Iyer–Wald Approach Links Generalized Entropy to Modified Gravity

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