On the Dynamics of Near-Extremal Black Holes (1802.09547v4)

Abstract: We analyse the dynamics of near-extremal Reissner-Nordstr\"om 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.

An Overview of "On the Dynamics of Near-Extremal Black Holes"

The paper "On the Dynamics of Near-Extremal Black Holes" explores the relationship between near-extremal Reissner-Nordström black holes in four-dimensional Anti de Sitter space (AdS$_4$) and the Jackiw-Teitelboim (JT) model of gravity. Focused on spherically symmetric configurations, the authors aim to connect the thermodynamics and low-energy dynamics of these black holes to the JT model, effectively drawing parallels between the behavior dictated by symmetry considerations in both frameworks.

Thermodynamics and Low-Energy Behavior

The authors begin by studying the large black holes within a gravity-Maxwell field system, characterized by a horizon radius significantly larger than the AdS radius (i.e., $r_h \gg L$). By adopting a spherically symmetric approach, the paper explores the near-extremal thermodynamics. It highlights a linear specific heat close to extremality and a temperature gap determined by $T_{\text{gap}} \sim G / (L^2 \, r_h)$, providing insights into the thermal properties of these entities.

Connection to the SYK and JT Models

One major contribution of the paper is its demonstration that the dynamics of near-extremal Reissner-Nordström black holes are well approximated by the JT model at low energies. The Jackiw-Teitelboim model, originally explored in two-dimensional contexts for its tractability, manifests features arising from broken time-reparametrization symmetry prevalent in SYK-type models—specifically, universality in chaos bounds, linear specific heat, and aspects contributing to the resolution of the information loss puzzle in black hole studies.

The JT model effectively captures the essence of two-dimensional phenomena via its coupling between a dilaton field and the AdS$_2$ geometry. This coupling breaks the $SL(2, \mathbb{R})$ symmetry, offering a simplified yet powerful framework to understand features present in highly complex interacting systems such as near-extremal black holes.

Scalar Field Probes and Four-Point Function

A notable section of the paper addresses the response to a probe scalar field. The authors focus on the four-point correlation function, using spherical symmetry to simplify the dynamics and reveal insights into the low-energy behavior of the black hole system. They argue that fluctuations in the boundary fluctuations—and their coupling to time reparametrizations—give rise to an action involving the Schwarzian derivative, key to determining the system's behavior. This supports the hypothesis that dynamics arising in the JT model through symmetry considerations are present more broadly in near-extremal black holes.

Dimensional Reduction and Charge Dynamics

A dimensional reduction approach is adopted to further understand how the two-dimensional dynamics relate back to the higher-dimensional system. The authors build upon this methodology to underline how divergences and boundary conditions characterize the two-dimensional framework's alignment with JT model predictions, despite nuances introduced by the gravitational and electromagnetic fields in the full four-dimensional theory.

Conclusion and Future Directions

The paper concludes by suggesting future directions to test the universality of these findings across different black hole configurations, dimensions, and models. For instance, extending similar analyses to asymptotically flat spacetime and studying the effects beyond spherical symmetry may yield valuable insights.

Overall, the authors suggest that the paper of near-extremal black hole dynamics offers significant theoretical and practical implications, particularly in advancing our understanding of how symmetry-driven processes dictate their low-energy behavior. Such investigations could bridge or refine existing models in quantum gravity, while offering hope for resolving long-standing issues related to black hole thermodynamics and information theory. Other works might connect these findings further with microscopic string-theoretic constructs and matrix models pivotal in advanced quantum theories, potentially leading to broader implications in the field of theoretical astrophysics and quantum gravity.