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Hamiltonian approach to near-extremal black hole evaporation and backreaction

Per Kraus

TL;DR

This work develops a Hamiltonian framework that captures large near-horizon gravitational fluctuations in near-extremal black holes by integrating out the s-wave gravitational degrees of freedom. It yields a gravity-dressed scalar action with a low-temperature enhanced coupling $\frac{G}{r_0^3T_H}$ and derives an explicit nonlocal-in-space, time-local effective Hamiltonian $H_{\rm ADM}$ that governs scalar backreaction. At leading order in perturbation theory, the authors compute the one-loop correction to the 2-point function, finding late-time growth terms that scale with $\frac{G}{T_H}$ and include both $\sim e^{\rho_h\tau}$ and $\sim \tau^2$ contributions, whose interpretation connects to black-hole energy fluctuations and potential equilibrium effects. The results pave the way for a dynamic, real-time understanding of backreaction in near-extremal black holes and motivate further connections to JT gravity, Schwarzian dynamics, and a full resummation in a shrinking-background setting with possible holographic interpretations.

Abstract

We investigate radiation from near-extremal black holes formed by collapse, focusing on the role of large backreaction effects arising from gravitational fluctuations in the near-horizon region. Such effects have previously been identified from computations based on JT gravity and its Schwarzian description, most notably for the Euclidean partition function. Restricting attention to the s-wave sector, we integrate out gravity by solving the constraint equations in the Hamiltonian formalism, obtaining an effective scalar action with a coupling that grows at low temperature, thus enabling a real-time treatment of quantum backreaction. We then take initial steps toward evaluating the impact of this interaction on correlations of the outgoing radiation, and compare our findings with earlier results.

Hamiltonian approach to near-extremal black hole evaporation and backreaction

TL;DR

This work develops a Hamiltonian framework that captures large near-horizon gravitational fluctuations in near-extremal black holes by integrating out the s-wave gravitational degrees of freedom. It yields a gravity-dressed scalar action with a low-temperature enhanced coupling and derives an explicit nonlocal-in-space, time-local effective Hamiltonian that governs scalar backreaction. At leading order in perturbation theory, the authors compute the one-loop correction to the 2-point function, finding late-time growth terms that scale with and include both and contributions, whose interpretation connects to black-hole energy fluctuations and potential equilibrium effects. The results pave the way for a dynamic, real-time understanding of backreaction in near-extremal black holes and motivate further connections to JT gravity, Schwarzian dynamics, and a full resummation in a shrinking-background setting with possible holographic interpretations.

Abstract

We investigate radiation from near-extremal black holes formed by collapse, focusing on the role of large backreaction effects arising from gravitational fluctuations in the near-horizon region. Such effects have previously been identified from computations based on JT gravity and its Schwarzian description, most notably for the Euclidean partition function. Restricting attention to the s-wave sector, we integrate out gravity by solving the constraint equations in the Hamiltonian formalism, obtaining an effective scalar action with a coupling that grows at low temperature, thus enabling a real-time treatment of quantum backreaction. We then take initial steps toward evaluating the impact of this interaction on correlations of the outgoing radiation, and compare our findings with earlier results.

Paper Structure

This paper contains 19 sections, 103 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Gravitational collapse of a charged shell, and free field Hawking radiation
  3. Reissner-Nordström solution
  4. Near-horizon limit
  5. Collapse geometry
  6. Hawking radiation in the free field limit
  7. Gravitationally dressed scalar field
  8. Action and constraints
  9. Solving the constraints
  10. Effective scalar field action
  11. Scalar action in the near-extremal, near-horizon limit
  12. Gravitational perturbation theory
  13. Perturbative setup
  14. Perturbative evaluation of late time correlators
  15. One-loop correction to 2-point function
  16. ...and 4 more sections

Figures (2)

  • Figure 1: Collapse of a charged null shell forming a Reissner-Nordström black hole.
  • Figure 2: Integration regions contributing in the second and third lines of (\ref{['e6a']}). Lines of constant $\tau$ are in red. The dotted line is a null ray of constant $\tilde{u}=\tilde{u}_1$. The black dots denote typical values of $\rho$ and $\rho'$ that contribute to the integrals, where $\rho \leq \rho'$. On the left panel we have a commutator involving $\partial_{\tilde{u}} \tilde{\phi}(\tilde{u})$ with $\partial_{\tilde{u}_1} \tilde{\phi}(\tilde{u}_1)$, which forces $\tilde{u}=\tilde{u}_1$. Similarly, in the right panel it is $\partial_{\tilde{u}'} \tilde{\phi}(\tilde{u}')$ that appears in a commutator with $\partial_{\tilde{u}_1} \tilde{\phi}(\tilde{u}_1)$, forcing $\tilde{u}' = \tilde{u}_1$. The lower bound on the $\rho$ integral is set by the shell location.