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Temperature Fluctuations and quantum corrections near Black Hole Horizon

Anamika Avinash Pathak, Swastik Bhattacharya

Abstract

Spatially varying near-horizon fluctuations of temperature of a Schwarzschild Black Hole is considered within the Euclidean Gravity approach. We present evidence that suggests that such fluctuations in temperature are closely related with the near-horizon supertranslations of a Black Hole. This allows one to express the temperature-dependent corrections to the near-horizon part of the Euclidean gravity action or Free energy in terms of polynomial functionals of a near-horizon supertranslation for all orders. The leading order term turns out to be proportional to the near-horizon supertranslation charge. We also show that this same term results from a microscopic state counting of the near-horizon field with the constraint of near-horizon supertranslation symmetry imposed. The constructed near-horizon partition function provides a physically appealing intuitive description of the low-energy part of horizon physics as a sum over all possible near-horizon supertranslations. This suggests a dual description of near-horizon physics in terms of alternate variables. The implications of these results are briefly discussed.

Temperature Fluctuations and quantum corrections near Black Hole Horizon

Abstract

Spatially varying near-horizon fluctuations of temperature of a Schwarzschild Black Hole is considered within the Euclidean Gravity approach. We present evidence that suggests that such fluctuations in temperature are closely related with the near-horizon supertranslations of a Black Hole. This allows one to express the temperature-dependent corrections to the near-horizon part of the Euclidean gravity action or Free energy in terms of polynomial functionals of a near-horizon supertranslation for all orders. The leading order term turns out to be proportional to the near-horizon supertranslation charge. We also show that this same term results from a microscopic state counting of the near-horizon field with the constraint of near-horizon supertranslation symmetry imposed. The constructed near-horizon partition function provides a physically appealing intuitive description of the low-energy part of horizon physics as a sum over all possible near-horizon supertranslations. This suggests a dual description of near-horizon physics in terms of alternate variables. The implications of these results are briefly discussed.
Paper Structure (13 sections, 38 equations)

This paper contains 13 sections, 38 equations.

Table of Contents

  1. Introduction
  2. Conical Singularity and Schwarzschild Black hole
  3. Incorporating Temperature variations along the horizon
  4. Analysing Near-horizon Temperature Fluctuations by constructing Local Grid
  5. Imposing the diffeosymmetry $\tau\to\tau+\delta\beta(\theta,\phi)$ in the Euclidean Near-horizon region
  6. From Temperature Fluctuations to Supertranslations
  7. A look at the basic relations between null shifts and temperature fluctuations
  8. Relating the diffeo-symmetries in the near-horizon region
  9. Effective Action and Black Hole Entropy
  10. 1st order correction from microstate counting
  11. Lorentzian action with a massless shockwave and Euclidean geometry with a conical defect
  12. The near-horizon partition function
  13. Discussion