Dissipative Spherical Gravitational Collapse of Isotropic Fluid

Abstract

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.

Gravitational collapse, shear-free anisotropic radiating star

“…While second one is diffusion approximation and in this case the dissipation is modeled by heat flow type vector and in this the model proposed by Glass [20] has been extensively studied by Santos [21] for the junction conditions of collapsing spherically symmetric shear-free non-adiabatic fluid with radial heat flow. On a similar ground a number of studies have been reported by de Oliveira et al [22]; de Oliveira-Santos [23]; Bonnor et al [24]; Banerjee et al [25]; Govinder-Govender [26]; Maharaj et al [27]; Herrera et al [28][29][30]; Naidu-Govender [31]; Sarwe-Tikekar [32]; Ivanov [33]; Pinheiro-Chan [34]; Tewari [35,36]; Tewari-Charan [37,38] and also references therein for describing a collapsing fluid radiating energy. A remarkable work for collapsing anisotropic radiating star is due to Herrera -Santos [39] explored the properties of anisotropic self-gravitating spheres using the perturbation method.…”

“…Here from (38) and (39), we are seeing that at the centre radial and tangential pressures are equal and anisotropy vanishes there.…”

Implications for vanishing complexity in dynamical spherically symmetric dissipative self-gravitating fluids

“…We followed the approach of Tewari and Fig. 1 Mass Charan [25] in which both metric functions A and B are spatially and temporally separable. In particular, the time dependence was not removed from gravitational potential A(r, t) = A 0 (r ) f (t) as it is common to set A(r, t) → A 0 (r ) [13,24].…”