Static magnetic dipole solutions of Einstein–Maxwell equations from the soliton solutions of a Kerr object

Abstract

Using the solution generating techniques of Das and Chaudhuri (Pramana J. Phys. 40, 277 (1993); Pramana J. Phys. 58, 449 (2002)), static magnetovac solutions of Einstein–Maxwell equations in general relativity are constructed from the stationary gravitational soliton solutions of Einstein's field equations corresponding to a Kerr object. The techniques followed in the present paper have not been much used in the literature so far although the results are obtained in a straightforward way. The stationary gravitational two-soliton solutions of Einstein's field equations for a Kerr object are generated using the soliton technique of Belinskii and Zakharov (Sov. Phys. JETP 48, 985 (1978); Sov. Phys. JETP 50, 1 (1979)). In the next step, following the procedure of Das and Chaudhuri, mentioned above, static magnetovac solutions of Einstein–Maxwell field equations corresponding to the generated stationary two-soliton solutions of the Kerr object are constructed. The solutions are found to be well behaved at spatial infinity and contain monopole, dipole, and other higher mass multipoles. The mass and the dipole moment of the source are evaluated. It is shown that by redefining some constants appearing in the solutions, Bonnor's (Z. Phys. 190, 444 (1966)) magnetic dipole solutions are faithfully reproduced.