Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity

Abstract

We derive Loop Quantum Gravity corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole and near the classical singularity. We show that the resulting effective equation implies defocusing of geodesics due to the appearance of repulsive terms. This prevents the formation of conjugate points, renders the singularity theorems inapplicable, and leads to the resolution of the singularity for this spacetime.

Testing loop quantum gravity from observational consequences of non-singular rotating black holes

“…Note that at this point, the metric function Ψ(y, θ) remains undetermined. By comparing the non-rotating LQGBH metric (8) and the seed metric of NJA (11), one identifies…”

“…On the other hand, LQG effective equations have been thoroughly investigated for static, spherically symmetric, and non-rotating spacetimes, resulting in quantum extensions of the Schwarzschild black hole and leading to new paradigms of singularity-free geometries (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] for an incomplete list of these models and their phenomenology, [16] for a critical review and [17,18] for signature-changing solutions). In this article, starting from a non-rotating LQGBH [1,2], we construct a rotating spacetime using the Newman-Janis-Algorithm (NJA) [19].…”

On the fate of quantum black holes

“…Works in the first category use the classical isometry between the black hole interior and the Kantowski-Sachs homogeneous space-time. This suggests a description of the black hole interior where LQC methods can be applied directly [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Although simple, this approach has several drawbacks: the isometry between the Schwarzschild interior and the Kantowski-Sachs space-time may not hold in full quantum gravity (it is known to fail for some modified gravity theories [28]); the isometry requires the presence of an outer horizon and assumes there is no inner horizon; and the standard improved dynamics scheme as applied in [11] fails near the horizon (likely due to the spatial coordinates becoming null).…”