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

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.

Figures (2)

• Figure 1: The normalized potential $V (r_o, \Phi) / \Omega^2$ is plotted as a function of the outside field $\Phi$ for several fixed values of $r_o > R_S$.
• Figure 2: The normalized potential $V (r, \Phi) / \Omega^2$ is plotted as a function of the inside field $\Phi$ for several fixed values of $r > R_S$.