Rationalizing Unphysical Radiation in the Unruh Effect by Extending Black Hole Spacetime

TL;DR

This paper extends Schwarzschild and Kerr spacetimes conformally to include black holes with timelike singularities, demonstrating that thermal radiation observed at null infinity can be physically explained through these extensions, supporting the plausibility of the Unruh effect.

Contribution

It introduces conformal extensions of Schwarzschild and Kerr spacetimes, providing a new framework to interpret thermal radiation and the Unruh effect in black hole physics.

Findings

Thermal radiation from extended black holes can be observed at null infinity.

The conformal extension clarifies the physical origin of the Unruh effect.

Kerr spacetime also admits a conformal extension with similar thermal radiation properties.

Abstract

We demonstrate that Schwarzschild spacetime has a conformal extension and that, beyond null infinity, there is a black hole with a timelike singularity. In conformal extended spacetime, every null infinity is a killing horizon with vanishing surface gravity. When a quantized massless scalar field is taken into this spacetime and different vacuums for the field are defined, thermal radiation coming from the extended black hole could be observed. This makes sense, much like the thermal radiation coming from the white hole. The Unruh effect is therefore plausible in conformal extended Schwarzschild spacetime. It is shown that the thermal radiation coming from past null infinity in Schwarzschild spacetime, which is difficult to imagine as the result of any physical process, is the result of the reduction of the thermal radiation passing through past null infinity in conformal extended spacetime. We also present a conformal extension of Kerr spacetime for the first time. Then, by examining a quantized massless scalar field on this spacetime, we get the meaningful conclusion that there is thermal radiation coming from a different rotating black hole passing through past null infinity. Similarly, the result of the Kerr black hole is consistent with that of the Schwarzschild black hole.