The mass of a Lifshitz black hole

TL;DR

This paper accurately determines the mass of Lifshitz black holes in 3D massive gravity using a robust method, resolving previous discrepancies and confirming consistency with holographic predictions.

Contribution

It introduces a reliable approach to compute the mass of Lifshitz black holes in higher-derivative gravity, clarifying previous conflicting results.

Findings

Mass of Lifshitz black hole is positive with proper normalization.

The computed mass aligns with holographic calculations.

The method is effective in the strong field regime.

Abstract

It is well known that massive 3D gravity admits solutions that describe Lifshitz black holes as those considered in non-relativistic holography. However, the determination of the mass of such black holes remained unclear as many different results were reported in the literature presenting discrepancies. Here, by using a robust method that permits to tackle the problem in the strong field regime, we determine the correct mass of the Lifshitz black hole of the higher-derivative massive gravity and compare it with other results obtained by different methods. Positivity of the mass spectrum demands an odd normalization of the gravity action. In spite of this fact, the result turns out to be consistent with computations inspired in holography.