We complete the stability study of general-relativistic spherically symmetric polytropic perfect fluid spheres, concentrating our attention on the newly discovered polytropes containing region of trapped null geodesics. We compare the methods of treating the dynamical stability based on the equation governing infinitesimal radial pulsations of the polytropes and the related Sturm-Liouville eigenvalue equation for the eigenmodes governing the pulsations, to the methods of stability analysis based on the energetic considerations. Both methods are applied to determine the stability of the polytropes governed by the polytropic index n in the whole range 0 < n < 5, and the relativistic parameter σ given by the ratio of the central pressure and energy density, restricted by the causality limit. The critical values of the adiabatic index for stability are determined, together with the critical values of the relativistic parameter σ. For the dynamical approach, we implemented a numerical method which is independent on the choice of the trial function, and compare its results with the standard trial function approach. We found that the energetic and dynamic method give nearly the same critical values of σ. We found that all the configurations having trapped null geodesics are unstable according to both methods.
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We present a review of the influence of cosmic repulsion and external magnetic fields on accretion disks rotating around rotating black holes and on jets associated with these rotating configurations. We consider both geometrically thin and thick disks. We show that the vacuum energy represented by the relic cosmological constant strongly limits extension of the accretion disks that is for supermassive black holes comparable to extension of largest galaxies, and supports collimation of jets at large distances from the black hole. We further demonstrate that an external magnetic field crucially influences the fate of ionized Keplerian disks causing creation of winds and jets, enabling simultaneously acceleration of ultra-high energy particles with energy up to 1021 eV around supermassive black holes with M∼1010M⊙ surrounded by sufficiently strong magnetic field with B∼104 G. We also show that the external magnetic fields enable existence of "levitating" off-equatorial clouds or tori, along with the standard equatorial toroidal structures, if these carry a non-vanishing, appropriately distributed electric charge.
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We present the particular case of the Stephani solution for shear-free perfect fluid with uniform energy density and nonuniform pressure. Such models appeared as possible alternative to the consideration of the exotic forms of matter like dark energy that would cause the acceleration of universe expansion. These models are characterized by the spatial curvature, depending on time. We analyze the properties of the cosmological model obtained on the basis of exact solution of the Stephani class, and adapt it to the recent observational data. The spatial geometry of the model is investigated. We show that despite possible singularities, the model can describe the current stage of the universe’s evolution.
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We study optical phenomena in generic regular, magnetically charged, spherically symmetric black hole spacetimes arising from coupling of the Einstein gravity and nonlinear electrodynamics (NED) with the Maxwellian weak-field limit, where photons follow null geodesics of an effective geometry, directly reflecting the electromagnetic nonlinearity. We compare the motion of photons with that of massless neutrinos, which are not affected directly by nonlinearities of the non-Maxwellian electromagnetic field and follow null geodesics of the background spacetime. We determine shadows of such black holes, compare the time delays of photons and neutrinos moving in their field, and construct images of the Keplerian disks. We demonstrate that in the case of the “Maxwellian” NED black holes the optical phenomena give relevant signatures of the NED effects detectable by GRAVITY or the Event Horizon Telescope, but they are not strong enough to be excluded by recent observations as in the case of regular Bardeen black holes.
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Considering the regular Bardeen black hole spacetimes, we test the observational effects of the general relativistic solutions coupled to non-linear electrodynamics (NED) by studying the photon motion in the effective geometry governed by the spacetime geometry and the NED Lagrangian. We focus our attention to the observationally important case of profiled spectral lines generated by rings radiating in a fixed frequency and orbiting the black hole along circular geodesics of the Bardeen spacetime. Such profiled spectral lines are observed in active galactic nuclei and in microquasars, giving sufficient data for the test of regular black holes. We expect that such radiating rings could arise around the Galaxy central supermassive black hole SgrA*, and the related profiled spectral lines could give important additional information to those obtained by direct observations due to the Event Horizon (GRAVITY) Telescope. We demonstrate that the profiled spectral lines of the radiating rings predict strong signatures of the NED effects on the photon motion - namely the frequency shift to the red edge of the spectrum, and narrowing of the profile, by more than one order in comparison with the case of the profiles generated purely by the spacetime geometry, for all values of the magnetic charge and the inclination angle of the observer. The specific flux is substantially suppressed and for extended Keplerian disks even the shape of the profiled line is significantly modified due to the NED effect.
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We employ the minimal geometric deformation approach to gravitational decoupling (MGD-decoupling) in order to generate an exact anisotropic and non-uniform version of the ultracompact Schwarzschild star, or ‘gravastar’, proposed by Mazur and Mottola. This new system represents an ultracompact configuration of radius whose interior metric can be matched smoothly to a conformally deformed Schwarzschild exterior. Remarkably, the model satisfies some of the basic requirements to describe a physically acceptable stellar model, such as a positive density everywhere and decreasing monotonously from the centre, as well as a non-uniform and monotonic pressure.
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We employ the gravitational decoupling approach for static and spherically symmetric systems to develop a simple and powerful method in order to (a) continuously isotropize any anisotropic solution of the Einstein field equations, and (b) generate new solutions for self-gravitating distributions with the same or vanishing complexity factor. A few working examples are given for illustrative purposes.
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Using the gravitational decoupling by the minimal geometric deformation approach, we build an anisotropic version of the well-known Tolman VII solution, determining an exact and physically acceptable interior two-fluid solution that can represent behavior of compact objects. Comparison of the effective density and density of the perfect fluid is demonstrated explicitly. We show that the radial and tangential pressure are different in magnitude giving thus the anisotropy of the modified Tolman VII solution. The dependence of the anisotropy on the coupling constant is also shown.
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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 ~ 108 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 ~ 1015 C for Sgr A*. Although the maximum theoretical limit of ~ 1015 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 a charged, massive scalar field around a static, spherically symmetric black hole immersed into an external asymptotically uniform magnetic field B . It is shown that for given multipole number ℓ there are 2 ℓ+1 numbers of modes due to the Zeeman effect appearing by an interaction of the external magnetic and charged scalar fields introducing an effective mass of the scalar field μeff=√{μ2-m q B } where m is the azimuthal number and q is the charge coupling constant. We calculate threshold value of effective mass in which quasinormal modes are arbitrarily long lived and beyond that value quasinormal modes vanish. In the case of m q B <0 quasinormal modes are longer lived with larger oscillation frequencies. Whenever, magnetic and massive scalar fields satisfies condition μeff2<0 , an instability appears, i.e., if q B >0 or q B <0 there is an instability for the values of azimuthal number m >μ2/q B or m <μ2/q B , respectively.
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