Spherically symmetric Einstein-Maxwell theory and loop quantum gravity corrections

TL;DR

This paper investigates how loop quantum gravity corrections, specifically inverse triad and holonomy effects, modify the properties of Reissner-Nordström black holes, revealing phenomena like multiple horizons, mass thresholds, and signature change.

Contribution

It analyzes the impact of inverse triad and holonomy corrections on black hole solutions, highlighting new features such as horizon structure changes and covariance issues within loop quantum gravity.

Findings

Inverse triad corrections can produce three horizons and a mass threshold.

Holonomy corrections prevent static solutions and suggest signature change.

Quantum effects can renormalize mass, charge, or wave function, but not Newton's constant.

Abstract

Effects of inverse triad corrections and (point) holonomy corrections, occuring in loop quantum gravity, are considered on the properties of Reissner-Nordstr\"om black holes. The version of inverse triad corrections with unmodified constraint algebra reveals the possibility of occurrence of three horizons (over a finite range of mass) and also shows a mass threshold beyond which the inner horizon disappears. For the version with modified constraint algebra, coordinate transformations are no longer a good symmetry. The covariance property of spacetime is regained by using a \emph{quantum} notion of mapping from phase space to spacetime. The resulting quantum effects in both versions of these corrections can be associated with renormalization of either mass, charge or wave function. In neither of the versions, Newton's constant is renormalized. (Point) Holonomy corrections are shown to preclude the undeformed version of constraint algebra as also a static solution, though time-independent solutions exist. A possible reason for difficulty in constructing a covariant metric for these corrections is highlighted. Furthermore, the deformed algebra with holonomy corrections is shown to imply signature change.