# Holographic entanglement first law for d + 1 dimensional rotating cylindrical black holes

## TL;DR

This paper derives a holographic entanglement first law for rotating cylindrical black holes in higher dimensions, incorporating effects of both energy and angular momentum through perturbative calculations.

## Contribution

It introduces a first law of holographic entanglement entropy that accounts for angular momentum in rotating black holes across arbitrary dimensions.

## Key findings

- Angular momentum affects the first order variation of entanglement entropy.
- A generalized holographic entanglement first law is formulated for rotating black holes.
- The law applies to spacetime dimensions d+1 ≥ 4.

## Abstract

We calculate the holographic entanglement entropy for the rotating cylindrical black holes in $d+1$ dimensions as perturbations over $AdS_{d+1}$. This is accomplished based on the first order variation of the area functional in arbitrary dimensions. For these types of black holes, the angular momentum appears at the first order of the perturbative expansion of the holographic entanglement entropy for spacetime dimensions of d +1 $\geq$ 4. We obtain a form of holographic entanglement first law in the presence of both energy and angular momentum.