Unsettling Physics in the Quantum-Corrected Schwarzschild Black Hole

Valerio Faraoni,Andrea Giusti

doi:10.3390/sym12081264

Abstract

We study a quantum-corrected Schwarzschild black hole proposed recently in Loop Quantum Gravity. Prompted by the fact that corrections to the innermost stable circular orbit of Schwarzschild diverge, we investigate time-like and null radial geodesics. Massive particles moving radially outwards are confined, while photons make it to infinity with infinite redshift. This unsettling physics, which deviates radically from both Schwarzschild (near the horizon) and Minkowski (at infinity) is due to repulsion by the negative quantum energy density that makes the quasilocal mass vanish as one approaches spatial infinity.

Highlights

Einstein’s theory of gravity is plagued by singularities, which occur generically if the matter fields satisfy reasonable energy conditions [1]
Loop Quantum Gravity and Loop Quantum Cosmology propose possible solutions in which quantum geometry avoids the classical singularities by making the curvature invariants finite and effectively discretizing spacetime
A quantum-corrected black hole which deviates from the Schwarzschild solution of general relativity was proposed recently in Refs. [16,17,18], with the explicit purpose of providing a singularity-free black hole which is free of problems induced by large quantum corrections in the low-curvature regions. In this solution, which corrects the prototypical black hole, i.e., the Schwarzschild geometry, loop corrections to the Schwarzschild geometry are quantified by a small dimensionless parameter e, which is mass-dependent

Summary

Introduction

Einstein’s theory of gravity is plagued by singularities, which occur generically if the matter fields satisfy reasonable energy conditions [1]. [16,17,18], with the explicit purpose of providing a singularity-free black hole which is free of problems induced by large quantum corrections in the low-curvature regions In this solution, which corrects the prototypical black hole, i.e., the Schwarzschild geometry, loop corrections to the Schwarzschild geometry are quantified by a small dimensionless parameter e, which is mass-dependent. We derive the pseudo-Newtonian potential associated with the quantum-corrected black hole (4) and we show that the quantum correction to the Schwarzschild ISCO diverges This fact prompts us to investigate radial time-like and null geodesics, to find that massive particles are confined by the negative quantum energy density and photons making it to infinity are infinitely redshifted.

Pseudo-Newtonian Potential for the Quantum-Corrected Black Hole

Conclusions