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.

16 pages, Revtex 4-1. To appear in Phys. Rev. D. Some references updated

References in corpus (15)

• All static spherically symmetric anisotropic solutions of Einstein's equations
• Equation of State of a Dense and Magnetized Fermion System
• Relativistic cosmology and large-scale structure
• Nonadiabatic charged spherical gravitational collapse
• Shearing Expansion-free Spherical Anisotropic Fluid Evolution
• Dynamics of viscous dissipative gravitational collapse: A full causal approach
• Dynamical laws of superenergy in General Relativity
• The inertia of heat and its role in the dynamics of dissipative collapse
• Anisotropic Pressures in Very Dense Magnetized Matter
• Why does gravitational radiation produce vorticity?
• Vorticity production through rotation, shear and baroclinicity
• Dynamics of Charged Plane Symmetric Gravitational Collapse
• Can cosmological perturbations produce early universe vorticity?
• Neutrino emissivity and bulk viscosity of iso-CSL quark matter in neutron stars
• Bulk viscosity in 2SC and CFL quark matter

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• Evolution of Cluster of Stars in f(R) Gravity
• Impact of Extended Starobinsky Model on Evolution of Anisotropic, Vorticity-free Axially Symmetric Sources
• Earliest stages of the non-equilibrium in axially symmetric, self-gravitating, dissipative fluids
• Stability of a Class of Non-Static Axial Self-Gravitating Systems in $f(R)$ Gravity
• Shearing and geodesic axially symmetric perfect fluids that do not produce gravitational radiation
• Acceptability Conditions and Relativistic Barotropic Equations of State
• The spacetime outside a source of gravitational radiation: The axially symmetric null fluid
• Self-similarity in static axially symmetric relativistic fluids
• Conformastationary disk-haloes in Einstein-Maxwell gravity
• On the Stability of Pressure Isotropy Condition in Palatini $f(R)$ Gravity
• Matter shear and vorticity in conformally flat spacetimes
• Gravitational radiation, vorticity and super-energy: A conspicuous threesome