Abstract
It was recently shown that a massive thin shell that is sandwiched between a flat interior and an exterior geometry given by the outgoing Vaidya metric becomes null in a finite proper time. We investigate this transition for a general spherically-symmetric metric outside the shell and find that it occurs generically. Once the shell is null its persistence on a null trajectory can be ensured by several mechanisms that we describe. Using the outgoing Vaidya metric as an example we show that if a dust shell acquires surface pressure on its transition to a null trajectory it can evade the Schwarzschild radius through its collapse. Alternatively, the pressureless collapse may continue if the exterior geometry acquires a more general form.
Highlights
Hypersurfaces of discontinuity are idealizations of narrow transitional regions between spacetime domains with different physical properties
The resulting joined geometry is a solution of the Einstein equations with an additional distributional stress-energy tensor that is concentrated on the hypersurface
The exterior spherical geometry is described by a Schwarzschild metric and the shell collapses into a black hole in finite proper time
Summary
Hypersurfaces of discontinuity are idealizations of narrow transitional regions between spacetime domains with different physical properties. The exterior spherical geometry is described by a Schwarzschild metric and the shell collapses into a black hole in finite proper time. Such models has been used in investigations of collapse-induced radiation [9, 10] anticipated before formation of the event horizon. An outgoing Vaidya metric [24] is often used as an example of the exterior geometry of this process despite its known limitations [25] This result is based on an implicit assumption that through their evolution a massive shell remains timelike and a massless shell remains null. The total proper time derivative dA/dτ is denoted as A, and the total derivative over some parameter λ is Aλ := ARRλ + AU Uλ
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