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On the Dynamics of Near-Extremal Black Holes

Pranjal Nayak, Ashish Shukla, Ronak M Soni, Sandip P. Trivedi, V. Vishal

TL;DR

The paper shows that near-extremal Reissner–Nordström black holes in AdS$_4$ possess low-energy dynamics that are universally captured by the Jackiw–Teitelboim model, with time reparametrisation symmetry breaking encoded by a Schwarzian action. By analyzing both thermodynamics and the four-point function of a probe scalar in the S-wave sector, it demonstrates that the near-horizon AdS$_2$ region governs the leading low-energy behaviour, and that the JT description reproduces these results precisely. A careful S-wave dimensional reduction confirms the JT match and clarifies the role of boundary fluctuations, while subleading corrections from the dimensional reduction are suppressed by $1/r_h$. Together, the findings suggest a universal, symmetry-driven mechanism for low-energy dynamics in near-extremal black holes, potentially extending beyond AdS$_4$ and the S-wave sector to a broader class of gravitational systems.

Abstract

We analyse the dynamics of near-extremal Reissner-Nordström black holes in asymptotically four-dimensional Anti-de Sitter space (AdS$_4$). We work in the spherically symmetric approximation and study the thermodynamics and the response to a probe scalar field. We find that the behaviour of the system, at low energies and to leading order in our approximations, is well described by the Jackiw-Teitelboim (JT) model of gravity. In fact, this behaviour can be understood from symmetry considerations and arises due to the breaking of time reparametrisation invariance. The JT model has been analysed in considerable detail recently and related to the behaviour of the SYK model. Our results indicate that features in these models which arise from symmetry considerations alone are more general and present quite universally in near-extremal black holes.

On the Dynamics of Near-Extremal Black Holes

TL;DR

The paper shows that near-extremal Reissner–Nordström black holes in AdS possess low-energy dynamics that are universally captured by the Jackiw–Teitelboim model, with time reparametrisation symmetry breaking encoded by a Schwarzian action. By analyzing both thermodynamics and the four-point function of a probe scalar in the S-wave sector, it demonstrates that the near-horizon AdS region governs the leading low-energy behaviour, and that the JT description reproduces these results precisely. A careful S-wave dimensional reduction confirms the JT match and clarifies the role of boundary fluctuations, while subleading corrections from the dimensional reduction are suppressed by . Together, the findings suggest a universal, symmetry-driven mechanism for low-energy dynamics in near-extremal black holes, potentially extending beyond AdS and the S-wave sector to a broader class of gravitational systems.

Abstract

We analyse the dynamics of near-extremal Reissner-Nordström black holes in asymptotically four-dimensional Anti-de Sitter space (AdS). We work in the spherically symmetric approximation and study the thermodynamics and the response to a probe scalar field. We find that the behaviour of the system, at low energies and to leading order in our approximations, is well described by the Jackiw-Teitelboim (JT) model of gravity. In fact, this behaviour can be understood from symmetry considerations and arises due to the breaking of time reparametrisation invariance. The JT model has been analysed in considerable detail recently and related to the behaviour of the SYK model. Our results indicate that features in these models which arise from symmetry considerations alone are more general and present quite universally in near-extremal black holes.

Paper Structure

This paper contains 19 sections, 188 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Spherically Symmetric Reissner-Nordström Black Holes
  3. Time Dependence
  4. Thermodynamics of the AdS$_4$ RN Black Hole
  5. The Four-Point Function
  6. On-shell Action
  7. The JT Model
  8. Thermodynamics
  9. Four-Point Function
  10. S-wave Reduction
  11. Comparison with the JT Model
  12. More Detailed Comparison with the JT Model
  13. Conclusions
  14. Details of 4D Thermodynamic Calculations
  15. 4D Calculation of the Four-Point Function
  16. ...and 4 more sections

Figures (1)

  • Figure 1: The near-extremal geometry. For $r\rightarrow \infty$ the geometry is asymptotically AdS$_4$. $r\rightarrow r_c$, where $\frac{r_c-r_h}{r_h}\ll 1$, $\frac{r_c-r_h}{L}\gg 1$, is the asymptotic AdS$_2\times$S$^2$ region. The horizon at extremality is at $r=r_h$.