conformal motion
• On The Temporal Evolution of Particle Production in $f(T)$ Gravity
• Entropy for gravitational Chern-Simons terms by squashed cone method
• Thick string-like braneworlds in f(T) gravity
• Towards a possible solution for the coincidence problem: f(G) gravity as background
• Geometrically contracted structure in teleparallel $f(T)$ gravity
• On solutions of loop quantum cosmology
• Generalized Teleparallel Theory
• Teleparallel gravity: Effects of torsion in 6D braneworlds
• Hidden conformal symmetry of the rotating charged AdS black holes in quadratic $f$($T$) gravity
• Generalized second law of thermodynamics on the apparent horizon in modified Gauss-Bonnet gravity
• The generalized second law of thermodynamics for the interacting in $f(T)$ gravity
• Analytical Stellar Models of Neutron Stars in Teleparallel Gravity
• The meaning of torsion in teleparallel theories
• Generalized Hidden Conformal Symmetry in Quadratic $f(T)$ Gravity
• Revisited apparent horizon entropy and GSL in modified gravity
• Radial derivatives as a test of pre-Big-Bang events on the Planck data