Quantum Ergoregion Instability

We have shown that, as in the case of black holes, an ergosphere itself with no event horizon inside can evaporate spontaneously, giving energy radiation to spatial infinity until the ergoregion disappears. However, the feature of this quantum ergoregion instability is very much different from black hole radiation. It is rather analogous to a laser amplification. This analysis is based on the canonical quantization of a neutral scalar field in the presence of unstable modes characterized by complex frequencies in a simple model for a rapidly rotating star. In general relativity, inertial frames around a rotating object are dragged in the sense of the rotation. If the object is rotating rapidly, this dragging effect can be so strong that in some region no physical object can remain at rest relative to an inertial observer at spatial infinity. This region of spacetime is called an ergoregion or an ergosphere. The most common example of ergoregions would be the outside of the event horizon of any rotating black hole. Ergoregions also arise in models of dense, rotating stars, in which cases no event horizon exists inside the ergosurface [1, 2]. The appearance of any ergoregion causes the well-known classical amplification phenomena such as Penrose process for particles and superradiance for waves. Let us consider a regular matter distribution with non-zero total angular momentum in the past such that the spacetime is almost flat. As the gravitational collapse occurs, the system may end up into a stationary rotating black hole in the future. As is well-known, quantum field theory in this evolving background spacetime shows that the black hole formed radiates spontaneously to infinity. In other words, there is no stable vacuum for matter fields in the presence of a rotating black hole which contains both event horizon and ergosphere. On the other hand, suppose the collapsing matter ends up into a stationary rotating star, which has an ergoregion but no horizon in the future. Now one may ask whether quantum field theory in this background spacetime also gives rise to a spontaneous radiation of the ergosphere as in the case of a collapsing black hole. As argued in Ref. [3], an ergosphere may not evaporate spontaneously since the transmitted part of an ingoing spherical wave packet in a superradiant mode, which carries a negative energy with respect to an observer at infinity, will come out again if there is no event horizon inside To appear in the Proceedings of the APCTP Winter School on Duality of String Theory, Korea, Feb. 17-28, 1997.