The aim of the present research is the analysis of the photon motion in the regular spacetimes arising as solutions of the Einstein gravity coupled with a non-linear electrodynamics (NED). The photons no longer follow the null geodesic of the background spacetime, but the null geodesics of an effective geometry where the electromagnetic non-linearity is directly reflected in addition to the spacetime geometry. Motion of photons is compared to the motion of neutrinos that are not directly affected by the non-linearities of a non-Maxwellian electromagnetic field, and follow null geodesics of the background spacetime. We determine shadows of the regular Bardeen black holes, representing a special solution of the general relativity coupled with NED related to a magnetic charge, both for photons and neutrinos, and compare them to the shadow of the related Reissner-Nordstrom black holes. We demonstrate that the direct NED effects give clear signature of the presence of the regular black holes, on the level going up to 20% that is detectable by recent observational techniques. We also demonstrate strong influence of the NED effects on deflection angle of photons moving in the Bardeen spacetimes, and on the time delay of the motion of photons and neutrinos in vicinity of the black hole horizon.
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It is well known that a hypothetical compact object that looks like an Einsteinian (Schwarzschild or Kerr) black hole everywhere except a small region near its surface should have the ringdown profile predicted by the Einstein theory at early and intermediate times, but modified by the so-called echoes at late times. A similar phenomenon appears when one considers an Einsteinian black hole and a shell of matter placed at some distance from it, so that astrophysical estimates could be made for the allowed mass of the black hole environment. While echoes for both systems have been extensively studied recently, no such analysis has been done for a system featuring phenomena simultaneously, that is, echoes due to new physics near the surface/event horizon and echoes due to matter at some distance from the black hole. Here, following Damour and Solodukhin [Phys. Rev. D 76, 024016 (2007), 10.1103/PhysRevD.76.024016] and Cardoso et al. [Phys. Rev. Lett. 116, 171101 (2016), 10.1103/PhysRevLett.116.171101], we consider a traversable wormhole obtained by identifying two Schwarzschild metrics with the same mass M at the throat, which is near the Schwarzschild radius, and add a nonthin shell of matter at a distance. This allows us to understand how the echoes of the surface of the compact object are affected by the astrophysical environment at a distance. The straightforward calculations for the time-domain profiles of such a system support the expectations that if the echoes are observed, they should most probably be ascribed to some new physics near the event horizon rather than some "environmental" effect.
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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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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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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 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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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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An exact solution of the Lemaître-Tolman-Bondi class is investigated as a possible model of the Schwarzschild-like black hole embedded in a nonstatic dust-filled universe for the three types of spatial curvature. The solution is obtained in comoving coordinates by means of the mass function method. It is shown that the central part of space contains a Schwarzschild-like black hole. The R-T structure of the resulting spacetime is built. It is shown that the solution includes both the Schwarzschild and Friedmann solutions as its natural limits. The geodesic equations for test particles are analyzed. The particle observable velocities are found. The trajectories of the test particles are built from the point of view of both comoving and distant observers. For the distant observer, the results coincide with the Schwarzschild picture within a second-order accuracy near the symmetry center.
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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 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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