Speculations about alternatives to black holes often involve models of exotic compact objects that feature a self-gravitating membrane at the body's surface. These membranes are dynamically unstable, which makes the physical reality of these objects doubtful. In a Newtonian description of the membrane's gravity, the object is linearly unstable, in the sense that a generic perturbation from a static and spherically symmetric state grows exponentially with time. In general relativity, the object possesses unstable modes, but lack of mode completeness prevents us from claiming that it is linearly unstable. I will describe the mathematics and physics of a self-gravitating membrane in both Newtonian theory and general relativity, and then discuss its dynamical stability.

Bio: Eric Poisson obtained a B.Sc. in physics from Laval University in 1987, a M.Sc. in theoretical physics from the University of Alberta in 1989, and a PhD in theoretical physics from the University of Alberta in 1991. He joined the University of Guelph's Department of Physics in 1995 where he is now a full professor. His field of research is general relativity, with an emphasis on black holes, neutron stars, and gravitational waves.