Generalized Lense-Thirring spacetimes: higher curvature corrections and solutions with matter

Generalized Lense-Thirring spacetimes: higher curvature corrections and solutions with matter

The Lense-Thirring spacetime describes a 4-dimensional slowly rotating approximate
solution of vacuum Einstein equations valid to a linear order in rotation parameter.
It is fully characterized by a single metric function of the corresponding static
(Schwarzschild) solution. We shall discuss a generalization of the Lense-Thirring
spacetimes to the case that is not necessarily fully characterized by a single (static)
metric function. This generalization lets us study slowly rotating spacetimes in
various higher curvature gravities as well as in the presence of non-trivial matter
such as non-linear electrodynamics.  In particular, we construct slowly multiply-spinning
solutions in Lovelock gravity and notably show that in four dimensions Einstein gravity is
the only non-trivial theory amongst all up to quartic curvature gravities that
admits a Lense-Thirring solution characterized by a single metric function.
We will also show discuss a `magic square' version of our ansatz and show that it
can be cast in the Painlevé-Gullstrand form (and thence is manifestly regular on
the horizon) and admits a tower of exact rank-2 and higher rank Killing tensors
that rapidly grows with the number of dimensions.