One of the most intriguing predictions of Einstein’s Theory of General Relativity is the formation of spacetime singularities. These are essentially regions of space and time where gravity, as manifested by spacetime curvature, becomes inconceivably strong that the theory itself and all the known laws of physics break down. Theoretically speaking, such singularities reside, for example, inside black holes, which are ubiquitous in the cosmos. These singularities would be interesting to observe, if for anything else, to guide us on how to extend the laws of physics in such regimes. But, alas, these singularities are well-hidden behind black hole event horizons, which do not allow anything to escape. It is of great interest then whether or not such singularities can ever be observable from the outside world. Can they ever be “naked”?
The so-called Cosmic Censorship Hypothesis asserts that such “naked singularities” cannot form from reasonably physical initial conditions. This conjecture however remains unproven, and is one of the biggest unsettled questions of classical relativity theory.
On the other hand, there do exist spacetimes not too different from black hole spacetimes that actually represent naked singularities. One is an “overcharged” Reissner-Nordstrom (RN) solution. This solution typically represents a charged non-rotating black hole. This is so only when its charge isn’t too big. More specifically, if the black hole’s charge isn’t greater than its mass. But one can imagine throwing charges into the black hole and “overcharging” it. If one is capable of doing this then the Reissner-Nordstrom solution turns from black hole into a naked singularity, leaving an “overcharged” RN spacetime. Such a simple scenario has been contemplated for many years, but with the unfolding story seeming to uphold cosmic censorship. Basically, as one gets closer to overcharging the black hole, the repulsion between the black hole and the succeeding charges gets stronger, and this repulsion ends up protecting the black hole.
In the paper “Overcharging higher-dimensional black holes with point particles,” Karl Simon Revelar and Dr. Ian Vega of the National Institute of Physics sought to contribute to this narrative by investigating what happens in higher dimensions, which is a popular hypothesis in various fields of theoretical physics. They asked: Can overcharging occur in higher-dimensional black holes? Is Cosmic Censorship also upheld in this context? How does the number of dimensions impact the basic scenario? Does increased dimensionality aid or oppose overcharging?
Using the spherically-symmetric charged Tangherlini-Schwarzschild solution, the researchers studied the dynamics of an in-falling charged particle. They showed that much like in four dimensions, there is a small region of parameter space that does allow for overcharging. However, this parameter region gets smaller and smaller as one increases the number of spacetime dimensions.
According to the authors, “there are indications that the self-force in higher dimensions gets divergently repulsive as the particle approaches the horizon, which would mean that none of the charged particles we identify as overcharging do, in fact, cross the horizon. However, the matter is far from settled. It would be interesting to see how this story unfolds, as self-force calculations in higher dimensions mature to the state that has been reached [in four dimensions]. We leave this problem for future work.”
Vega is a recipient of the Balik-PhD grant managed by the Office of the Vice President for Academic Affairs.
(Article written by Karl Simon Revelar and Ian Vega)