Virial tests for post-Newtonian stationary black-hole—disk systems

Spanish Relativity Meeting: almost 100 years after Einstein's revolution

Jaranowski, Piotr^1 ; Mach, Patryk^2 ; Malec, Edward^2 ; Piróg, Michal^2

Wydzial Fizyki, Uniwersytet W Bialymstoku, Ciolkowskiego 1L, Bialystok

15-245, Poland^1

Instytut Fizyki Im. Mariana Smoluchowskiego, Uniwersytet Jagielloski, Lojasiewicza 11, Kraków

30-348, Poland^2

关键词: Black holes;    Disk systems;    Equatorial planes;    Newtonian model;    Newtonians;    Numerical solution;    Relativistic correction;    Rotation axis;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/600/1/012011/pdf
DOI  :  10.1088/1742-6596/600/1/012011

来源: IOP

【 摘 要 】

We investigated hydrodynamical post-Newtonian models of selfgravitating stationary black-hole-disk systems. The post-Newtonian scheme presented here and also in our recent paper is a continuation of previous, purely Newtonian studies of selfgravitating hydrodynamical disks rotating according to the Keplerian rotation law. The post-Newtonian relativistic corrections are significant even at the 1PN level. The 1PN correction to the angular velocity can be of the order of 10% of its Newtonian value. It can be expressed as a combination of geometric and hydrodynamical terms. Moreover, in contrast to the Newtonian Poincaré-Wavre theorem, it depends both on the distance from the rotation axis and the distance from the equatorial plane. In the technical part of this note we derive virial relations valid up to 1PN order. We show that they are indeed satisfied by our numerical solutions.