SOAP BUBBLES IN OUTER-SPACE - INTERACTION OF A DOMAIN-WALL WITH A BLACKHOLE - ART. NO. 085008

We discuss the generalized Plateau problem in the (3+1)-dimensional Sc hwarzschild background. This represents the physical situation, which could for instance have appeared in the early universe, where a cosmic membrane (thin domain wall) is located near a black hole. Considering stationary axially symmetric membranes, three different membrane topo logies are possible depending on the boundary conditions at infinity: 2+1 Minkowski topology, 2+1 wormhole topology, and 2+1 black hole topo logy. Interestingly, we find that the different membrane topologies ar e connected via phase transitions of the form first discussed by Chopt uik in investigations of scalar field collapse. More precisely, we fin d a first order phase transition (finite mass gap) between wormhole to pology and black hole topology, the intermediate membrane being an uns table wormhole collapsing to a black hole. Moreover, we find a second order phase transition (no mass gap) between Minkowski topology and bl ack hole topology, the intermediate membrane being a naked singularity . For the membranes of black hole topology, we find a mass scaling rel ation analogous to that originally found by Choptuik. However, in our case the parameter p is replaced by a 2-vector (p) over right arrow pa rametrizing the solutions. We fmd that mass proportional to \(p) over right arrow-(p) over right arrow()\(gamma) where gamma approximate to 0.66. We also find a periodic wiggle in the scaling relation. Our res ults show that black hole formation as a critical phenomenon is far mo re general than expected. [S0556-2821(98)07518-3].