n-DBI gravity, maximal slicing and the Kerr geometry

TL;DR

This paper shows that the Kerr black hole solution in Einstein's gravity also solves n-DBI gravity when using maximal slicing, linking a common numerical relativity technique to a modified gravity theory.

Contribution

It demonstrates that the Kerr geometry satisfies n-DBI gravity equations under maximal slicing, extending the class of known solutions in this modified gravity framework.

Findings

Kerr geometry is a solution of n-DBI gravity in Boyer-Lindquist coordinates.

Maximal slicing fulfills the geometric condition for solutions of n-DBI gravity.

The work connects numerical relativity techniques with modified gravity solutions.

Abstract

Recently, in arXiv:1110.0832, we have established that solutions of Einstein's gravity admitting foliations with a certain geometric condition are also solutions of n-DBI gravity, arXiv:1109.1468. Here we observe that, in vacuum, the required geometric condition is fulfilled by the well known maximal slicing, often used in numerical relativity. As a corollary, we establish that the Kerr geometry is a solution of n-DBI gravity in the foliation adapted to Boyer-Lindquist coordinates.