Phase structure of the de Sitter Spacetime with KR field based on the Lyapunov exponent

TL;DR

This paper explores the thermodynamic phase structure, stability, and shadow properties of de Sitter black holes influenced by a Lorentz-violating Kalb-Ramond field, revealing new insights into black hole thermodynamics in modified gravity.

Contribution

It introduces a novel analysis of de Sitter black holes with a KR field, examining thermodynamics, Lyapunov exponents, and shadows in Lorentz-violating gravity.

Findings

Lorentz-violating parameter affects black hole thermodynamics

Lyapunov exponent analysis reveals stability properties

Black hole shadow characteristics are influenced by the KR field

Abstract

Since the spontaneously broken of the Lorentz symmetry in the gravity theory with the non-minimally coupling between the Kalb-Ramond (KR) field (that acquires a nonzero vacuum expectation value) and the Einstein gravity, there exists the exactly static and spherically symmetric black holes solutions related with the Lorentz violating parameter. Based on this, we consider the corresponding black hole solution in the de-Sitter (dS) spacetime with the KR field and investigate the thermodynamic properties in the expanded phase space through introducing the interplay entropy between the black hole and cosmological horizons. Especially we analyze the effect of the Lorentz-violating parameter on the thermodynamic properties. Furthermore, the Lyapunov exponent and the shadow of these static and spherically symmetric black holes in this Lorentz-violating gravity theory are also investigated. These study will open a new perspective to probe the thermodynamics of black holes.