Chronology Protection Conjecture in the Kerr–Newman black hole spacetime

In this work, we investigate the dynamics of relativistic quantum scalar fields inside the inner horizon of the 3+1 dimensional subextremal Kerr–Newman black hole, where closed timelike curves (CTCs) exist. We start by constructing the governing Klein–Gordon equation in the black hole background and present the derivation to obtain analytical exact solutions in detail. Thanks to the recent developments of the Heun-family special functions, we can express the exact Klein–Gordon’s radial solutions in terms of the Confluent Heun functions. The scalar fields’ relativistic energy quantization is then obtained from the Confluent Heun function’s polynomial condition. The complex eigenenergies with positive real part, in the region inside the inner horizon of the charged rotating black hole, are found to have a positive imaginary part, describing states that grow in time. It turns out that the revealed phenomena of instabilities follow Hawking’s prediction, known as the Chronology Protection Conjecture (CPC), i.e., fields of particles entering the aforementioned region will experience blue-shifting. In this work, it is for the first time that an exact investigation is carried out to examine Hawking’s Chronology Protection Conjecture (CPC) by investigating the exact eigensolutions of the Klein–Gordon equation in the region inside the inner horizon of a subextremal Kerr–Newman black hole.