Description
I will discuss a recently proposed class of Generalized Lense–Thirring spacetimes in all dimensions. The class represent an ansatz for slowly rotating black holes which can be applied to solve the equations of motion, to linear order in the rotation parameters, for a wide variety of gravitational theories including Einstein--Gravity. In this case it is equivalent to the original Lense--Thiring solution to linear order. However, the class has the following remarkable properties which go beyond ordinary Lense--Thrring spacetimes: 1) It is regular on the horizon, 2) it can be put into Painlevé--Gullstrand (in-falling) coordinates, and most remarkably 3), it has a growing tower of hidden symmetries which in higher dimensions is greater than the number of explicit isometries. In this construction, the key ingredient is the non-commutativity of the underlying Killing vectors of the base space. The growing rank irreducible Killing tensors are determined by the structure constants of the corresponding Lie algebra. These hidden symmetries and the resultant constants of motion underpin the integrability and separability of test particles and fields in these spacetimes, thus allowing physical observables to be easily characterized.