# Thermodynamic analysis of gravitational field equations in Lyra manifold

## TL;DR

This paper explores the thermodynamic properties of gravitational field equations within Lyra manifold, deriving horizon entropy and examining thermodynamic laws in various spacetime models.

## Contribution

It derives the entropy of apparent horizons in Lyra manifold and analyzes the validity of thermodynamic laws in this geometric framework.

## Key findings

- Entropy of apparent horizon in Lyra manifold is obtained.
- Second law of thermodynamics holds in the studied scenarios.
- Horizon entropy for static spherically symmetric spacetimes is derived.

## Abstract

Considering the Einstein field equations in Lyra manifold, and applying the unified first law of thermodynamics as well as the Clausius relation to the apparent horizon of FRW universe, we find the entropy of apparent horizon in Lyra manifold. In addition, the validity of second law of thermodynamics and its generalized form are also studied. Finally, we use the first law of thermodynamics in order to find the horizon entropy of static spherically symmetric spacetimes. Some results of considering (anti)de-Sitter and Schwarzschild metrics have also been addressed.