ARE HIGHER-ORDER MEMBRANES STABLE IN BLACK-HOLE SPACETIMES

We continue the study of the existence and stability of static spheric al membrane configurations in curved spacetimes. We first consider hig her order membranes described by a Lagrangian which, in addition to th e Dime term. includes a term proportional to the scalar curvature of t he world volume ((3))R. Notably, in this case, the equations of motion can be reduced to second order ones and an effective potential analys is can be made. The conditions for stability are then explicitly deriv ed. We find a self-consistent static spherical membrane, determining t he spacetime generated by the membrane itself. In this case we find, h owever, that the total energy of the membrane has to be negative, and no stable equilibrium can be achieved, We then generalize the discussi on to a membrane described by a Lagrangian including all possible seco nd derivative terms. We conclude the paper with some discussion on the generality of the results obtained.