String Gyratons in Supergravity

In this paper we study solutions of supergravity equations generated by string-like sources moving with the speed of light. Study of solutions of the Einstein equations for objects moving with the velocity of light has long story. In 1934 Tolman [1] obtained solutions for the gravitational field of beams of light in the linear approximation. The exact solutions of the non-linear Einstein equations for this problem were obtained later [2–4]. For the infinitely small cross-section of the beam and for the delta-type distribution of the light-pulse in time, these solutions reduce to the Aichelburg-Sexl metric [5]. These 4-dimensional solutions were generalized to the case the matter of beam is either charged or spinning by Bonnor [6, 7] in 1970. Higher-dimensional generalizations of the solutions of Einstein equations for spinning relativistic beam-like sources (gyratons) were obtained and studied in [8, 9]. Solutions for charged higher-dimensional gyratons and for gyratons moving in an asymptotically anti-de Sitter space were found in [10] and [12], respectively. The aim of this paper is to discuss generalization of electrically charged gyraton solutions to the theory of supergravity. More concretely, we study solutions of higher-dimensional gravitational equations with the rank 3 antisymmetric Kalb-Ramon field generated by stringlike sources moving with the velocity of light. The basic equations, the metric and field ansatz are presented in sections 2 and 3, respectively. In section 4 we demonstrate, that the field equations for the problem under consideration reduce to the set of linear equations in a flat Euclidean space. Special solutions of these equations for rink-like string gyratons are obtained in section 5. Section 6 contains brief summary and discussions.