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On Quantization of AdS3 Gravity I: Semi-Classical Analysis

M. M. Sheikh-Jabbari, Hossein Yavartanoo

Abstract

In this work we explore ideas in quantizing AdS$_3$ Einstein gravity. We start with the most general solution to the 3d gravity theory which respects Brown-Henneaux boundary conditions. These solutions are specified by two holomorphic functions and satisfy simple superposition rule. These geometries generically have a bifurcate Killing horizon (with a noncompact bifurcation curve) which is not an event horizon and are hence not black holes. Nonetheless, there are superpositions of these geometries which have event horizon. We propose to view these geometries as "semiclassical fuzzball microstates" of BTZ black holes appearing as superposition of these geometries. The details of quantization of these semiclassical microstates will be discussed in an upcoming work.

On Quantization of AdS3 Gravity I: Semi-Classical Analysis

Abstract

In this work we explore ideas in quantizing AdS Einstein gravity. We start with the most general solution to the 3d gravity theory which respects Brown-Henneaux boundary conditions. These solutions are specified by two holomorphic functions and satisfy simple superposition rule. These geometries generically have a bifurcate Killing horizon (with a noncompact bifurcation curve) which is not an event horizon and are hence not black holes. Nonetheless, there are superpositions of these geometries which have event horizon. We propose to view these geometries as "semiclassical fuzzball microstates" of BTZ black holes appearing as superposition of these geometries. The details of quantization of these semiclassical microstates will be discussed in an upcoming work.

Paper Structure

This paper contains 25 sections, 77 equations.

Table of Contents

  1. Introduction
  2. Local and global isometries of the general geometries
  3. Local isometries, the six Killing vectors
  4. Constructing the Killing vector generators $K_a$
  5. Further analysis of global isometries of the generic geometries
  6. Horizon structure of the general geometries
  7. Killing horizons.
  8. Surface gravity.
  9. BTZ example.
  10. Is the bifurcate Killing horizon compact and simply-connected?
  11. Is the Killing horizon also an event horizon?
  12. The degenerate horizon case
  13. Concluding remarks and outlook
  14. 1. Promoting $f_\pm$ to operators $\boldsymbol{f_\pm}$
  15. 2. Boundary gravitons as "edge-states."
  16. ...and 10 more sections