The spectrum of electromagnetic jets from Kerr black holes and naked singularities in the Teukolsky perturbation theory

Abstract

We give a new theoretical basis for examination of the presence of the Kerr black hole (KBH) or the Kerr naked singularity (KNS) in the central engine of different astrophysical objects around which astrophysical jets are typically formed: X-ray binary systems, gamma ray bursts (GRBs), active galactic nuclei (AGN), etc.Our method is based on the study of the exact solutions of the Teukolsky master equation for electromagnetic perturbations of the Kerr metric. By imposing original boundary conditions on the solutions so that they describe a collimated electromagnetic outflow, we obtain the spectra of possible primary jets of radiation, introduced here for the first time. The theoretical spectra of primary electromagnetic jets are calculated numerically.Our main result is a detailed description of the qualitative change of the behavior of primary electromagnetic jet frequencies under the transition from the KBH to the KNS, considered here as a bifurcation of the Kerr metric. We show that quite surprisingly the novel spectra describe linearly stable primary electromagnetic jets from both the KBH and the KNS. Numerical investigation of the dependence of these primary jet spectra on the rotation of the Kerr metric is presented and discussed.

Application of the confluent Heun functions for finding the quasinormal modes of nonrotating black holes

“…The RWE, the Zerilli equation and TRE, however, can be solved analytically in terms of confluent Heun functions, as done for the first time in [16][17][18][19]. Imposing the boundary conditions on those solutions directly (see [13,17]) one obtains a system of spectral equations (1) and (2) featuring the confluent Heun functions which can be solved numerically.…”

“…For example, by comparing the theoretically obtained gravitational QNMs with the frequencies of the gravitational waves, one can confirm or refute the nature of the central engines of many astrophysical objects, since those modes differ for the different types of objects -black holes, superspinars (naked singularities), neutron stars, black hole mimickers etc. [8][9][10][11][12][13].…”

“…The choice of the local solution in terms of the Heun function takes into account the boundary condition on the horizon. Then, it remains to impose the following boundary condition on the space infinity (for details see [13,16]):…”

“…For example, by comparing the theoretically obtained gravitational QNMs with the frequencies of the gravitational waves, one can confirm or refute the nature of the central engines of many astrophysical objects, since those modes differ for the different types of objects -black holes, superspinars (naked singularities), neutron stars, black hole mimickers etc. [8][9][10][11][12][13].To find the QNMs, one needs to solve the second-order linear differential equations describing the linearized perturbations of the metric: the Regge-Wheeler equation (RWE) and the Zerilli equation for the Schwarzschild metric or the Teukolsky radial equation (TRE) for the Kerr metric and to impose the appropriate boundary conditions -the so-called black hole boundary conditions (waves going simultaneously into the horizon and into infinity) [1,3]. Additionally, one requires a regularity condition for the angular part of the solutions.…”

“…The RWE, the Zerilli equation and TRE, however, can be solved analytically in terms of confluent Heun functions, as done for the first time in [16][17][18][19]. Imposing the boundary conditions on those solutions directly (see [13,17]) one obtains a system of spectral equations (1) and (2) featuring the confluent Heun functions which can be solved numerically.In this article, for the first time we present finding l and ω directly in the case for gravitational perturbation s = −2 in a Schwarzschild metric, i.e. we solve the RWE and TRE analytically in terms of confluent Heun functions and we use a newly developed method (the two-dimensional generalization of the Müller method described in the internal technical report [20]) to solve the system of two transcendental equations with two complex variables.…”