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^{9}M

_{⊙ and being at distance d0=16.8 Mpc from observer corresponding to those observed in M87. We show that the sensitivity of image magnification, image separation, and shadow angular size on KS parameter ω and plasma parameter k are of order from 1 to 10 % for R and 16 % for S. Read More }

_{e},σ

_{m}) on the instability of the circular orbits. On the other hand, it is also possible to investigate the fundamental frequencies, such as Keplerian, Larmor, and epicyclic frequencies of charged particles orbiting around a charged black hole. Lastly, we investigate the synchrotron radiation by charged particles accelerated by charged black hole and estimate the intensity of relativistic radiating charged particles. Finally, we comment on the possible utilization of our findings for the relativistic jets and magneto-hydrodynamical outflows.

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_{rot}=580 Hz (290 Hz) of the compact star in the atoll source 4U 1636-53, and a wide range of equations of state (EoS) giving sequences of allowed states governed by the relations a(M), q(M). These sequences are used in the framework of the resonant switch (RS) model combining pairs of geodesic oscillation models to match the data of the twin high-frequency quasi-periodic oscillations observed in the 4U 1636-53 source. The results of the matching procedure using the H-T models are compared to those based on the Kerr approximation of the exterior of the neutron stars. The best H-T matches fix the only variant of the RS model combining particular modifications of the relativistic precession model, exclude the rotation frequency f

_{rot}=290 Hz, restrict the considered EoS to six of them, excluding the strange quark stars, and significantly improve precision of the matches given by any single geodesic oscillations model. The Kerr matching allows two variants of the RS model, thus, giving false information, and only three EoS, thus, giving insufficient information. Our results demonstrate that in the matching procedure, the Kerr approximation can be used only for neutron stars governed by the H-T models with q<2, implying an important restriction on the applicability of the Kerr approximation for description of the oscillatory phenomena around neutron stars. On the other hand, the RS model is sufficiently discriminating for the spacetime metric to be largely determined by fitting to the data. The ranges of the external spacetime parameters of the neutron stars related to the best H-T matches are determined to be M≈2.10-2.13 M

_{⊙}, a≈0.21-0.25, q≈1.8-2.3. Most compact neutron star is predicted by the Gandolfi EoS, when M≈2.10 M

_{⊙}, a≈0.21, q≈1.8, with the equatorial radius R≈10.83 km and eccentricity ɛ=0.03.

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