Stationary axisymmetric solutions of five dimensional gravity

TL;DR

This paper explores the symmetry transformations in five-dimensional gravity, demonstrating how static solutions can be transformed into rotating black holes like Myers-Perry, revealing a method to generate all stationary axisymmetric solutions.

Contribution

It identifies an SO(2,1) subgroup within the hidden SL(3,R) symmetry that generates stationary solutions with angular momentum from static solutions in five-dimensional gravity.

Findings

Derived Myers-Perry black hole from Schwarzschild solution.

Identified symmetry subgroup preserving boundary conditions.

Proposed a method to generate all stationary solutions.

Abstract

We consider stationary axisymmetric solutions of general relativity that asymptote to five dimensional Minkowski space. It is known that this system has a hidden SL(3,R) symmetry. We identify an SO(2,1) subgroup of this symmetry group that preserves the asymptotic boundary conditions. We show that the action of this subgroup on a static solution generates a one-parameter family of stationary solutions carrying angular momentum. We conjecture that by repeated applications of this procedure one can generate all stationary axisymmetric solutions starting from static ones. As an example, we derive the Myers-Perry black hole starting from the Schwarzschild solution in five dimensions.