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We investigate the late-time tail of the retarded Green function for the dynamics of a linear field perturbation of Kerr spacetime. We develop an analytical formalism for obtaining the late-time tail up to arbitrary order for general integer spin of the field. We then apply this formalism to obtain the details of the first five orders in the late-time tail of the Green function for the case of a scalar field: to leading order we recover the known power law tail $t^{-2ell-3}$, and at third order we obtain a logarithmic correction, $t^{-2ell-5}ln t$, where $ell$ is the field multipole.
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We present an analysis of the behaviour at late-times of linear field perturbations of a Schwarzschild black hole space-time. In particular, we give explicit analytic expressions for the field perturbations (for a specific multipole) of general spin up to the first four orders at late times. These expressions are valid at arbitrary radius and include, apart from the well-known power-law tail decay at leading order ($sim t^{-2ell-3}$), a new logarithmic behaviour at third leading order ($sim t^{-2ell-5}ln t$). We obtain these late-time results by developing the so-called MST formalism and by expanding the various MST Fourier-mode quantities for small frequency. While we give explicit expansions up to the first four leading orders (for small-frequency for the Fourier modes, for late-time for the field perturbation), we give a prescription for obtaining expressions to arbitrary order within a `perturbative regime.
We consider the entanglement dynamics between two-level atoms in a rotating black hole background. In our model the two-atom system is envisaged as an open system coupled with a massless scalar field prepared in one of the physical vacuum states of interest. We employ the quantum master equation in the Born-Markov approximation in order to describe the time evolution of the atomic subsystem. We investigate two different states of motion for the atoms, namely static atoms and also stationary atoms with zero angular momentum. The purpose of this work is to expound the impact on the creation of entanglement coming from the combined action of the different physical processes underlying the Hawking effect and the Unruh-Starobinskii effect. We demonstrate that, in the scenario of rotating black holes, the degree of quantum entanglement is significantly modified due to the phenomenon of superradiance in comparison with the analogous cases in a Schwarzschild spacetime. In the perspective of a zero angular momentum observer (ZAMO), one is allowed to probe entanglement dynamics inside the ergosphere, since static observers cannot exist within such a region. On the other hand, the presence of superradiant modes could be a source for violation of complete positivity. This is verified when the quantum field is prepared in the Frolov-Thorne vacuum state. In this exceptional situation, we raise the possibility that the loss of complete positivity is due to the breakdown of the Markovian approximation, which means that any arbitrary physically admissible initial state of the two atoms would not be capable to hold, with time evolution, its interpretation as a physical state inasmuch as negative probabilities are generated by the dynamical map.
We consider radiative processes of an atom in a rotating black-hole background. We assume the atom, represented by a hypothetical two-level system, is coupled via a monopole interaction with a massless quantum scalar field prepared in each one of the usual physical vacuum states of interest. We constrain ourselves to two different states of motion for the atom, namely a static situation in which the atom is placed at a fixed radial distance, and also the case in which it has a stationary motion but with zero angular momentum. We study the structure of the rate of variation of the atomic energy. The intention is to clarify in a quantitative way the effect of the distinguished contributions of vacuum fluctuations and radiation reaction on spontaneous excitation and on spontaneous emission of atoms. In particular, we are interested in the comprehension of the combined action of the different physical processes underlying the Hawking effect in the scenario of rotating black holes as well as the Unruh-Starobinskii effect. We demonstrate that, in the case of static atoms, spontaneous excitation is also connected with the Unruh-Starobinskii effect, but only in the case of the quantum field prepared in the Frolov-Thorne vacuum state. In addition, we show that, in the ZAMOs perspective, the Boulware vacuum state contains an outward flux of particles as a consequence of the black-hole superradiance. The possible relevance of the findings in the present work is discussed.
Sorce and Wald proposed a new version of gedanken experiments to examine the weak cosmic censorship conjecture (WCCC) in Kerr-Newmann black holes. However, their discussion only includes the second-order approximation of perturbation and there exists an optimal condition such that the validity of the WCCC is determined by the higher-order approximations. Therefore, in this paper, we extended their discussions into the high-order approximations to study the WCCC in a nearly extremal Kerr black hole. After assuming that the spacetime satisfies the stability condition and the perturbation matter fields satisfy the null energy condition, based on the Noether charge method by Iyer and Wald, we completely calculate the first four order perturbation inequalities and discuss the corresponding gedanken experiment to overspin the Kerr black hole. As a result, we find that the nearly extremal Kerr black holes cannot be destroyed under the fourth-order approximation of perturbation. Then, by using the mathematical induction, we strictly prove the $n$th order perturbation inequality when the first $(n-1)$ order perturbation inequalities are saturated. Using these results, we discuss the first $100$ order approximation of the gedanken experiments and find that the WCCC in Kerr black hole is valid under the higher-order approximation of perturbation. Our investigation implies that the WCCC might be strictly satisfied in Kerr black holes under the perturbation level.
By introducing a specific etheric-like vector in the Dirac equation with Lorentz Invariance Violation (LIV) in the curved spacetime, an improved method for quantum tunneling radiation of fermions is proposed. As an example, we apply this new method to a charged axisymmetric Kerr-Newman black hole. Firstly, considering LIV theory, we derive a modified dynamical equation of fermion with spin 1/2 in the Kerr-Newman black hole spacetime. Then we solve the equation and find the increase or decrease of black holes Hawking temperature and entropy are related to constants $a$ and $c$ of the Dirac equation with LIV in the curved spacetime. As $c$ is positive, the new Hawking temperature is about $ frac{sqrt{1+2a+2cmk_r^2}}{sqrt{1+2a}}$ times higher than that without modification, but the entropy will decrease. We also make a brief discussion for the case of high spin fermions.
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