Paradoxes before the paradox: surface gravity and the information loss problem

TL;DR

This paper examines the surface gravity in dynamical black holes and argues that inconsistencies in its definitions challenge the standard formulation of the black hole information loss paradox.

Contribution

It highlights the discrepancies between two principal definitions of surface gravity in dynamical settings, questioning the standard assumptions of the paradox.

Findings

Two definitions of surface gravity do not agree dynamically.

Standard formulation of the information loss paradox may be inconsistent.

Dynamical black hole models challenge traditional Hawking radiation assumptions.

Abstract

The information loss paradox is widely regarded as one of the biggest open problems in theoretical physics. Several classical and quantum features must be present to enable its formulation. First, an event horizon is needed to justify the objective status of tracing out degrees of freedom inside the black hole. Second, evaporation must be completed (or nearly completed) in finite time according to a distant observer, and thus the formation of the black hole should also occur in finite time. In spherical symmetry these requirements constrain the possible metrics strongly enough to obtain a unique black hole formation scenario and match their parameters with the semiclassical results. However, the two principal generalizations of surface gravity, the quantity that determines the Hawking temperature, do not agree with each other on the dynamical background. Neither can correspond to the emission of nearly-thermal radiation. We infer from this that the information loss problem cannot be consistently posed in its standard form.