Small deformations of extreme five dimensional Myers-Perry black hole initial data

TL;DR

This paper constructs a family of initial data sets for five-dimensional vacuum Einstein equations, representing small deformations of the extreme Myers-Perry black hole while preserving key geometric features.

Contribution

It introduces a one-parameter family of initial data with specific symmetries that extend previous results to five dimensions and extreme black hole solutions.

Findings

Existence of a one-parameter family of initial data for 5D extreme Myers-Perry black holes.

Preservation of angular momenta and horizon geometry in the deformations.

Extension of previous 4D results to higher dimensions.

Abstract

In this note we demonstrate the existence of a one-parameter family of initial data for the vacuum Einstein equations in five dimensions representing small deformations of the extreme Myers-Perry black hole. This initial data set has `$t-\phi^i$' symmetry and preserves the angular momenta and horizon geometry of the extreme solution. Our proof is based upon an earlier result of Dain and Gabach-Clement concerning the existence of $U(1)$-invariant initial data sets which preserve the geometry of extreme Kerr (at least for short times)