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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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 study spherically symmetric magnetically charged generic black hole solutions of general relativity coupled to non-linear electrodynamics (NED). For characteristic values of the generic spacetime parameters we give the position of horizons in dependence on the charge parameter, demonstrating separation of the black hole and no-horizon solutions, and possibility of existence of solutions containing three horizons. We show that null, weak and strong energy conditions are violated when the outer horizon is approaching the center. We study effective potentials for photons and massive test particles and location of circular photon orbits (CPO) and innermost stable circular orbit (ISCO). We show that the unstable photon orbit can become stable, leading to the possibility of photon capture which affects on silhouette of the central object. The position of ISCO approaches the horizon with increasing charge parameter q and the energy at ISCO decreases with increasing charge parameter. We investigate this phenomenon and summarize for a variety of the generic spacetime parameters the upper estimate on the spin parameter of the Kerr black which can be mimicked by the generic charged black hole solutions.
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The Schwarzschild star is an ultracompact object beyond the Buchdahl limit, which has Schwarzschild geometry outside its surface and positive pressure in the external layer which vanishes at the surface. Recently, it has been shown that the Schwarzschild star is stable against spherically symmetric perturbations. Here we study arbitrary axial nonspherical perturbations and show that the observable quasinormal modes can be as close to the Schwarzschild limit as one wishes, what makes the Schwarzschild star a very good mimicker of a black hole. The decaying time-domain profiles prove that the Schwarzschild star is stable against nonspherical perturbations as well. Another peculiar feature is the absence of echoes at the end of the ringdown. Instead we observe a nonoscillating mode which might belong to the class of algebraically special modes. At asymptotically late times, Schwarzschildian power-law tails dominate in the signal.
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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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Classical (quasinormal) and quantum (Hawking) radiations are investigated for test fields in the background of a four dimensional, spherically symmetric and asymptotically flat black hole in the Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The geometry of the EdGB black hole deviates from the Schwarzschild geometry only slightly. Therefore, here we observe that the quasinormal spectrum also deviates from its Schwarzschild limit at most moderately, allowing for a 9% decrease in the damping rate and up to a 6% decrease in the real oscillation frequency. However, the intensity of Hawking radiation of an electromagnetic and Dirac fields turned out to be much more sensitive characteristic than its quasinormal spectrum, allowing for a 57% and 48% increase of the energy emission rate respectively. The analytical formula for the eikonal regime of quasinormal modes is derived for test fields and it is shown that the correspondence between the eikonal quasinormal modes and null geodesics is indeed fulfilled for test fields, but is not expected for the gravitational one.
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The external Hartle-Thorne geometry, which describes the spacetime outside a slowly rotating compact star, is characterized by the gravitational mass M, angular momentum J, and quadrupole moment Q of the star and gives a convenient description, which, for the rotation frequencies of more than 95% of known pulsars, is sufficiently accurate for most purposes. We focus here on the motion of particles in these spacetimes, presenting a detailed systematic analysis of the frequency properties of radial and vertical epicyclic motion and of orbital motion. Our investigation is motivated by X-ray observations of binary systems containing a rotating neutron star that is accreting matter from its binary companion. In these systems, twin high-frequency quasi-periodic oscillations (QPOs) are sometimes observed with a frequency ratio approaching 3:2 or 5:4, and these may be explained by models involving the orbital and epicyclic frequencies of quasi-circular geodesic motion. In our analysis, we use realistic equations of state for the stellar matter and proceed in a self-consistent way, following the Hartle-Thorne approach in calculating both the corresponding values of Q, M, and J for the stellar model and the properties of the surrounding spacetime. Our results are then applied to a range of geodetical models for QPOs. A key feature of our study is that it implements the recently discovered universal relations among neutron-star parameters so that the results can be directly used for models with different masses M, radii R, and rotational frequencies f rot.
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We study behaviour of ionized region of a Keplerian disk orbiting a Schwarzschild black hole immersed in an asymptotically uniform magnetic field. In dependence on the magnetic parameter B, and inclination angle θ of the disk plane with respect to the magnetic field direction, the charged particles of the ionized disk can enter three regimes: (1) regular oscillatory motion, (2) destruction due to capture by the magnetized black hole, (3) chaotic regime of the motion. In order to study transition between the regular and chaotic type of the charged particle motion, we generate time series of the solution of equations of motion under various conditions, and study them by non-linear (box counting, correlation dimension, Lyapunov exponent, recurrence analysis, machine learning) methods of chaos determination. We demonstrate that the machine learning method appears to be the most efficient in determining the chaotic region of the θ -r space. We show that the chaotic character of the ionized particle motion increases with the inclination angle. For the inclination angles θ ∼ 0 whole the ionized internal part of the Keplerian disk is captured by the black hole.
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We employ the minimal geometric deformation approach to gravitational decoupling (MGD-decoupling) in order to build an exact anisotropic version of the Schwarzschild interior solution in a space-time with cosmological constant. Contrary to the well-known Schwarzschild interior, the matter density in the new solution is not uniform and possesses subluminal sound speed. It therefore satisfies all standard physical requirements for a candidate astrophysical object.
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We study the optical properties of the Kehagias-Sfetsos (KS) compact objects, characterized by the "Hořava" parameter ω _{_{KS}}, in the presence of plasma, considering its homogeneous or power-law density distribution. The strong effects of both "Hořava" parameter ω _{_{KS}} and plasma on the shadow cast by the KS compact objects are demonstrated. Using the weak field approximation, we investigate the gravitational lensing effect. Strong dependence of the deflection angle of the light on both the "Hořava" and plasma parameter is explicitly shown. The magnification of image source due to the weak gravitational lensing is given for both the homogeneous and inhomogeneous plasma.
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