Physics is the attempt to describe, predict and understand a vast range of phenomena in nature, — ranging from elementary particles to the entire Universe — in terms of mathematical expressions and equations. One of the most astonishing physical theories is Einstein’s general relativity (GR) that describes the gravitational interaction between all kinds of objects in terms of differential geometry and, ultimately, differential equations. One of most dreaded features in any kind of theory are so-called singularities, i.e. points where the physical system can no longer be described in terms of finite numbers. Famous examples include the big bang or the centre of black holes where curvature and mass-energy acquire infinite values. Singularities are dreaded because our physical theories lose their predictive power at these points. One of the most astonishing properties of GR is its prediction — the Hawking-Penrose singularity theorems — that seemingly innocent physical systems can form singularities; for example a sufficiently heavy star will end its life by collapsing to a black hole. In principle, this feature calls into question the predictive power of Einstein’s theory. The situation seems to be rescued, however, by Penrose’s Weak Cosmic Censorship Conjecture, which proposes that singularities formed in dynamical evolution must be hidden inside black-hole horizons. Through active investigation in over half a century, counter-examples to cosmic censorship in settings beyond astrophysics have been found, which can be regarded as a possibility to access the quantum regime of gravity, at least theoretically. They fall into two major categories: i) critical collapse, which involves fine tuning of initial data such that a zero-mass singularity is formed; ii) death by fragmentation, which results from elongated horizons becoming unstable and eventually pinching off in finite time.

Figure: Snapshots from the simulation of two black holes colliding at half the speed of light in 7 spacetime dimensions. The elongated horizons forming in this collision evolve into multiple generations of satellites connected by ever thinner string segment that ultimately pinch off, forming a naked singularity. The full animation is available on .

All these setups, however, have in common that the initial state is either arbitrarily improbable or already represents an inherently unstable configuration. One may thus wonder if the so-obtained singularities are a truly generic feature of the evolution in GR. In our work, we have explored a new and truly generic mechanism for violation of cosmic censorship: the collision of black holes in higher dimensions. The figure shows snapshots from such a simulation, performed with the GRChombo code, of two black holes approaching each other with half the speed of light in 7 spacetime dimensions (upper left). At time zero, they merge into a single peanut-shaped black hole (upper right) which then evolves into an increasingly elongated horizon (centre left). The resulting “neck” grows ever thinner (centre right) and develops local satellite bulges through a mechanism known as the Gregory-Laflamme instability (bottom left). This phenomenon repeats itself along the ever thinner string segments connecting the second-generation bulges (bottom right), leading to a cascade into ever thinner string segments that ultimately pinch off, leading to a so-called naked singularity, i.e. a singular point that is not veiled by a black-hole horizon. We observe this behaviour over a wide range of initial conditions in 6 and 7 spacetime dimensions, but never in 4 dimensions, where black-hole collisions ubiquitously obey Penrose’s Cosmic Censorship. It appears that the 4 spacetime dimensions we live in represent a particularly benign setup not only for GR, but also for those who exist in it.

Categories: 2021 Highlights