Dynamical gravastars may evade no-go results for exotic compact objects, together with further analytical and numerical results for the dynamical gravastar model

Abstract

Using graphs plotted from the Mathematica notebooks posted with our paper ``Dynamical Gravastars'', we show that a dynamical gravastar has no hard surface, and that a second light sphere resides in the deep interior where there is maximum time dilation. These facts may permit dynamical gravastars to evade no-go results for exotic compact objects relating to light leakage inside the shadow, and nonlinear instabilities arising from an interior light sphere. Testing these surmises will require further detailed modeling calculations, beyond what we commence in this paper, using the numerical dynamical gravastar solution. We also discuss the effect of replacing the sigmoidal function in the gravastar calculation by a unit step function, and we analyze why the dynamical gravastar evades the singularities predicted by the Penrose and Hawking singularity theorems, despite satisfying both the null and strong energy conditions. We then give a simplified two-step process for tuning the initial value $\nu(0)={\rm nuinit}$ to achieve $\nu(\infty)=0$, and give exact integrals for the pressure differential equation in terms of $\nu(r)$ in the interior and exterior regions. Finally, we briefly discuss an extension of the model that includes an external shell of massive particles.