# Phase transitions in Born-Infeld AdS black holes in D-dimensions

## TL;DR

This paper studies phase transitions in Born-Infeld AdS black holes across various spacetime dimensions, revealing second-order transitions and the increasing stability of small black holes with higher dimensions.

## Contribution

It introduces a comprehensive analysis of phase transitions in D-dimensional Born-Infeld AdS black holes using heat capacity, Ehrenfest, and Ruppeiner methods, and derives a generalized Smarr relation.

## Key findings

- Phase transition is of second order.
- Small black hole stability increases with spacetime dimension.
- Results from Ehrenfest and Ruppeiner methods agree.

## Abstract

In this paper, we have investigated phase transitions in arbitrary spacetime dimensions for Born-Infeld AdS black holes. The phase transition points are characterised from the divergence of heat capacity of the black hole. Two well established techniques, namely, the Ehrenfest scheme and the Ruppeiner state space geometry approach are used to identify the order of phase transition the black hole undergoes. It is observed that the results obtained from these two methods agree with each other. Our analysis reveals that the phase transition is of second order. It is also observed from the variation of the heat capacity with entropy that the small unstable black hole phase becomes more and more stable with increase in the spacetime dimensions. We speculate that this dependence of the stability of the black hole on the spacetime dimension can put an upper limit to the dimension of spacetime from the physical condition of the improbability of the formation of a small stable black hole. We have also derived a Smarr relation in D-spacetime dimensions using scaling arguments and first law of black hole thermodynamics which includes the cosmological constant and the Born-Infeld parameters as thermodynamic variables.