Across-Horizon Propagation and Infinite Time-Dilation: An Independent Approach to Hawking Radiation

TL;DR

This paper explores how infinite time-dilation at the Schwarzschild black hole horizon leads to Hawking radiation, linking the propagator's properties to the emission process and emphasizing the role of causal structure and energy conservation.

Contribution

It provides an explicit connection between the scalar propagator and Hawking radiation, demonstrating the effect of time-dilation and energy constraints in a unified framework.

Findings

Hawking radiation arises from infinite time-dilation effects.

Energy conservation modifies the thermal spectrum of emitted particles.

The approach aligns with semi-classical results of Parikh and Wilczek.

Abstract

The conformal scalar propagator as an explicit function of the Schwarzschild black-hole space-time has been established in the preceding three projects. The present project examines the precise relation which that propagator has to the amplitude the Schwarzschild black hole emit a scalar particle in a particular mode of positive energy. It is thereby established that the effect of infinite time-dilation on the event horizon results in both, the thermal radiation in the background of a static exterior space-time geometry and the detraction from thermality if energy-conservation is properly imposed as a constraint on scalar propagation. The derivation of the latter signifies an equivalent approach to the result of Parikh and Wilczek from the semi-classical perspective of the distant observer. From that perspective for that matter, Hawking radiation emerges in both contexts as the exclusive consequence of infinite time-dilation on the event horizon. These results are consistent with Hawking radiation as the exclusive consequence of the causal structure of the Schwarzschild black-hole space-time both, in a static exterior geometry and in such dynamical exterior geometry as energy-conservation signifies. The extension of the thermal case to other spin-fields and black-hole geometries is discussed.