Dissipative collapse of axially symmetric, general relativistic sources: A general framework and some applications

Abstract

We carry out a general study on the collapse of axially (and reflection-)symmetric sources in the context of general relativity. All basic equations and concepts required to perform such a general study are deployed. These equations are written down for a general anisotropic dissipative fluid. The proposed approach allows for analytical studies as well as for numerical applications. A causal transport equation derived from the Israel-Stewart theory is applied, to discuss some thermodynamic aspects of the problem. A set of scalar functions (the structure scalars) derived from the orthogonal splitting of the Riemann tensor are calculated and their role in the dynamics of the source is clearly exhibited. The characterization of the gravitational radiation emitted by the source is discussed.

Shearing and geodesic axially symmetric perfect fluids that do not produce gravitational radiation

“…Our original goal, here as well as in [1] and [6], has been to describe the gravitational radiation process, through the physical properties of its source. Such an endeavour, should, eventually, lead to the obtention of a specific source of gravitational radiation.…”

“…Besides some results exhibited in [1], the above mentioned framework has been applied to the shear-free case [6]. As the result of such a study, it follows that all geodesic and shear-free fluids, are irrotational, and as consequence of this, also purely electric.…”

“…For vacuum, it is represented by the Bondi metric [10]. Here, following the framework developed in [1], we have restricted the line element as much as possible, always allowing for the existence of gravitational radiation (at least for the most general matter distribution). As the result of these restrictions, we are able to manipulate the resulting expressions, by purely analytical procedures.…”

“…We shall heavily rely on the general framework developed in [1], keeping the same notation, and just reducing the general equations to the particular case considered here. These will be presented in an Appendix.…”

“…In a recent paper [1] the 1 + 3 formalism [2][3][4][5] has been used to develop a general framework for studying axially symmetric dissipative fluids. Besides some results exhibited in [1], the above mentioned framework has been applied to the shear-free case [6].…”