Equation of state and transport processes in self-similar spheres

Abstract

We study the effect of transport processes ͑diffusion and free streaming͒ on a collapsing spherically symmetric distribution of matter in a self-similar space-time. A very simple solution shows interesting features when it is matched with the Vaidya exterior solution. In the mixed case ͑diffusion and free streaming͒, we find a barotropic equation of state in the stationary regime. In the diffusion approximation the gravitational potential at the surface is always constant; if we perturb the stationary state, the system is very stable, recovering the barotropic equation of state as time progresses. In the free-streaming case the self-similar evolution is stationary, but with a nonbarotropic equation of state.

Self-similar and charged radiating spheres: an anisotropic approach

“…IV. B in [55]). The energetic at the boundary surface in conjunction with the pull of gravity and push of electric charge, explain the dependence between the amplitude and period with the total electric charge.…”

Self–similar and charged spheres in the free–streaming approximation

“…This power-law dependence on ζ is based on the fact that any function of ζ is solution of £ ξ g =2g. Demanding continuity of the first fundamental form we get the following metric solutions [15,52]: (20) and…”

“…It is well established that in the critical gravitational collapse of an scalar field the spacetime can be self-similar [48][49][50]. We have applied characteristic methods to study the self-similar collapse of spherical matter and charged distributions [15,[51][52][53]. The assumption of selfsimilarity reduces the problem to a system of ODE's, subject to boundary conditions determined by matching to an exterior Reissner-Nordström-Vaidya solution.…”

Characteristic Evolution and Matching

“…Barreto’s group in Venezuela applied characteristic methods to study the self-similar collapse of spherical matter and charge distributions [20, 24, 21]. The assumption of self-similarity reduces the problem to a system of ODE’s, subject to boundary conditions determined by matching to an exterior Reissner-Nordström-Vaidya solution.…”