Wald Entropy in Extended Modified Myrzakulov Gravity Theories: \(f(R, T, Q, R_{\mu\nu}T^{\mu\nu}, R_{\mu\nu}Q^{\mu\nu}, \dots)\)

TL;DR

This paper derives a generalized Wald entropy formula for a broad class of extended modified gravity theories involving curvature, torsion, and non-metricity, revealing how additional geometric features influence black hole entropy.

Contribution

It extends the Wald entropy formalism to include non-Riemannian geometric contributions in modified gravity theories with generalized Lagrangians.

Findings

Derived explicit entropy expressions for extended gravity models.

Showed geometric degrees of freedom systematically modify entropy.

Confirmed invariance under diffeomorphisms in extended frameworks.

Abstract

We investigate black hole entropy in a broad class of modified Myrzakulov gravity theories defined by generalized Lagrangians of the form \( \mathcal{L} = \alpha R + F(T, Q, R_{\mu\nu}T^{\mu\nu}, R_{\mu\nu}Q^{\mu\nu}, \dots) \), where \( R \), \( T \), and \( Q \) represent curvature, torsion, and non-metricity scalars. Using the vielbein formalism, we derive the Wald entropy for various subclasses of these models, extending the classical entropy formula to accommodate non-Riemannian geometry. Our focus is on how the additional geometric degrees of freedom modify the entropy expression. The analysis shows that such corrections arise systematically from the extended structure of the action and preserve diffeomorphism invariance. These results refine the theoretical framework for gravitational thermodynamics in extended geometry settings.