Cosmic censorship: Hiding naked singularities

A mathematician from the National University of Singapore (NUS) has made a significant breakthrough in understanding cosmic censorship in our universe.

A naked singularity is an unusual object in our universe. In general relativity, a naked singularity refers to a theoretical gravitational singularity that is not hidden behind a black hole region, meaning it is exposed and visible to distant observers. The existence of naked singularities challenges our fundamental understanding of the nature of spacetime. According to the weak cosmic censorship conjecture, first proposed by Roger PENROSE in 1969, nature would prevent the stable formation of naked singularities, ensuring that generic singularities are cloaked by the black hole region and singular information is invisible to outside observers.

To study this conjecture, Christodoulou constructed a mathematical example of a naked-singularity solution to Einstein’s field equations in 1994. Later, in 1999, he further proved that within spherical symmetry, his constructed naked-singularity example is associated with 2 unstable directions.

In a 90-page sole-author paper, “Naked singularity censoring with anisotropic apparent horizon” soon to appear in the journal, Annals of Mathematics, Assistant Professor AN Xinliang from the Department of Mathematics at NUS extended this result by removing the aforementioned spherically symmetric condition. He proved that Christodoulou’s naked singularity is always associated with a co-dimensional 2K nonlinear instability, with K being any positive integer (previously, only K = 1 was known). Intuitively, this new result means that even a tiny perturbation of the naked-singularity initial data from any angle would lead to a blue-shift effect and eventually form an anisotropic apparent horizon (the boundary of the black hole) to hide the naked singularity. This means that nature inherently prevents the visibility of naked singularities, reinforcing the cosmic censorship conjecture.

This work by Prof An greatly expands the understanding of naked-singularity instability mechanism to the fully anisotropic scenario, marking a major advancement in the study of the weak cosmic censorship conjecture.

Illustration showing how a small disturbance creates an anisotropic apparent horizon, covering the naked singularity at point 𝑂 and preventing it from being seen.

Reference

X. An*, “Naked singularity censoring with anisotropic apparent horizon”, 90 pages, to appear in Annals of Mathematics.