nLab Kerr-Schild spacetime

Idea

A Kerr-Schild spacetime $(\mathbb{R}^{d,1}, g)$, is a spacetime which is deformation of Minkowski spacetime $(\mathbb{R}^{d,1}, \eta)$ whose pseudo-Riemannian metric is of the form

$$g_{\mu \nu} = \eta_{\mu \nu} + H \cdot k_\mu k_\nu$$

where $k$ is a lightlike vector field with respect to both metrics, and $H$ is any scalar function.

Related concepts

• classical double copy

References

The original article is

• Roy Kerr, Alfred Schild, Some algebraically degenerate solutions of Einstein’s gravitational field equations, Proc. Symp. Appl. Math 17, 199, 1965

Further developments:

• Tomáš Málek, Extended Kerr-Schild spacetimes: General properties and some explicit examples, Class. Quant. Grav. 31 185013 (2014) (arXiv:1401.1060)

See also

• Wikipedia, Kerr-Schild perturbation