Phase transition for a black hole with matter fields and the relation with the Lyapunov exponent

TL;DR

This paper constructs black hole solutions with matter fields in anti-de Sitter space, analyzes their phase transitions and stability, and explores the connection between black hole phases and Lyapunov exponents derived from geodesic instability.

Contribution

It introduces new black hole geometries with matter fields, studies their phase transition behavior, and links these phases to Lyapunov exponents indicating chaos.

Findings

Black hole with matter fields exhibits a phase transition from small to large black holes.

Constructed geometries resemble Reissner-Nordström black holes.

Lyapunov exponents from geodesic instability relate to black hole phase behavior.

Abstract

We construct black hole geometries coexisting with anisotropic matter in (anti)-de Sitter spacetime. We specifically focus on the black hole phase transitions that occur in anti-de Sitter spacetime and analyze the effects of the incorporated matter fields. Its local stability is examined by evaluating the heat capacity, while global stability is investigated in greater detail through phase transition analysis. The black hole system coexisting with the matter field allows for a phase transition from a small black hole to a large black hole. This demonstrates that the constructed geometry with the matter field would resemble that of the Reissner-Nordstr\"om black hole. We examine null geodesics, particularly unstable homoclinic orbits, which allow us to obtain Lyapunov exponents that characterize sensitivity to initial conditions. Finally, we analyze the relationship between the different black hole phases and the behavior of these Lyapunov exponents.