# Perspectives on the dynamics in a loop quantum gravity effective description of black hole interiors

## TL;DR

This paper explores the relationship between loop quantum gravity effective models of black hole interiors and full quantum gravity, proposing new Hamiltonians and analyzing their dynamical implications for singularity resolution.

## Contribution

It introduces two novel effective Hamiltonians for Kantowski-Sachs spacetime derived from loop quantum gravity principles, bridging the gap between minisuperspace models and full theory.

## Key findings

- New effective Hamiltonians derived from quantum gravity principles
- Comparison shows differences with classical and previous models
- Insights into the dynamics and potential singularity resolution

## Abstract

In the loop quantum gravity context, there have been numerous proposals to quantize the reduced phase space of a black hole, and develop a classical effective description for its interior which eventually resolves the singularity. However, little progress has been made towards understanding the relation between such quantum/effective minisuperspace models and what would be the spherically symmetric sector of loop quantum gravity. In particular, it is not clear whether one can extract the phenomenological predictions obtained in minisuperspace models, such as the singularity resolution and the spacetime continuation beyond the singularity, based on results in full loop quantum gravity. In this paper, we present an attempt in this direction in the context of Kantowski-Sachs spacetime, through the proposal of two new effective Hamiltonians for the reduced classical model. The first is derived using Thiemann classical identities for the regularized expressions, while the second is obtained as a first approximation of the expectation value of a Hamiltonian operator in loop quantum gravity in a semi-classical state peaked on the Kantowski-Sachs initial data. We then proceed with a detailed analysis of the dynamics they generate and compare them with the Hamiltonian derived in General Relativity and the common effective Hamiltonian proposed in earlier literature.