Verification of the First Law of Horizon Thermodynamics for Schwarzschild, Reissner-Nordstr\"om, Kerr, and Kerr-Newman Black Holes in Four-Dimensional f(R) Gravity with Dual Scalar Fields

TL;DR

This paper verifies the first law of horizon thermodynamics for various black holes in four-dimensional f(R) gravity with dual scalar fields, derived from a five-dimensional membrane scenario, confirming the robustness of thermodynamics in extended gravity theories.

Contribution

It demonstrates the validity of the first law of horizon thermodynamics for multiple black hole solutions in four-dimensional f(R) gravity with dual scalar fields, derived from higher-dimensional theories.

Findings

First law holds for Schwarzschild, RN, Kerr, and KN black holes in this framework.

Derived black hole solutions from a five-dimensional membrane scenario.

Confirmed the robustness of horizon thermodynamics in extended gravity theories.

Abstract

This paper demonstrates the validity of the first law of horizon thermodynamics for Schwarzschild, RN, Kerr, and Kerr-Newman (KN) black holes within the framework of four-dimensional f(R) gravity coupled with dual scalar fields. Starting from a five-dimensional membrane world scenario, we derive the four-dimensional effective f(R) gravity action and obtain the corresponding black hole solutions. We then verify that these solutions satisfy the first law of black hole thermodynamics by explicitly calculating the variations of thermodynamic quantities. The analysis confirms the robustness of the horizon thermodynamics framework in extended gravitational theories, providing insights into the interplay between higher-dimensional theories and four-dimensional black hole thermodynamics.