Instability of charged black holes in anti-de Sitter space

TL;DR

This paper analyzes linear perturbations of large $AdS_4$ Reissner–Nordström black holes, showing a tachyonic mode appears in the black-brane limit once the system becomes thermodynamically unstable. The authors derive coupled perturbation equations for gauge and scalar fields, reduce them to a fourth-order scalar equation, and identify a single tachyonic mode for $ abla$-space parameter $oxed{oldsymbol{ ext{χ}}}$ in a narrow range ($1.007<oldsymbol{ ext{χ}} leq 1.091$), consistent with AdS/CFT expectations of Bose condensation in the dual theory. They interpret this as a Gregory-Laflamme-type instability and propose a broader conjecture linking thermodynamic instability to GL-instability for black branes, while discussing potential proofs and the implications for AdS spacetime evolution and naked singularities. The work strengthens the holographic link between black hole thermodynamics and dynamical instabilities, suggesting a structured correspondence between Hessian instabilities and tachyonic perturbations. It also highlights the role of negative-mass-squared scalars in enabling such instabilities and points to future avenues for rigorous proofs and broader applicability.

Abstract

We exhibit a tachyonic mode in a linearized analysis of perturbations of large anti-de Sitter Reissner-Nordstrom black holes in four dimensions. In the large black hole limit, and up to a 0.7% discrepancy which is probably round-off error in the numerical analysis, the tachyon appears precisely when the black hole becomes thermodynamically unstable.

Figures (1)

• Figure 1: The boundaries at which various partial wave numbers begin to exhibit tachyons. The vertical axis is $\chi$ and the horizontal axis is $\sigma$.