Scalar instabilities inside the extremal dyonic Kerr–Sen black hole: novel exact solutions and Chronology Protection Conjecture

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 $$0\le \Omega _0&lt;2(n+1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and negative branch with $$\Omega _0&gt;2(n+1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> that grow exponentially has the ability to destroy spacetime. Remarkably, a new mass scale $$M_{p}^{2}/M$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>/</mml:mo> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> , 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.