Evolution of Massive Scalar Fields in the Spacetime of a Tense Brane Black Hole

TL;DR

This paper investigates how massive scalar fields decay in the spacetime of a higher-dimensional black hole with a tense brane, revealing that increased brane tension accelerates decay, supported by numerical analysis.

Contribution

It provides a detailed analysis of scalar field decay in tense brane black hole spacetimes, including numerical confirmation for five- and six-dimensional cases, highlighting the effect of brane tension.

Findings

Scalar fields decay via oscillatory inverse power-law behavior.

Higher brane tension leads to faster decay of scalar fields.

Numerical results confirm analytical predictions.

Abstract

In the spacetime of a $d$-dimensional static tense brane black hole we elaborate the mechanism by which massive scalar fields decay. The metric of a six-dimensional black hole pierced by a topological defect is especially interesting. It corresponds to a black hole residing on a tensional 3-brane embedded in a six-dimensional spacetime, and this solution has gained importance due to the planned accelerator experiments. It happened that the intermediate asymptotic behaviour of the fields in question was determined by an oscillatory inverse power-law. We confirm our investigations by numerical calculations for five- and six-dimensional cases. It turned out that the greater the brane tension is, the faster massive scalar fields decay in the considered spacetimes.