Super-entropy bumblebee AdS black holes

TL;DR

This paper investigates how the bumblebee field, which introduces Lorentz violation, affects the thermodynamic stability and super-entropy conditions of AdS black holes in both extended and non-extended phase spaces.

Contribution

It provides a detailed analysis of the thermodynamic behavior of bumblebee AdS black holes, highlighting their super-entropy nature when certain conditions are met.

Findings

Bumblebee field influences the event horizon and thermodynamic stability.

Bumblebee AdS black holes are super-entropy when the AdS radius is positive.

The study links super-entropy condition to negative heat capacity.

Abstract

Motivated by the effect of the bumblebee field on thermodynamic instability in (non)extended phase space, we study the thermodynamic instability for the bumblebee AdS black holes. For this purpose, first, we evaluate the effect of the bumblebee field (or Lorentz-violating parameter) on the event horizon for AdS black holes. Then, in non-extended phase space, we study the effect of the bumblebee field on the heat capacity and the Helmholtz free energy to investigate the local and global thermal stability areas, respectively. Next, we extend our study on the extended phase space by seeking on stable area by using the heat capacity at constant pressure ($C_{P}$). Finally, we evaluate the super-entropy black hole condition and indicate that the bumblebee AdS black holes are super-entropy black holes when $l>0$, which is consistent with the condition $C_{P}<0$.