Axisymmetric black holes allowing for separation of variables in the Klein-Gordon and Hamilton-Jacobi equation

Understand

We determine the class of axisymmetric and asymptotically flat black-hole spacetimes for which the test Klein-Gordon and Hamilton-Jacobi equations allow for the separation of variables.

• The known Kerr, Kerr-Newman, Kerr-Sen and some other black-hole metrics in various theories of gravity are within the class of spacetimes described here.
• It is shown that although the black-hole metric in the Einstein-dilaton-Gauss-Bonnet theory does not allow for the separation of variables (at least in the considered coordinates), for a number of applications it can be effectively approximated by a metric within the above class.
• This gives us some hope that the class of spacetimes described here may be not only generic for the known solutions allowing for the separation of variables, but also a good approximation for a broader class of metrics, which does not admit such separation.