Are There Four-Dimensional Small Black Rings?

TL;DR

The paper investigates the possibility of small black rings in four dimensions, concluding that stringy corrections prevent their existence and invalidate classical theorems that rule out toroidal black holes in four-dimensional spacetime.

Contribution

It demonstrates that scaling arguments used for higher dimensions do not apply in four dimensions due to dominant stringy corrections, challenging classical black hole topology theorems.

Findings

Scaling arguments fail for d=4 due to stringy corrections.

Classical theorems prohibiting toroidal black holes do not hold when string effects are considered.

Stringy corrections are crucial in understanding black hole topology in four dimensions.

Abstract

In d>4 dimensions, one can argue for the existence of small black rings using a scaling argument. We apply the same scaling argument to the d=4 case and demonstrate that it fails to say anything about the existence of d=4 small black rings, because stringy corrections get out of control. General relativity theorems say that there does not exist a black hole with toroidal topology for d=4, but we interpret this as saying that, for d=4 small black rings, stringy corrections are crucial which invalidate the assumptions those theorems are based on.