Research on the Tunneling Radiation of Bosons from the Kerr-Sen-like Black Hole by Einstein-Bumblebee Gravitational Theory

Abstract

Lorentz-breaking theory not only affects the curved space-time background, but also modifies the dynamic equations of bosons and fermions in curved space-time to some extent. Therefore, we need to make appropriate corrections for the quantum tunneling radiation of bosons and fermions in different black hole spacetimes. New expressions of black hole Hawking temperature and other physical quantities modified by Lorentz-breaking theory and their physical meanings are obtained. In this paper, according to the Kerr-Sen-like (KSL) black hole spacetime metric obtained from Einstein-Bumblebee gravitational theory, by introducing the correction term of the aether-like field vector into the scalar field action and the d'Alembert operator in curved spacetime, and applying the variational principle in curved spacetime, the Lorentzbreaking correction term in the spacetime metric and the new form of the dynamic equation of the bosons with zero spin in KSL spacetime are studied. By correctly selecting the aether-like field vector corresponding to the KSL spacetime metric and solving the modified bosons dynamic equation, the modified quantum tunneling rate is obtained. On this basis, the Hawking temperature and Bekenstein- Hawking entropy of the black hole with Lorentz-breaking correction term are studied. The effects of Lorentz-breaking theory on the distribution of positive and negative energy levels of bosons and the maximum crossing of energy levels are also studied, and then the conditions of quantum non-thermal radiation in the black hole space-time is studied. At the end of this paper, the physical significance of a series of results obtained in this paper is discussed in depth. The results show that the modified form of the bosons dynamic equation in curved spacetime, taking into account Lorentz-breaking theory, is shown in equation (26) and equation (27). The new expressions of the quantum tunneling rate, Bekenstein-Hawking entropy, Hawking temperature and quantum non-thermal radiation energy range of KSL black hole are obtained by applying equation (26) to KSL black hole space-time. These results are useful for studying the quantum tunneling radiation characteristics of black holes. It should be noted that the above research results are obtained under the WKB theory and the semiclassical case. If the effects of different powers of Planck are to be considered, the above research methods and related results need to be used for further modified research by using beyond the semi-classical theory.