How the cosmological constant affects gravastar formation

Abstract

Here we generalized a previous model of gravastar consisted of an internal de Sitter spacetime, a dynamical infinitely thin shell with an equation of state, but now we consider an external de Sitter-Schwarzschild spacetime. We have shown explicitly that the final output can be a black hole, a "bounded excursion" stable gravastar, a stable gravastar, or a de Sitter spacetime, depending on the total mass of the system, the cosmological constants, the equation of state of the thin shell and the initial position of the dynamical shell. We have found that the exterior cosmological constant imposes a limit to the gravastar formation, i.e., the exterior cosmological constant must be smaller than the interior cosmological constant. Besides, we have also shown that, in the particular case where the Schwarzschild mass vanishes, no stable gravastar can be formed, but we still have formation of black hole.

Dynamical evolution of an unstable gravastar with zero mass

“…Note also that if L e = L i , the mass of the shell is zero and no object is formed. Recently we have shown that in order to have a physically acceptable stable shell between two spacetimes with cosmological constants, the inner cosmological constant must be greater than that outer one (Chan et al 2009b), which is in agreement to the gravastar requirement proposed by Horvat and Ilijic (2007). Our present work is completely coherent with this previous result since here it is not possible to have a stable thin shell.…”

“…Instead of it reduces itself to a point-like object. This can be seen directly from the analysis of the potential and confirmed by the relation between the cosmological constants (L i > L e ), which is imposed in order to have a positive shell mass, and which violates the condition which had been already proposed by two of us, in another paper (Chan et al 2009b), that is, L i < L e to have stable structures. It is remarkable that if i = e there is no shell (its mass is zero), although it is not true if m = 0 .…”

“…In this section, we will summarize the gravastar model with an exterior de Sitter-Schwarzschild spacetime (Chan et al 2009b). Since we assume that total energy of the system is zero, the motion of the surface of the gravastar can be written in the form (Visser and Wiltshire 2004),…”

“…Substituting (19), into (16) and solving it forṘ 2 /2 we obtain the potential V (R, L i , L e ), given by (Chan et al 2009b)…”

“…The first work to consider gravastar solutions with de Sitter exterior were analyzed in Carter (2005). In this work we will use the same kind of exterior spacetime (Chan et al 2009b). In recent works, two of us showed that gravastars do not substitute black holes (Rocha et al 2008a(Rocha et al , 2008bChan et al 2009aChan et al , 2009bChan and da Silva 2010;Chan et al 2011 ).…”