Holographic dictionary for Lifshitz and hyperscaling violating black holes

TL;DR

This paper develops a new holographic dictionary for black holes with Lifshitz and hyperscaling violating asymptotics, linking their thermodynamics to boundary theories and generalizing previous AdS-based frameworks.

Contribution

It introduces a holographic dictionary tailored for Lifshitz and hyperscaling violating black holes, extending the AdS black hole thermodynamics framework.

Findings

Holographic Euler equation matches a generalized Smarr formula.

The boundary first law aligns with the extended bulk first law.

The central charge in the Euler relation depends on the hyperscaling parameter.

Abstract

We develop a novel holographic dictionary for the thermodynamics of black holes with Lifshitz and hyperscaling violating asymptotics, generalizing the dictionary for Anti-de Sitter black holes. Using our dictionary we show that the holographic Euler equation is dual to a generalized Smarr formula for these black holes, and we find a precise match between the extended bulk and boundary first law. Notably, the dictionary for the central charge appearing in the Euler relation depends on the hyperscaling violating parameter, but not on the Lifshitz dynamical exponent.