Revisiting chronology protection conjecture in the Dyonic Kerr–Sen black hole spacetime

Abstract The chronology protection conjecture (CPC) was first introduced by Hawking after his semi-classical investigation of the behaviour of a spacetime with closed timelike curves (CTCs) in response to scalar perturbations. It is argued that there would be instabilities leading to amplification of the perturbation and finally causing collapse of the region with CTCs. In this work, we investigate the CPC by exactly solving the Klein–Gordon equation in the region inside the inner horizon of the non-extremal Dyonic Kerr–Sen (DKS) black hole, where closed timelike curves exist. Successfully find the exact radial solution, we apply the polynomial condition that turns into the rule of energy quantization. Among the quasi-resonance modes, only certain modes satisfy the boundary conditions of quasinormal modes (QNMs). QNMs in the region inside the inner horizon of the rotating black hole with nonzero energy have only positive imaginary parts which describe states that grow in time. The exponentially growing modes will backreact and deform the spacetime region where CTC exists, hence the CPC is proven to be valid in the non-extremal Dyonic Kerr–Sen black hole spacetime. Since the Dyonic Kerr–Sen black hole is the most general axisymmetric black hole solution of the string inspired Einstein–Maxwell-dilaton-axion (EMDA) theory, the semiclassical proof in this work is also valid for all simpler rotating black holes of the EMDA theory. The structure of the Dyonic KS spacetime distinctive from the Kerr–Newman counterpart is also explored.