First Law of Black Rings Thermodynamics in Higher Dimensional Dilaton Gravity with p + 1 Strength Forms

TL;DR

This paper derives the first law of thermodynamics for black rings in higher-dimensional Einstein dilaton gravity with p+1 form fields, generalizing previous five-dimensional results to more complex theories.

Contribution

It introduces a method to derive the first law for black rings in n-dimensional Einstein dilaton gravity with (p+1)-form fields, extending prior work to higher dimensions and additional field strengths.

Findings

Derived the first law of black ring thermodynamics in higher dimensions.

Extended the thermodynamic analysis to include (p+1)-form field strengths.

Provided a framework for analyzing black rings with dipole charge in complex gravity theories.

Abstract

We derive the first law of black rings thermodynamics in n-dimensional Einstein dilaton gravity with additional (p+1)-form field strength being the simplest generalization of five-dimensional theory containing a stationary black ring solution with dipole charge. It was done by means of choosing any cross section of the event horizon to the future of the bifurcation surface.