Thermodynamic and tachyonic instability for asymptotically flat black holes

TL;DR

This paper explores the connection between thermodynamic and tachyonic instabilities in asymptotically flat black holes, showing that tachyonic instability signals thermodynamic instability and extends the analysis to Schwarzschild-AdS black holes.

Contribution

It establishes a link between thermodynamic instability and tachyonic instability in asymptotically flat black holes, including those with scalar hair and in AdS space.

Findings

Tachyonic instability indicates thermodynamic instability in these black holes.

The study extends to black holes with scalar couplings to Gauss-Bonnet and Maxwell terms.

It confirms the relation for Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman black holes.

Abstract

It was confirmed that the negative modes of the Euclidean section for asymptotically flat black holes reveal the thermodynamic instability of these black holes in the grand canonical ensemble (GCE). These include Schwarzschild, Reissner-Nordstr\"{o}m, Kerr, and Kerr-Newman black holes. In this work, we develop the relation between thermodynamic instability in the GCE and tachyonic instability for asymptotically flat black holes, where the latter is the onset for obtaining black holes with scalar hair. This implies that the tachyonic instability of black holes when introducing scalar coupling to the Gauss-Bonnet term or Maxwell term reflects thermodynamic instability of these black holes in the GCE. We go on further to consider the Schwarzschild-AdS black hole.