Abstract
In this paper we discuss some mathematical aspects of the horizon wave-function formalism, also known in the literature as horizon quantum mechanics. In particular, first we review the structure of both the global and local formalism for static spherically symmetric sources. Then, we present an extension of the global analysis for rotating black holes and we also point out some technical diffculties that arise while attempting the local analysis for non-spherically symmetric sources.
Highlights
Black hole physics, in the classical framework, is known to have an extremely fascinating and elegant mathematical formulation in terms of Lorentzian manifold
In this paper we discuss some mathematical aspects of the horizon wave-function formalism, known in the literature as horizon quantum mechanics
We present an extension of the global analysis for rotating black holes and we point out some technical difficulties that arise while attempting the local analysis for non-spherically symmetric sources
Summary
In the classical framework, is known to have an extremely fascinating and elegant mathematical formulation in terms of Lorentzian manifold Such a purely classical description leads to some major physical issues such as the appearance of curvature singularities, which is one of the main feature of black holes in general relativity [1, 2]. A first attempt at introducing some quantum mechanical effects in the context of Einstein’s gravity was first proposed by Hawking [3], whose pioneering lead to the so called semi-classical picture of gravity The latter basically consist in regarding black hole spacetimes as purely classical (i.e. geometrical) objects on which one can study the dynamics of some quantum fields. The key idea is to consider the source for the black hole spacetime to be a quantum mechanical object from which we wish to infer what are the effects on the behaviour of the horizon due to the quantum nature of the source
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