Although this surface extends infinitely to the right, its cross-sectional radius tends to zero sufficiently quickly, such that its total surface area remains finite.
It might seem at first that pseudospheres are just mathematical curiosities. However, Prof Edward TEO and Dr CHEN Yu at the Department of Physics, NUS have recently found that there exist black holes whose event horizons have a similar shape to pseudospheres, as illustrated below:
Like a pseudosphere, the event horizon extends infinitely to the right, but has a finite total area. The only difference is that the base of the pseudosphere (left edge in the first figure above) has been closed up to form a rounded bottom. Because their shape resembles bottles, these black holes have been named “black bottles”.
Why is a finite horizon area significant? It is because the horizon area is proportional to the entropy of the black hole. The fact that black bottles have finite horizon area means that their entropy is also finite. This implies that there is a finite amount of information hidden inside these infinitely extended objects. Up to now, there is only one other type of black hole known with this very unusual property. It was discovered by D. KLEMM in 2014, and is essentially two identical pseudospheres joined at their bases, and spun into rotation.
Black bottles do not exist in normal space, but in a space with a negative cosmological constant known as anti-de Sitter space. Although we do not live in anti-de Sitter space, the study of black holes in anti-de Sitter space has gained importance in modern day theoretical physics because of the so-called anti-de Sitter / conformal field theory correspondence. This correspondence allows physicists to use black holes in anti-de Sitter space to understand other systems more closely related to the real world, such as heavy-ion collisions and high-temperature superconductors.
Their current work is focused on further understanding the properties of the black bottle, as well as possible applications of it using the anti-de Sitter/ conformal field theory correspondence.
Reference
ChenY; Teo E, “Black holes with bottle-shaped horizons.” PHYSICAL REVIEW D Volume: 93 Issue: 12 Article Number: 124028 DOI: 10.1103/PhysRevD.93.124028 Published: 2016
