Scalar Instabilities Inside The Extremal Dyonic Kerr-Sen Black Hole: Novel Exact Solutions and Chronology Protection Conjecture

TL;DR

This paper analyzes the stability of scalar fields inside an extremal Dyonic Kerr-Sen black hole, finding exact solutions and demonstrating that the spacetime generally remains stable and respects the Chronology Protection Conjecture, with specific conditions leading to potential spacetime destruction.

Contribution

The study provides the first exact solutions to the Klein-Gordon equation in this spacetime and explores the implications of scalar quasiresonances on spacetime stability and chronology protection.

Findings

Scalar quasiresonances are double branched with positive and negative imaginary parts.

The spacetime is stable against scalar perturbations, supporting the Chronology Protection Conjecture.

A new mass scale influences the transition between damping and growth of scalar modes.

Abstract

We investigate the stability of test scalar fields in the region inside the extremal Dyonic Kerr-Sen black hole (DKSBH) horizon, where closed timelike curves exist. We successfully find and present the novel exact solutions to the Klein-Gordon equation in the extremal DKSBH spacetime in terms of the Double Confluent Heun functions. The spacetime stability is explored by investigating the scalar's quasiresonance~(QS) frequencies obtained from polynomial condition of the Double Confluent Heun function. We found that both massive and massless scalar quasiresonances are double branched, having purely positive and negative imaginary frequencies, therefore, do not propagate, prohibiting time travel and suggesting no violation of Hawking's Chronology Protection Conjecture (CPC). However, only the positive branch with $0\leq\Omega_0<2(n+1)$ and negative branch with $\Omega_0>2(n+1)$ that grow exponentially has the ability to destroy spacetime. Remarkably, a new mass scale $M_{p}^{2}/M$, where $M$ is the black hole mass, is found to play a crucial role. The QS zeroth modes flip sign between purely damping and purely growing when the scalar mass is at this mass scale.