Effects of Schwarzschild's Black Hole Singularities on Complex Scalar Field

TL;DR

This paper investigates the behavior of a complex scalar field near Schwarzschild black hole singularities, revealing unique properties such as scalar hair formation and tachyonic condensation, differing from minimal coupling predictions.

Contribution

It introduces a novel Klein-Gordon equation derived from gauge and group theories to analyze scalar fields at black hole singularities, highlighting new behaviors and implications.

Findings

Scalar field is well-behaved near singularities and reaches zero at both.

The field forms scalar hair outside the event horizon.

Interior field exhibits tachyonic behavior and condensation.

Abstract

Complex scalar fields described by a novel Klein-Gordon equation derived from gauge and group theories are considered at the Schwarzschild's black hole singularities. It is shown that the field is well-behaved in the vicinity of these singularities and that its value reaches zero at both singularities. The obtained results also demonstrate that the field forms a scalar hair that exists outside of the event horizon, and that the interior field is tachyonic and undergoes a tachyonic condensation to reach its true vacuum at the central singularity. The described field's behavior is very different from that predicted by the Klein-Gordon equation minimally coupled to gravity. Physical implications of these results for the interior structure of black holes are discussed.