The thermal properties of blackfold and calculation of stress energy tensor

TL;DR

This paper analyzes the thermodynamical properties of higher-dimensional charged and neutral blackfolds, deriving stress energy tensors, exploring their stability, and relating Ricci-flat and AdS spacetimes.

Contribution

It introduces a method to compute stress energy tensors of blackfolds and compares thermodynamical properties of charged and neutral cases, including their stability analysis.

Findings

Charged blackfolds have brane-tension components in their stress energy tensor.

Neutral blackfolds are Ricci-flat and related to AdS spacetimes.

No phase transition or critical point found, indicating thermodynamical stability.

Abstract

In this paper, we determine thermodynamical quantities for one kind of higher dimensional black holes. We take two charged and neutral blackfold which are higher dimension. We investigate the thermodynamical properties of such black hole at near horizon. By expanding those metrics around horizon, considering periodicity condition of imaginary time and applying some thermodynamical constraints, we extract stress energy tensor of blackfolds. We compare the thermodynamical properties of charged and neutral blackfold. We see here that the stress energy tensor of charged blackfold has brane-tension component in addition to thermal properties. Then by knowing that the spacetime of neutral blackfold is Ricci-flat and there is a nice relation between Ricci-flat and AdS spacetimes we determine the AdS form of Ricci-flat. Also we calculate the corresponding temperature which is satisfied by our previous calculation. Finally, we check the phase transition of blackfolds and show that there is not any critical point for them. So, the thermodynamical stability of both blackfolds will be proven, this result agree with literature.