Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Nested Apparent Horizons and Quantized Separation from Intense Hawking Backreaction

Steven J. Silverman

TL;DR

The paper investigates how intense Hawking backreaction in a dynamical, spherically symmetric spacetime can temporarily generate a second exterior apparent horizon, forming nested horizons in a simple Vaidya-like model. It shows that strong outgoing null energy can reshape the Misner–Sharp mass profile to produce multiple trapping surfaces, with the outer horizon forming and then vanishing as the shell passes. Building on this, the authors propose semiclassical quantization of the horizon separation via adiabatic invariants (Bohr–Sommerfeld and action–angle formalisms), yielding a discrete area spacing $\Delta A \approx \tilde{\epsilon}\, n \, \ell_{\mathrm{P}}^2$ and a corresponding relation $r_2^2-r_1^2=2n\ell_{\mathrm{P}}^2$, thereby offering a geometric route to quantum-gravity discreteness. The work further connects these ideas to quantum-gravity programs (LQG, holography) and discusses implications for black-hole entropy, potential experimental or numerical probes, and the limitations of a purely semiclassical treatment in extreme backreaction regimes.

Abstract

When Hawking radiation from a rotating or non-rotating black hole becomes sufficiently intense, its own stress energy can no longer be treated as a perturbation on a fixed background. In this regime the outgoing flux may generate an additional, transient trapping surf ace exterior to the original event horizon. Using a simple spherically symmetric semi classical model we demonstrate that strong outgoing null energy can create nested apparent horizons, a feature reminiscent of the Penrose process but mediated by quantum back reaction. The effect is illustrated using a smooth Vaidya type mass profile, and conditions for bifurcation and merger of horizons are derived. We further propose that the separation between nested horizons may obey a discrete quantization rule analogous to the Bohr Sommerfeld condition,suggesting a geometric route toward quantum-gravity discreteness.

Nested Apparent Horizons and Quantized Separation from Intense Hawking Backreaction

TL;DR

The paper investigates how intense Hawking backreaction in a dynamical, spherically symmetric spacetime can temporarily generate a second exterior apparent horizon, forming nested horizons in a simple Vaidya-like model. It shows that strong outgoing null energy can reshape the Misner–Sharp mass profile to produce multiple trapping surfaces, with the outer horizon forming and then vanishing as the shell passes. Building on this, the authors propose semiclassical quantization of the horizon separation via adiabatic invariants (Bohr–Sommerfeld and action–angle formalisms), yielding a discrete area spacing and a corresponding relation , thereby offering a geometric route to quantum-gravity discreteness. The work further connects these ideas to quantum-gravity programs (LQG, holography) and discusses implications for black-hole entropy, potential experimental or numerical probes, and the limitations of a purely semiclassical treatment in extreme backreaction regimes.

Abstract

When Hawking radiation from a rotating or non-rotating black hole becomes sufficiently intense, its own stress energy can no longer be treated as a perturbation on a fixed background. In this regime the outgoing flux may generate an additional, transient trapping surf ace exterior to the original event horizon. Using a simple spherically symmetric semi classical model we demonstrate that strong outgoing null energy can create nested apparent horizons, a feature reminiscent of the Penrose process but mediated by quantum back reaction. The effect is illustrated using a smooth Vaidya type mass profile, and conditions for bifurcation and merger of horizons are derived. We further propose that the separation between nested horizons may obey a discrete quantization rule analogous to the Bohr Sommerfeld condition,suggesting a geometric route toward quantum-gravity discreteness.

Paper Structure

This paper contains 19 sections, 28 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Hawking Radiation Summary
  3. Backreaction and the Vaidya framework
  4. Smooth shell toy model
  5. Quantized separation hypothesis and quantum-gravity implications
  6. Bohr--Sommerfeld quantization of horizon motion
  7. Action--angle quantization for nested horizon shells
  8. Effective potential and resonant states
  9. Relation to quantum-gravity proposals
  10. Prospects
  11. Discussion of Black Hole Entropy
  12. Pair Production and Entropy Discussion
  13. Discussion
  14. Appendix: Worked example --- action--angle evaluation for the smooth $\tanh$ shell
  15. From $\oint \kappa\,dA$ to a 1D radial integral
  16. ...and 4 more sections

Figures (1)

  • Figure 1: Example of nested apparent horizons for $M_0=1$, $r_s=2.5$, $\delta=0.05$, and increasing shell energy $M_s$. The intersection of $2m(r)$ with $r$ gives the apparent horizons. For $M_s\lesssim0.2$ there is a single root; for $M_s\gtrsim0.3$ two additional roots appear, representing a transient outer horizon due to intense outgoing flux.