Spherically symmetric collapse of an anisotropic fluid body into an exotic black hole

Abstract

The classical gravitational equations of Einstein are investigated for an anisotropic fluid body in the case of spherical symmetry. An equation of state T (4)(4)+k2T (1)(1)=0 is imposed. The junction conditions [T ba]nb=0 of Synge are required to be satisfied on the boundary of the fluid body. A class of exact, analytical solutions depending on four parameters is obtained. The solutions satisfy the equation of state and the weak energy conditions prior to the collapse of the boundary inside the event horizon. However, in the interior of the event horizon, the matter undergoes a transition into an exotic state. A portion of the fluid turns tachyonic with T44<0, a second portion has complex eigenvalues for [T ba], and a third part has signature +4.