(b,v)-type variables for black to white hole transitions in effective loop quantum gravity

TL;DR

This paper introduces a simplified, physically viable model for black to white hole transitions in loop quantum gravity using adapted variables in the $$-scheme, enabling straightforward quantization and broad initial condition applicability.

Contribution

It constructs new variables for black-white hole transition models in loop quantum gravity, simplifying the Hamiltonian and supporting symmetric transitions with broad initial conditions.

Findings

Model uses $$-scheme with sensible physics for various initial conditions.

Hamiltonian is very simple, at most quadratic, facilitating quantization.

Model favors symmetric black-white hole transitions.

Abstract

Quantum gravity effects in effective models of loop quantum gravity, such as loop quantum cosmology, are encoded in the choice of so-called polymerisation schemes. Physical viability of the models, such as an onset of quantum effects at curvature scales near the Planck curvature, severely restrict the possible choices. An alternative point of view on the choice of polymerisation scheme is to choose adapted variables so that the scheme is the simplest possible one, known as $\mu_0$-scheme in loop quantum cosmology. There, physically viable models with $\mu_0$-scheme polymerise the Hubble rate $b$ that is directly related to the Ricci scalar and the matter energy density on-shell. Consequently, the onset of quantum effects depends precisely on those parameters. In this letter, we construct similar variables for black to white hole transitions modelled using the description of the Schwarzschild interior as a Kantowski-Sachs cosmology. The resulting model uses the $\mu_0$-scheme and features sensible physics for a broad range of initial conditions (= choices of black and white hole masses) and favours symmetric transitions upon invoking additional qualitative arguments. The resulting Hamiltonian is very simple and at most quadratic in its arguments, allowing for a straight forward quantisation.