Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Introduction to Black Hole Microscopy

Theodore A. Jacobson

TL;DR

This work analyzes the robustness of Hawking radiation to short-distance (Planck-scale) physics by linking the Hawking effect to the Unruh effect and by studying models with modified dispersion relations. The Unruh model and related non-Lorentz-invariant cutoffs show that leading Hawking flux remains thermally distributed at low frequencies, while high-frequency deviations depend on the specifics of the cutoff and horizon microphysics. The analysis highlights mode-conversion near horizon turning points as a central mechanism for particle creation and demonstrates that horizon fluctuations and cutoff implementations can induce small but quantifiable deviations. Overall, the results argue for a universal, thermally structured Hawking radiation that is mostly insensitive to ultraviolet physics, with measurable but typically suppressed corrections in realistic scenarios.

Abstract

The aim of these notes is both to review the standard understanding of the Hawking effect, and to discuss the modifications to this understanding that might be required by new physics at short distances. The fundamentals of the Unruh effect are reviewed, and then the Hawking effect is explained as a ``gravitational Unruh effect", with particular attention to the state-dependence of this picture. The order of magnitude of deviations from the thermal spectrum of Hawking radiation is estimated under various hypotheses on physics at short distances. The behavior of black hole radiation in a linear model with altered short distance physics---the Unruh model---is discussed in detail. [Based on lectures given at the First Mexican School on Gravitation and Mathematical Physics, Guanajuato, December 1994.]

Introduction to Black Hole Microscopy

TL;DR

This work analyzes the robustness of Hawking radiation to short-distance (Planck-scale) physics by linking the Hawking effect to the Unruh effect and by studying models with modified dispersion relations. The Unruh model and related non-Lorentz-invariant cutoffs show that leading Hawking flux remains thermally distributed at low frequencies, while high-frequency deviations depend on the specifics of the cutoff and horizon microphysics. The analysis highlights mode-conversion near horizon turning points as a central mechanism for particle creation and demonstrates that horizon fluctuations and cutoff implementations can induce small but quantifiable deviations. Overall, the results argue for a universal, thermally structured Hawking radiation that is mostly insensitive to ultraviolet physics, with measurable but typically suppressed corrections in realistic scenarios.

Abstract

The aim of these notes is both to review the standard understanding of the Hawking effect, and to discuss the modifications to this understanding that might be required by new physics at short distances. The fundamentals of the Unruh effect are reviewed, and then the Hawking effect is explained as a ``gravitational Unruh effect", with particular attention to the state-dependence of this picture. The order of magnitude of deviations from the thermal spectrum of Hawking radiation is estimated under various hypotheses on physics at short distances. The behavior of black hole radiation in a linear model with altered short distance physics---the Unruh model---is discussed in detail. [Based on lectures given at the First Mexican School on Gravitation and Mathematical Physics, Guanajuato, December 1994.]

Paper Structure

This paper contains 20 sections, 40 equations, 8 figures.

Table of Contents

  1. Introduction
  2. The Unruh effect
  3. Two-point function and KMS condition
  4. The vacuum state as a thermal density matrix
  5. Some references
  6. Hawking radiation
  7. Imposing a cutoff
  8. Invariant cutoff
  9. non-Lorentz-invariant cutoff
  10. Horizon fluctuations
  11. Models with a non-Lorentz-invariant cutoff
  12. Sonic black hole
  13. Unruh model
  14. Quantization
  15. Computing the particle creation rate
  16. ...and 5 more sections

Figures (8)

  • Figure :
  • Figure :
  • Figure :
  • Figure :
  • Figure :
  • ...and 3 more figures