Spherically symmetric dissipative anisotropic fluids: A general study

Abstract

The full set of equations governing the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses is deployed and used to carry out a general study on the behaviour of such systems, in the context of general relativity. Emphasis is given to the link between the Weyl tensor, the shear tensor, the anisotropy of the pressure and the density inhomogeneity. In particular we provide the general, necessary and sufficient, condition for the vanishing of the spatial gradients of energy density, which in turn suggests a possible definition of a gravitational arrow of time. Some solutions are also exhibited to illustrate the discussion.Comment: 28 pages Latex. To appear in Phys.Rev.

Nonadiabatic charged spherical gravitational collapse

“…However the fact that such a relationship is no longer valid in the presence of local anisotropy of the pressure and/or dissipative processes, already discussed in [46], explains its failure in scenarios where the above-mentioned factors are present. Here we see how the electric charge distribution affects the link between the Weyl tensor and density inhomogeneity, suggesting that electric charge (whenever present) should enter into any definition of a gravitational arrow of time.…”

“…In fact, the assumption of local anisotropy of pressure, which seems to be very reasonable for describing the matter distribution under a variety of circumstances, has been proved to be very useful in the study of relativistic compact objects (see [46,54] and references therein).…”

Stationary cylindrical anisotropic fluid

“…This last question is in turn motivated by the very conspicuous link existing in the spherically symmetric case between the Weyl tensor, the inhomogeneity of the energy density and the anisotropy of pressure [3]. For doing so we have calculated the Weyl components as well as the components of its electric and magnetic parts.…”

Gravitational collapse of cylindrical anisotropic fluid: a source of gravitational waves

“…Further, consideration of dissipative matter is more realistic as gravitational collapse is a highly dissipative process [4][5][6]. Gravitational collapse of a radiating star was considered by Chan [7] with dissipation in the form of radial heat flow and shear viscosity.…”