ON THE STABILITY OF SPHERICAL MEMBRANES IN CURVED SPACE-TIMES

We study the existence and stability of spherical membranes in curved space-times. For Dirac membranes in the Schwarzschild-de Sitter backgr ound we find that there exists an equilibrium solution. By fine-tuning the dimensionless parameter Lambda M(2), the static membrane can be a t any position outside the black hole event horizon, even at the stret ched horizon, but the solution is unstable. We show that modes having l = 0 (and for Lambda M(2) < 16/243 also l = 1) are responsible for th e instability. We also find that spherical higher order membranes (mem branes with extrinsic curvature corrections), contrary to what happens in flat Minkowski space, do have equilibrium solutions in a general c urved background and, in particular, also in the ''plain'' Schwarzschi ld geometry (while Dirac membranes do not have equilibrium solutions t here). These solutions, however, are also unstable. We shah discuss a way of bypassing these instability problems, and we also relate our re sults to the recent ideas of representing the black hole event horizon as a relativistic bosonic membrane.