We discuss the effects of electric charging on the equilibrium
configurations of magnetized, rotating fluid tori around black holes of
different mass. In the context of gaseous/dusty tori in galactic nuclei,
the central black hole dominates the gravitational field and it remains
electrically neutral, while the surrounding material acquires some
electric charge and exhibits non-negligible self-gravitational effect on
the torus structure. The structure of the torus is influenced by the
balance between the gravitational and electromagnetic forces. A cusp may
develop even in Newtonian tori due to the charge distribution.
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We study in the weak field limit the gravitational lensing by spherically symmetric compact object immersed in an asymptotically uniform magnetic field in the presence of plasma and our approach is based on the medium modified Hamiltonian one. We show that the magnetized plasma in the environment of compact object may lead to split of the Einstein cross, creating additional lensed components. Finally we calculate magnification and time delay related to the individual images.
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In this contribution, we summarize our results concerning the
observational constraints on the electric charge associated with the
Galactic centre black hole - Sgr A*. According to the no-hair theorem,
every astrophysical black hole, including supermassive black holes, is
characterized by at most three classical, externally observable
parameters - mass, spin, and the electric charge. While the mass and the
spin have routinely been measured by several methods, the electric
charge has usually been neglected, based on the arguments of efficient
discharge in astrophysical plasmas. From a theoretical point of view,
the black hole can attain charge due to the mass imbalance between
protons and electrons in fully ionized plasmas, which yields about $sim
10^8,{rm C}$ for Sgr A*. The second, induction mechanism concerns
rotating Kerr black holes embedded in an external magnetic field, which
leads to electric field generation due to the twisting of magnetic field
lines. This electric field can be associated with the induced Wald
charge, for which we calculate the upper limit of $sim 10^{15},{rm
C}$ for Sgr A*. Although the maximum theoretical limit of $sim
10^{15},{rm C}$ is still 12 orders of magnitude smaller than the
extremal charge of Sgr A*, we analyse a few astrophysical consequences
of having a black hole with a small charge in the Galactic centre. Two
most prominent ones are the effect on the X-ray bremsstrahlung profile
and the effect on the position of the innermost stable circular orbit.
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Here we show that the phenomenon of arbitrarily long-lived quasinormal modes (called quasiresonances) of a massive scalar field in the vicinity of a black hole is not an artifact of the test field approximation, but takes place also when the (derivative) coupling of a scalar field with the Einstein tensor is taken into consideration. We observe that at large coupling and high multipole numbers, the growing modes appear in the spectrum, which are responsible for the eikonal instability of the field. For small coupling, when the configuration is stable, there appear the purely imaginary quasinormal modes which are nonperturbative in the coupling constant. At the sufficiently small coupling the nonminimal scalar field is stable and the asymptotic late-time tails are not affected by the coupling term. The accurate calculations of quasinormal frequencies for a massive scalar field with the derivative coupling in the Reissner-Nordström black-hole background are performed with the help of the Frobenius method, time-domain integration and WKB expansion.
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We investigate how a spherically symmetric fluid modifies the Schwarzschild vacuum solution when there is no exchange of energy-momentum between the fluid and the central source of the Schwarzschild metric. This system is described by means of the gravitational decoupling realised via the minimal geometric deformation approach, which allows us to prove that the fluid must be anisotropic. Several cases are then explicitly shown.
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For the Kerr naked singularity (KNS) spacetimes, we study properties of spherical photon orbits (SPOs) confined to constant Boyer-Lindquist radius r. Some new features of the SPOs are found, having no counterparts in the Kerr black hole (KBH) spacetimes, especially stable orbits that could be pure prograde/retrograde, or with turning point in the azimuthal direction. At r>1 (r<1) the covariant photon energy E> 0 (E< 0), at r=1 there is E= 0. All unstable orbits must have E> 0. It is shown that the polar SPOs can exist only in the spacetimes with dimensionless spin a < 1.7996. Existence of closed SPOs with vanishing total change of the azimuth is demonstrated. Classification of the KNS and KBH spacetimes in dependence on their dimensionless spin a is proposed, considering the properties of the SPOs. For selected types of the KNS spacetimes, typical SPOs are constructed, including the closed paths. It is shown that the stable SPOs intersect the equatorial plane in a region of stable circular orbits of test particles, depending on the spin a. Relevance of this intersection for the Keplerian accretion discs is outlined and observational effects are estimated.
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We investigate how a spherically symmetric scalar field can modify the Schwarzschild vacuum solution when there is no exchange of energy-momentum between the scalar field and the central source of the Schwarzschild metric. This system is described by means of the gravitational decoupling by Minimal Geometric Deformation (MGD-decoupling), which allows us to show that, under the MGD paradigm, the Schwarzschild solution is modified in such a way that a naked singularity appears.
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The axial electromagnetic (EM) perturbations of the black hole (BH) solutions in general relativity coupled to nonlinear electrodynamics (NED) were studied for both electrically and magnetically charged BHs, assuming that the EM perturbations do not alter the spacetime geometry in our preceding paper [Phys. Rev. D 97, 084058 (2018), 10.1103/PhysRevD.97.084058]. Here, as a continuation of that work, the formalism for the polar EM perturbations of the BHs in general relativity coupled to the NED is presented. We show that the quasinormal modes (QNMs) spectra of polar EM perturbations of the electrically and magnetically charged BHs in the NED are not isospectral, contrary to the case of the standard Reissner-Nordström BHs in the classical linear electrodynamics. It is shown by the detailed study of QNMs properties in the eikonal approximation that the EM perturbations can be a powerful tool to confirm that in the NED light ray does not follow the null geodesics of the spacetime. By specifying the NED model and comparing axial and polar EM perturbations of the electrically and magnetically charged BHs, it is shown that QNM spectra of the axial EM perturbations of magnetically (electrically) charged BH and polar EM perturbations of the electrically (magnetically) charged BH are isospectral, i.e., ωmagax≈ωelpol (ωmagpol≈ωelax).
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The exact axisymmetric and static solution of the Einstein equations coupled to the axisymmetric and static gravitating scalar (or phantom) field is presented. The spacetimes modified by the scalar field are explicitly given for the so-called γ -metric and the Erez-Rosen metric with quadrupole moment q , and the influence of the additional deformation parameters γ* and q* generated by the scalar field is studied. It is shown that the null energy condition is satisfied for the phantom field, but it is not satisfied for the standard scalar field. The test particle motion in both the modified γ -metric and the Erez-Rosen quadrupole metric is studied; the circular geodesics are determined, and near-circular trajectories are explicitly presented for characteristic values of the spacetime parameters. It is also demonstrated that the parameters γ* and q* have no influence on the test particle motion in the equatorial plane.
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We investigate how a spherically symmetric scalar field can modify the Schwarzschild vacuum solution when there is no exchange of energy-momentum between the scalar field and the central source of the Schwarzschild metric. This system is described by means of the gravitational decoupling by Minimal Geometric Deformation (MGD-decoupling), which allows us to show that, under the MGD paradigm, the Schwarzschild solution is modified in such a way that a naked singularity appears.
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