On a radiating fluid in a general relativistic context (original) (raw)
Related papers
Radiation hydrodynamics and Radiating Spheres in General Relativity
Astrophysics and Space Science, 1994
We comment on a method proposed to study the evolution of General Relativistic Radiating Spheres in both radiation limits, i.e. free streaming out and diffusion, extending it to handle any general radiating spherically symmetric distribution of matter. It is also shown that several dynamic models may emerge from a sole static equation of state. Previous erroneous calculations concerning this method are also commented.
A Riccati equation in radiative stellar collapse
We model the behaviour of a relativistic spherically symmetric shearing fluid undergoing gravitational collapse with heat flux. It is demonstrated that the governing equation for the gravitational behaviour is a Riccati equation. We show that the Riccati equation admits two classes of new solutions in closed form. We regain particular models, obtained in previous investigations, as special cases. A significant feature of our solutions is the general spatial dependence in the metric functions which allows for a wider study of the physical features of the model, such as the behaviour of the causal temperature in inhomogeneous spacetimes.
Dissipative Spherical Gravitational Collapse of Isotropic Fluid
We present a number of parametric class of exact solutions of a radiating star and the matching conditions required for the description of physically meaningful fluid. A number of previously known class of solutions have been rediscovered which describe well behaved nature of fluid distributions. The interior matter fluid is shear-free spherically symmetric isotropic and undergoing radial heat flow. The interior metric obeyed all the relevant physical and thermodynamic conditions and matched with Vaidya exterior metric over the boundary. Initially the interior solutions represent a static configuration of perfect fluid which then gradually starts evolving into radiating collapse. The apparent luminosity as observed by the distant observer at rest at infinity and the effective surface temperature are zero in remote past at the instant when collapse begins and at the stage when collapsing configuration reaches the horizon of the black hole.
Physical Review D, 2001
The description of general relativistic radiation hydrodynamics in spherical symmetry is presented in natural coordinate choices. For hydrodynamics, comoving coordinates are chosen and the momentum phase space for the radiation particles is described in comoving frame four momenta. We also investigate a description of the momentum phase space in terms of particle impact parameter and energy at infinity and derive a simple approximation to the general relativistic Boltzmann equation. Further developed are, however, the exact equations in comoving coordinates since the description of the interaction between matter and radiation particles is best described in the closely related orthonormal basis comoving with the fluid elements. We achieve a conservative and concise formulation of radiation hydrodynamics that is well suited for numerical implementation by a variety of methods. The contribution of radiation to the general relativistic jump conditions at shock fronts is discussed and artificial viscosity is consistently included in the derivations in order to support approaches relying on this option.
Dynamics of spherically symmetric spacetimes: Hydrodynamics and radiation
Physical Review D, 2002
Using the 3+1 formalism of general relativity we obtain the equations governing the dynamics of spherically symmetric spacetimes with arbitrary sources. We then specialize for the case of perfect fluids accompanied by a flow of interacting massless or massive particles (e.g. neutrinos) which are described in terms of relativistic transport theory. We focus in three types of coordinates: 1) isotropic gauge and maximal slicing, 2) radial gauge and polar slicing, and 3) isotropic gauge and polar slicing.
Relativistic Model for Radiating Spherical Collapse
2018
The relativistic models for radiating spherical collapse is important for to explain the emission process on very high energy in Supernova burst and Quasars. A general method is reviewed, to obtain models which describe non static radiating spheres, without having to make any hypothesis about the emission of radiation during the collapse. It is concluded that the field equations together with the conservation laws (Bianchi’s Identity) form a complete set of integrable equations that do not require additional the emissivation hypothesis of a Gaussian pulse on at an arbitrary instant to trigger the collapse. The emissivation hypothesis of a Gaussian pulse is not only unnecessary, but also leads to qualitatively and quantitatively different solutions. Calculations were performed using the computer algebra package GRTensorII, running on Maple 13, along with several Maple routines that we have used specifically for this type of problems. The Schwarzschild and Tolman VI models are shown a...
Revisiting spherically symmetric relativistic hydrodynamics
2012
In this paper we revise two classical examples of Relativistic Hydrodynamics in order to illustrate in detail the numerical methods commonly used in fluid dynamics, specifically those designed to deal with shocks, which are based on a finite volume approximation. The two cases we consider are the relativistic blast wave problem and the evolution of a Tolman-Oppenheimer-Volkoff star model, in spherical symmetry. In the first case we illustrate the implementation of relativistic Euler's equations on a fixed background space-time, whereas in the second case we also show how to couple the evolution of the fluid to the evolution of the space-time.
The European Physical Journal C
We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing the model parameters in our formulation, we generate closed-form solutions which may be treated as an anisotropic generalization of a large class of solutions describing isotropic fluid spheres. From the resultant solutions, a particular solution is taken up to show its physical acceptability. Making use of the current estimate of mass and radius of a known pulsar, the effects of anisotropic stress on the gross physical behaviour of a relativistic compact star is also highlighted.
Fluid accretion onto relativistic stars and gravitational radiation
2004
This article reports results from numerical simulations of the gravitational radiation emitted from nonrotating relativistic stars as a result of the axisymmetric accretion of layers of perfect fluid matter, shaped in the form of quadrupolar shells. We adopt a {\em hybrid} procedure where we evolve numerically the polar nonspherical perturbations equations of the star coupled to a fully nonlinear hydrodynamics code that calculates the motion of the accreting matter. Self-gravity of the accreting fluid as well as radiation reaction effects are neglected.