Brane-world stars with solid crust and vacuum exterior

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 ∆ inversely proportional to both the brane tension σ and the radius R of the star, i.e. ∆−1 ∼ R σ. 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.

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