Naked singularities

Exactly how shy is the universe? Does the universe permit naked singularities? It seems that there may now be an observational means of answering this question.

To understand what a naked singularity is, it is first necessary to recognise that space-time singularities come in two forms: spacelike singularities and timelike singularities. The former are consistent with determinism, whilst the latter are not. Even if one specifies the state of the entire 3-dimensional universe at a moment in time, if timelike singularities exist, then the state of the universe at a moment in time is insufficient to predict what will emerge in the future from the timelike singularity. Note that the Schwarzschild space-time for a non-rotating, electrically neutral black hole, and the corresponding space-time for a white hole, both possess spacelike singularities.

However, the maximally extended Kerr space-time for a rotating black hole contains a timelike singularity. Whilst this is strictly inconsistent with determinism, those Kerr space-times which possess a physically realistic angular momentum, contain an event horizon which prevents the unpredictable output from the singularity reaching the outside world. In contrast, a naked singularity is a timelike singularity which is not confined within an event horizon.

The family of Kerr space-time solutions to the Einstein field equations are such that the event horizon disappears if the angular momentum-to-mass ratio exceeds a certain extremal value. Arguments have thus raged for some years over whether a naked singularity could form by a physically realistic process, or whether it is merely a theoretical artifact.

Arlie Petters (Duke University) and Marcus Werner (University of Cambridge) now suggest that the space-time of such a rapidly spinning, naked singularity, would form a distinctive gravitational lens, enabling astronomers to spot such an object, if it exists, in our own galaxy.