Analysis of Unbalanced Black Ring Solutions within the Quasilocal Formalism

TL;DR

This paper analyzes unbalanced rotating black ring solutions in five-dimensional Einstein-Maxwell-dilaton gravity using a novel quasilocal formalism, deriving their thermodynamics and balance conditions with implications for their conserved charges.

Contribution

It introduces a new method to derive the balance condition for black rings via the quasilocal formalism and studies their thermodynamics with conical singularities.

Findings

Balance condition derived using boundary stress-energy conservation.

Thermodynamics computed with conical singularities affecting quantities.

Smarr and quantum statistical relations hold despite singularities.

Abstract

We investigate the properties of rotating asymptotically flat black ring solutions in five-dimensional Einstein-Maxwell-dilaton gravity with the Kaluza-Klein coupling. Within the quasilocal formalism, the balance condition for these solutions is derived by using the conservation of the renormalized boundary stress-energy tensor, which is a new method proposed by Dumitru Astefanesei and his collaborators. We also study the thermodynamics of unbalanced black rings. The conserved charges and the thermodynamical quantities are computed. Due to the existence of a conical singularity in the boundary, these quantities differ from the original regular ones. It is shown that the Smarr relation and the quantum statistical relation are still satisfied. However, we get an extra term in the first law of thermodynamics. As the balance condition is imposed this extra term vanishes.