MG15 - Talk detail

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Abstract

I will discuss models composed of a rotating black hole and a massive self-gravitating torus/disk rotating in the Keplerian motion. Such ''black-hole-torus'' systems are common across the Universe---they are present in the galactic centres and also they are considered as quasi-stationary configurations arose in the merger of compact binaries consisting of pairs of black holes or neutron stars. Such model is not available for analytical methods because of their high mathematical complexity. I am going to present the result of the numerical calculation which was done in our group in Krakow. Mathematically it is numerical approach to the stationary, free boundary, elliptic, integro-algebraic Einstein-Euler system. Physically we investigated the nature of the ''Keplerian rotation'' which is completely different in the Newtonian theory and in the general relativity. In the Newtonian gravity---according to the Poincar\'{e}-Wavre theorem---the angular velocity is the function of the one parameter---the distance from the rotation axis. In general relativity it is a function of both---the radial and polar coordinates. We have here two important contexts: 1) in astrophysics---because of the rotation curves analysis, 2) in gravitational waves: such configurations are considered as quasi-stationary systems, which form during the last stage of neutron stars binary coalescence---the process during which the gravitational waves are emitted. Such approach gives the possibility to investigate this process using the stationary models instead of difficult, dynamical simulations.

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