Spin fluctuations and black hole singularities: the onset of quantum gravity is spacelike

Hal M Haggard,Eugenio Bianchi

doi:10.1088/1367-2630/aae71d

Hal M Haggard, Eugenio Bianchi

Open Access

https://doi.org/10.1088/1367-2630/aae71d

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Abstract

Due to quantum fluctuations, a black hole of mass M represents an average over an ensemble of black hole geometries with angular momentum. This observation is apparently at odds with the fact that the curvature singularity inside a rotating black hole is timelike, while the one inside a non-rotating black hole is spacelike. Is the average of timelike singularities really spacelike? We use the Bekenstein–Hawking entropy formula to introduce a microcanonical ensemble for spin fluctuations and show that the onset of quantum gravity is always spacelike. We discuss the impact of this result on singularity resolution in quantum gravity and hint at the possibility of an observational test.

Highlights

THE PUZZLEIn the quantum gravitational treatment of a spherically symmetric black hole a puzzle arises
The analysis of spin fluctuations of a quantum Schwarzschild black holes provides a new probe of the spacelike nature of the onset of quantum gravity
We discuss the relation of our results to previous investigations of the onset of quantum gravity inside black holes and elaborate on the role played by the spin ensemble

Summary

INTRODUCTION

In the quantum gravitational treatment of a spherically symmetric black hole a puzzle arises. The symmetric Schwarzschild black hole has a singularity at its core where the curvature diverges and general relativity breaks down This singularity is sometimes described as a moment of time, or as the end of spacetime, because all observers that enter the black hole horizon reach it in a finite time no matter where or how they enter. (i) that quantum black holes fluctuate according to a probability distribution determined by the Bekenstein-Hawking entropy, and (ii) that Planckian values for any curvature invariant lead to quantum gravity. These two assumptions are compatible with all current approaches to quantum gravity. We describe in more detail the two assumptions, offer several elaborations on them, and discuss their consequences

BEKENSTEIN-HAWKING ENTROPY AND THE BLACK-HOLE SPIN ENSEMBLE

THE ONSET OF QUANTUM GRAVITY

DISCUSSION