# Conformally flat spaces admitting complete separation of variables in the eikonal equation

* V.V. Obukhov, K.E. Osetrin and Yu.A. Rybalov*^{1}

(1) Tomsk State Pedagogical University, Tomsk, Russia

### Abstract

A classification of conformally flat space-times, admitting complete separation of variables in the eikonal equation, is carried out. The metric tensors, corresponding to different complete sets of integrals of motion, are found. With these metrics, as an example, some solutions to the Einstein equations with a cosmological constant are obtained. For the space-times obtained, examples of integration of the eikonal and scalar field equations are presented.

### References

- V. G. Bagrov, V. V. Obukhov, and K. E. Osetrin, Isotropic conformally Stackel metrics of conformally flat space-times, Izv. VUZov, Fizika, 1998, No. 11, 92-96.
- A. N. Makarenko and K. E. Osetrin, Conformally Stackel metrics of Einstein spaces, Izv. VUZov, Fizika, 1999, No. 10, 34-43.
- V. V. Obukhov and K. E. Osetrin, Variables separation in gravity, 4th Int. Winter Conf. on Mathematical Methods in Physics (WC 2004), Rio de Jeneiro, Brazil, 9-13 Aug. 2004, PoS WC 2004: 027, 2004.
- K. E. Osetrin, V. V. Obukhov, and A. E. Filippov, Homogeneous spacetimes and separation of variables in the Hamilton-Jacobi equation, J. Phys. A 39, 6641-6647 (2006).

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