Does nature hide strong curvature regions?

Quantum gravitational effects are strong when space-time curvature becomes large, so large that it reaches the Planckian regime. Unfortunately, space-time around us is barely curved. For all practical purposes, you sit in a flat space-time. This is why you don’t have to worry about post-post Newtonian corrections if you ask Siri for directions, but also why it takes some experimental effort to detect the subtle consequences of Einstein’s theory of General Relativity – and that’s the classical case. In the almost flat background around us, quantum effects of gravity are hopelessly small.

But space-time curvature isn’t small everywhere. When matter collapses to a black hole, the matter density and also the curvature become very large, and eventually, long after you’d been spaghettified by tidal forces, reach the regime where quantum gravitational effects are sizeable. The problem is that this area, even though it almost certainly exists inside the black holes that astronomers watch, is hidden below the black hole’s horizon and not accessible to observation.

Or is it? Could there be strong curvature regions in our universe that are not hidden behind event horizons and allow us to look straight onto large quantum gravitational effects?

The “Cosmic Censorship” conjecture states that singularities which form when matter density becomes infinitely large are always hidden behind horizons. But more than 40 years after this conjecture was put forward by Roger Penrose, there is still no proof that it is correct. On the contrary, recent developments, supported by numerical calculations which were impossible in the 1970s, indicate that singularities might form without being censored. These singularities might be “naked”, and yes that is the technical expression.

It has been known for a long time that General Relativity admits for solutions that have naked singularities, but it was believed that these do not form in realistic systems because they require special initial conditions which are never to be found in nature. However, today several physically realistic situations are known to result in naked singularities. Now that we cannot rule out naked singularities on theoretical grounds, we are left to wonder how we could detect them if they exist for real. And if this means strong curvature regions are within sight, what is the potential for observational evidence of quantum gravity?

It turns out these questions are more difficult to answer than you’d expect. Evidence for black hole horizons comes primarily from not seeing evidence of the surface of a compact object. A naked singularity however also doesn’t have a hard surface, so these observations are not of much use. If matter collapses and heats up, it makes a difference for the emitted radiation whether a horizon forms or not. This difference however is so small that it cannot be detected.

This has lead researchers to look for other ways to distinguish between a black hole and a naked singularity. For example by asking how a naked singularity would act as a gravitational lens in comparison to a black hole. However, the timelike naked singularities considered in this work is not of the type that has shown to be created in physically realistic collapse.

The so far most promising study is a recent paper by a group of physicists located in Morelia, Mexico

Observational distinction between black holes and naked singularities: the role of the redshift function
Néstor Ortiz, Olivier Sarbach, Thomas Zannias
arXiv:1401.4227 [gr-qc]

In this paper, the authors have studied if one can distinguish between black holes and naked singularities not by the light that is emitted from the object itself during collapse but by light from a different source that travels through the collapse region. They find that the luminosity curves of the two cases differ on a timescale that, for a stellar black hole, is about 10^-5s. In this work the authors do not evaluate if it is feasible to detect the difference with presently existing technology, but the signal does not seem hopelessly small.

The space-times that are considered in the above have a Cauchy-horizon, which is an interesting but also somewhat troubling concept which the cosmic censorship conjecture is supposed to avoid. The presence of the Cauchy-horizon basically means that after a certain moment in time you need additional initial data. You could interpret this as a classical instance of indeterminism. However, quantum gravity is generally expected to remove the singularity anyway, so don’t get too much of a headache over this. More interesting is the question if not the difference between the presence and absence of the horizon would be easier to detect if quantum gravitational effects were taken into account.

I am sure we will hear more about this in the soon future. Maybe we’ll even see it.