**Publication date:** Apr 2018

**Abstract:**

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. Finally, the generic form of the

axisymmetric metric is expanded in the radial direction in terms of the

continued fractions and the connection with other black-hole

parametrizations is discussed.

**Authors:**

Konoplya, R. A.; Stuchlík, Z.; Zhidenko, A.;