Characteristic Time Scales for the Geometry Transition of a Black Hole to a White Hole from Spinfoams

TL;DR

This paper investigates the quantum transition time from black holes to white holes using Lorentzian Loop Quantum Gravity, confirming linear mass scaling and clarifying the distinction between characteristic and lifetime time scales.

Contribution

It computes and clarifies the characteristic time scales for black hole to white hole transition within Loop Quantum Gravity, refining previous results and interpretations.

Findings

Characteristic time scale scales linearly with mass

Distinction between transition time and lifetime clarified

Lifetime scales exponentially with mass

Abstract

Quantum fluctuations of the metric provide a decay mechanism for black holes, through a transition to a white hole geometry. Old perplexing results by Ambrus and H\'aj\'i\v{c}ek and more recent results by Barcel\'o, Carballo-Rubio and Garay, indicate a characteristic time scale of this process that scales linearly with the mass of the collapsed object. We compute the characteristic time scales involved in the quantum process using Lorentzian Loop Quantum Gravity amplitudes, corroborating these results but reinterpreting and clarifying their physical meaning. We first review and streamline the classical set up, and distinguish and discuss the different time scales involved. We conclude that the aforementioned results concern a time scale that is different from the lifetime, the latter being the much longer time related to the probability of the process to take place. We recover the exponential scaling of the lifetime in the mass, a result expected from na\"ive semiclassical arguments for the probability of a tunneling phenomenon to occur.