Iyer–Wald Approach Links Generalized Entropy to Modified Gravity

Grant Pearson — Wed, 21 Oct 2026 20:02:15 +0000

A theoretical study finds that generalized mass-to-horizon entropy for black holes can be reconstructed within modified $f(R)$ gravity using the Iyer–Wald approach. The analysis considers spherically symmetric vacuum solutions with constant curvature in the massive branch of the theory and identifies a generalized Lagrangian proportional to $R^{1+\epsilon}$ , where $\epsilon=(n-1)/2$ measures departures from the standard formulation of general relativity.

The paper studies the gravitational basis of a generalized entropy description characterized by an entropic exponent index $n$ and a multiplicative parameter $\gamma$ . Applying the Iyer–Wald method in modified $f(R)$ gravity, the authors show that the generalized mass-to-horizon entropy can be recovered from the specified curvature-dependent Lagrangian. The relation between the Lagrangian structure and the entropic exponent provides the central mathematical result of the work.

The finding is a formal connection between a class of modified-gravity solutions and the thermodynamic description of black-hole horizons. It is not an observational result and does not establish that a particular black hole in nature has a measured entropy beyond the standard general-relativistic treatment. The analysis is limited to the stated spherically symmetric vacuum configurations with constant curvature in the massive branch, so its conclusions should not be treated as a general demonstration for all black holes, gravitational fields or modified-gravity models.

The authors also discuss possible implications for cosmology and for the thermodynamic instability of Schwarzschild black holes. Those implications are presented as prospects within the theoretical framework; the supplied research summary does not report a new observation or demonstrate that the instability has been experimentally resolved. Overall, the work shows how an Iyer–Wald entropy calculation in modified $f(R)$ gravity can reproduce generalized mass-to-horizon entropy under its stated assumptions, while leaving the broader physical consequences unresolved.

Subject of Research: Generalized black-hole horizon entropy in modified f(R) gravity using the Iyer–Wald approach

Article Title: Gravity theory of the generalized mass-to-horizon entropy: the Iyer–Wald approach

Article References: Mondal, S., & Choudhuri, A. (2026). Gravity theory of the generalized mass-to-horizon entropy: the Iyer–Wald approach. General Relativity and Gravitation, 58(10), Article 122. https://doi.org/10.1007/s10714-026-03625-z

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DOI: 10.1007/s10714-026-03625-z

Keywords: black hole entropy, modified gravity, f(R) gravity, Iyer–Wald method, general relativity, Schwarzschild black holes, thermodynamic instability, spherically symmetric vacuum, cosmology, Gravity, theory, generalized

black hole thermodynamics in modified gravity – Science

Iyer–Wald Approach Links Generalized Entropy to Modified Gravity