3 years ago

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

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

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 described here class of spacetimes. 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 described here class of spacetimes may be not only a generic for the known solutions, for which the variables can be separated in the Klein-Gordon and Hamilton-Jacobi equations, but also a good approximation for a broader class of metrics, which does not allow for such a 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 parameterizations is discussed.

Publisher URL: http://arxiv.org/abs/1801.07195

DOI: arXiv:1801.07195v2

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