Relativistic Hydrodynamics and Dynamics of Accretion Disks Around Black Holes
We give a brief overview of a formulation of the equations of general relativistic hydrodynamics, and one method for their numerical solution. The system of equations can be cast as first-order, hyperbolic system of conservation laws, following a explicit
- PDF / 255,456 Bytes
- 7 Pages / 439.37 x 666.142 pts Page_size
- 26 Downloads / 203 Views
Abstract We give a brief overview of a formulation of the equations of general relativistic hydrodynamics, and one method for their numerical solution. The system of equations can be cast as first-order, hyperbolic system of conservation laws, following a explicit choice of an Eulerian observer and suitable vector of variables. We also present a brief overview of the numerical techniques used to solve this equation, providing an example of their applicability in one scenario of relativistic astrophysics namely, the quasi periodic oscillations of a thick accretion disk.
1 Introduction Relativistic hydrodynamics is a branch of physics related to the study of both: flows in which the velocities attained by the fluid as a whole approaching the speed of light, or those for which the strength of the gravitational is very strong and it is mandatory a description in terms of Einsteins theory of gravity. Scenarios J. C. Degollado (&) C. Moreno Departamento de Astrofísica Teórica, Instituto de Astronomía, Universidad Nacional Autónoma de México, Circuito Exterior Ciudad Universitaria, Apdo 70-264, CU, 04510 Mexico, D.F., Mexico e-mail: [email protected] C. Moreno e-mail: [email protected] J. C. Degollado C. Moreno Departamento de Matemáticas y Departamento de Física, Centro Universitario de Ciencias Exactas e Ingeniería, Universidad de Guadalajara, Revolución 1500 Colonia Olímpica, 44430 Guadalajara, Jalisco, Mexico
J. Klapp et al. (eds.), Fluid Dynamics in Physics, Engineering and Environmental Applications, Environmental Science and Engineering, DOI: 10.1007/978-3-642-27723-8_45, Ó Springer-Verlag Berlin Heidelberg 2013
481
482
J. C. Degollado and C. Moreno
involving compact objects such as supernova explosions leading to neutron stars, micro quasars, active galactic nuclei, and coalescing neutron stars, all contain flows at relativistic speeds and, in many cases, strong shock waves. The correct description of the dynamics and evolution of such astrophysical systems strongly relies on the use of accurate large-scale numerical simulations. Our claim is to present a brief overview of a 3 ? 1 formulation of general relativistic hydrodynamics, applied to a simple example, the dynamics of an accretion disk around a stationary black hole. The simplest model of accretion disks in General Relativity is the one proposed by Abramowicz et al. (1978). This model is based on the assumption that the disk is formed by a barotropic fluid that has reached a stationary configuration in the background of a black hole space time. We chose this configuration as initial data and after adding a radial perturbation, we study the response of the disk that is reflected as a quasi periodic oscillation that resembles the epicyclic frequencies of point particles orbiting a black hole.
2 General Relativistic Hydrodynamics The General Relativistic Hydrodynamics (GRHD) equations are crucial in situations involving strong gravitational fields or flows approaching the speed of light. Generally these set of equations are des
Data Loading...
