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

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.

💡 Research Summary

The paper investigates sub‑leading corrections to the Bekenstein–Hawking entropy formula for black holes, focusing on two distinct contexts: (i) classical, spherically symmetric black holes in F(R) modified gravity, and (ii) quantum black holes described by Wheeler’s “It‑from‑Bit” picture supplemented with Loop Quantum Gravity (LQG) inputs.

Using the Wald entropy functional, the authors adopt the Jacobson‑Kang‑Myers (JKM) generalisation that allows the Noether charge to be integrated over any two‑dimensional cross‑section of the horizon. For an F(R) theory with Lagrangian L = F(R)√−g, the entropy of a static, spherically symmetric solution reduces to
S_bh = F′(R_S) A_S,
where R_S is the Ricci scalar evaluated on the horizon and A_S its area. For astrophysical black holes with A_S ≫ A_F (the analogue of the Planck area in the theory), R_S ≪ 1, so F′(R_S) can be expanded in a Taylor series around R = 0. This yields an entropy expression of the form

S_bh = S_BH + Σ_{n≥1} s_n S_BH^{1−n},

with S_BH ≡ A_S/A_F and coefficients

s_n = F^{(n+1)}(0) /