Stability of a shell around a black hole

Details Stability of a shell around a black hole Stability of a shell around a black hole

Sep 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrvd..44.1891b&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 44, Issue 6, 15 September 1991, pp.1891-1894

Computer Science

Sound

37

Scientific paper

We study the mechanical stability of a static, infinitely thin, spherically symmetric massive shell surrounding a classical Schwarzschild black hole. The shell is taken to have a non-negative surface energy density, and a speed of sound not greater than the speed of light. We show that the shell is stable against radial perturbations only outside a critical radius which is always larger than the radius of the circular photon orbit. The surface energy density of a stable shell is always larger than twice the surface pressure, and thus satisfies the dominant energy condition by a wide margin. We briefly discuss the effects of Hawking radiation in view of a path-integral approach to black-hole thermodynamics developed by York and collaborators. Our results suggest that a macroscopic thermal equilibrium situation associated with the canonical ensemble in this approach may not be realizable with a thin matter shell in Lorentzian spacetime.

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