Inverse Area Corrections to Black Hole Entropy Area Formula in F(R) Gravity and Gravitational Wave Observations

TL;DR

The paper addresses how inverse-area corrections modify the black-hole entropy in classical $F(R)$ gravity and tests their compatibility with gravitational-wave observations that support Hawking's Area Theorem. It employs the Wald entropy framework, generalized by Jacobson, Kang, and Myers, to derive an inverse-area expansion of the black-hole entropy for static, spherically symmetric solutions, with coefficients set by derivatives of $F$ at $R=0$. By enforcing an absolute consistency with GW data, it obtains inequalities such as $F^{(2)}_{R_{ m S}}(0)<0$ and a resummed bound $F^{(1)}_{R_{ m S}}(A_{ m S}^{-1})<F^{(1)}_{R_{ m S}}(0)$, constraining the form of $F(R)$. The work also compares these classical results with subleading inverse-area corrections from quantum gravity via It From Bit/LQG, which yield $S_{bh}\simeq S_{BH}-\frac{3}{2}\log S_{BH}-2 S_{BH}^{-1}+\cdots$ and remain consistent with GW observations. Overall, the study connects modified gravity phenomenology with astrophysical data, offering concrete bounds on $F(R)$-gravity derivatives near $R=0$, and highlights the compatibility of quantum-gravity-inspired corrections with observational constraints.

Abstract

We consider corrections to the Bekenstein Hawking Area Formula for black hole entropy, which have inverse powers of the horizon area for very large horizon areas, for classical spherically symmetric black hole solutions of F(R) modified gravity theory, using the Wald formula for the entropy function with modifications suggested by Jacobson, Kang and Myers. Requiring that the coefficient of such corrections be absolutely consistent with gravitational wave observational results validating the Hawking Area Theorem for binary black hole coalescences, implies constraints on parameters of F(R) gravity. For the sake of comparison, we present a computation of inverse area corrections for quantum black holes in quantum general relativity, using the It from Bit approach of Wheeler modified by some tenets of Loop Quantum Gravity.