Three well-known exact regular solutions of general relativity coupled
to nonlinear electrodynamics (NED), namely the Maxwellian, Bardeen, and
Hayward regular spacetimes, which can describe either a regular black
hole or a geometry without horizons, have been considered. Relaxation
times for the scalar, electromagnetic (EM) and gravitational
perturbations of black holes and no-horizon spacetimes have been
estimated in comparison with the ones of the Schwarzschild and Reissner-
Nordström spacetimes. It has been shown that the considered geometries
in general relativity coupled to the NED have never-vanishing circular
photon orbits, and on account of this fact, these spacetimes always
oscillate the EM perturbations with quasinormal frequencies. Moreover,
we have shown that the EM perturbations in the eikonal regime can be a
powerful tool to confirm (i) that the light rays do not follow null
geodesics in the NED by the relaxation rates and (ii) if the underlying
solution has a correct weak field limit to the Maxwell electrodynamics
by the angular velocity of the circular photon orbit.
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A recent study of the X-ray source XMMUJ134736.6+173403 has revealed a
strong quasi-periodic modulation in the X-ray flux. The observation of
two quasiperiodic oscillations (QPOs) that occur on a daily timescale
and exhibit a 3:1 frequency ratio strongly supports the evidence for the
presence of an active galactic nucleus black hole (AGN BH). Assuming an
orbital origin of QPOs, we calculated the upper and lower limit on AGN
BH mass M and found M ≈ 107 - 109 M☉.
When we compare this to mass estimates of other sources,
XMMUJ134736.6+173403 appears to be the most massive source with
commensurable QPO frequencies, and its mass represents the current
observational upper limit on AGN BH mass based on QPO observations. We
note that it will be crucial for the falsification of particular
resonance models of QPOs whether only a single QPO with a frequency that
completes the harmonic sequence 3 : 2 : 1 is found in this source, or if
a new different pair of QPOs with frequencies in the 3 : 2 ratio is
found. The former case would agree with the prediction of the 3 : 2
epicyclic resonance model and BH mass M ≈ (5a2 + 8a +
8)×107 M☉, where a is a dimensionless BH spin.
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In this paper we describe the potential of the enhanced X-ray Timing and
Polarimetry (eXTP) mission for studies related to accretion flows in the
strong field gravity regime around both stellar-mass and supermassive
black-holes. eXTP has the unique capability of using advanced "spectral-
timing-polarimetry" techniques to analyze the rapid variations with
three orthogonal diagnostics of the flow and its geometry, yielding
unprecedented insight into the inner accreting regions, the effects of
strong field gravity on the material within them and the powerful
outflows which are driven by the accretion process. X-spinmeasurements
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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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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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