Axisymmetric black holes allowing for separation of variables in the KleinGordon and HamiltonJacobi equations
Abstract
We determine the class of axisymmetric and asymptotically flat blackhole spacetimes for which the test KleinGordon and HamiltonJacobi equations allow for the separation of variables. The known Kerr, KerrNewman, KerrSen and some other blackhole metrics in various theories of gravity are within the class of spacetimes described here. It is shown that although the blackhole metric in the EinsteindilatonGaussBonnet 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 blackhole parametrizations is discussed.
 Publication:

Physical Review D
 Pub Date:
 April 2018
 DOI:
 10.1103/PhysRevD.97.084044
 arXiv:
 arXiv:1801.07195
 Bibcode:
 2018PhRvD..97h4044K
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 14 pages