WATPHYS TH-97/03 Black Holes of Negative Mass

I demonstrate that, under certain circumstances, regions of negative energy density can undergo gravitational collapse into a black hole. The resultant exterior black hole spacetimes necessarily have negative mass and non-trivial topology. A full theory of quantum gravity, in which topologychanging processes take place, could give rise to such spacetimes. 2 Internet: [email protected] The gravitational collapse of a region of sufficiently large density into a black hole is one of the more striking predictions of general relativity. It can occur via several mechanisms, including stellar collapse, collapse of star clusters, primordial collapse of a region of sufficiently enhanced density in the early universe, or perhaps even via quantum fluctuations of the vacuum energy density at sufficiently short distances and/or early times. A generic feature of black hole formation is the positivity of the initial energy density, which in turn can collapse into a singularity which is cloaked by an event horizon, leaving behind an exterior black hole spacetime of positive mass. A simple inspection of the KerrNewman de Sitter class of metrics indicates that the existence of the event horizon crucially depends upon the positivity the ADM mass – a reversal of its sign yields a spacetime with a naked singularity. The purpose of this essay is to demonstrate that a region of negative energy density (which might be produced, say, from quantum fluctuations) can also undergo gravitational collapse to a black hole. In order for such a process to take place, the event horizon of the black hole must be a negatively curved compact surface. This in turn implies that it is not simply connected, and the spacetime manifold containing the black hole inheirits a similar topology. I shall model the region of negative energy with a stress energy tensor for cloud of freely-falling dust that is given by Tμν = −|ρ|uμuν , where the energy density ρ < 0 and uν is the associated four velocity, defined such that guμuν = −1. The form of the metric within the dust is ds = −dt + a(t) ( dr kr2 + c + rdω )