Brane-world stars with solid crust and vacuum exterior

TL;DR

This paper demonstrates the existence of brane-world stellar models with a solid crust and vacuum exterior, satisfying physical criteria and consistent with observational constraints, using the minimal geometric deformation approach.

Contribution

It introduces a new class of brane-world star solutions with a solid crust and vacuum exterior, ensuring physical acceptability and observational compatibility.

Findings

Interior is regular and physically acceptable

Crust thickness inversely proportional to brane tension and star radius

Star appears thermally radiating and matches observational constraints

Abstract

The minimal geometric deformation approach is employed to show the existence of brane-world stellar distributions with vacuum Schwarzschild exterior, thus without energy leaking from the exterior of the brane-world star into the extra dimension. The interior satisfies all elementary criteria of physical acceptability for a stellar solution, namely, it is regular at the origin, the pressure and density are positive and decrease monotonically with increasing radius, finally all energy conditions are fulfilled. A very thin solid crust with negative radial pressure separates the interior from the exterior, having a thickness $\Delta $ inversely proportional to both the brane tension $\sigma $ and the radius $R$ of the star, i.e. $\Delta ^{-1}\sim R\,\sigma $. This brane-world star with Schwarzschild exterior would appear only thermally radiating to a distant observer and be fully compatible with the stringent constraints imposed on stellar parameters by observations of gravitational lensing, orbital evolutions or properties of accretion disks.