Surface counterterms and boundary stress-energy tensors for asymptotically non-anti-de Sitter spaces

TL;DR

This paper develops a method to define finite boundary stress-energy tensors and Euclidean actions for non-anti-de Sitter spaces with scalar deformations, demonstrated on various black hole solutions.

Contribution

It introduces a systematic approach to construct boundary counterterms for asymptotically non-AdS spaces, enabling well-defined boundary quantities and thermodynamic analysis.

Findings

Successfully computed boundary stress-energy tensors for various black holes.

Derived finite Euclidean actions for non-AdS black hole solutions.

Discovered new thermodynamic features of topological black holes.

Abstract

For spaces which are not asymptotically anti-de Sitter where the asymptotic behavior is deformed by replacing the cosmological constant by a dilaton scalar potential, we show that it is possible to have well-defined boundary stress-energy tensors and finite Euclidean actions by adding appropriate surface counterterms. We illustrate the method by the examples of domain-wall black holes in gauged supergravities, three-dimensional dilaton black holes and topological dilaton black holes in four dimensions. We calculate the boundary stress-energy tensor and Euclidean action of these black configurations and discuss their thermodynamics. We find new features of topological black hole thermodynamics.