Gravastar on the brane with a timelike extra dimension

TL;DR

The paper addresses singularities in gravitational collapse by constructing a gravastar on the Shtanov–Sahni brane with a timelike extra dimension. It solves the modified brane Einstein equations to produce a non-singular interior with EOS $p=-\rho$ (BEC core), a finite-thickness shell with $p=\rho$, and a Weyl-induced exterior with tidal charge $Q$, all while enforcing proper junction conditions. Bulk Weyl corrections generate intrinsic pressure anisotropy and can suppress the active gravitational mass via the effective density $\rho^{\mathrm{eff}}$, with all energy conditions satisfied. The result is a fully analytic, finite-thickness gravastar on the SS brane, offering a geometrically motivated alternative to black holes and potential observational discriminants in gravitational-wave and lensing signals.

Abstract

We construct a gravastar configuration within the Shtanov-Sahni (SS) braneworld scenario, characterized by a timelike extra dimension and negative brane tension. Unlike classical black holes, which inevitably culminate in central curvature singularities, our model demonstrates that the SS braneworld dynamics naturally regularize the interior geometry and prevent singularity formation. By solving the modified Einstein field equations induced on the brane, we obtain explicit interior, shell, and exterior solutions without invoking the idealized thin-shell approximation. The gravastar core is modeled as a Bose--Einstein condensate, while the intermediate shell consists of ultra-dense stiff matter. Bulk Weyl corrections induce anisotropic effective pressures on the brane, a feature that emerges intrinsically in this scenario and supports stability. We analyze the active gravitational mass, energy, entropy, and proper thickness of the shell, and establish the junction conditions at the interfaces. Our analysis reveals that the SS gravastar exhibits suppressed or even negative effective mass, reflecting the repulsive nature of the interior condensate, and admits stable equilibrium solutions consistent with energy conditions. This highlights the SS braneworld gravastar as a physically viable compact object and a compelling alternative to black holes. A key novelty of our construction is that the stabilizing pressure anisotropy and suppressed effective gravitational mass arise dynamically from higher-dimensional Weyl corrections, rather than being imposed through ad hoc matter sources or thin-shell idealizations. This provides the first fully analytic realization of a finite-thickness, stable gravastar in the Shtanov-Sahni braneworld, highlighting a genuinely geometric mechanism for singularity avoidance in compact objects.

Figures (4)

• Figure 1: Variation of the effective density w.r.t. the radial coordinate $r$.
• Figure 2: Variation of the energy of the shell with respect to $r$.
• Figure 3: Variation of the Surface redshift of the shell with respect to $r$.
• Figure 4: Variation of the different energy conditions w.r.t. the radial coordinate $r$.