Volume 141, number 5,6 PHYSICS LETFERS A 6 November 1989 GRAVITATIONAL INTERACTION OF MASSLESS PARTICLES Valeria FERRARI International Centerfor Relativistic Astrophysics — ICRA, Dipartimento di Fisica “G. Marconi’~ Università di Roma, Rome, Italy and Jesus IBAREZ’ Departamento de Fisica, Universidad de Las Islas Baleares, Spain Received 21 June 1989; revised manuscript received 31 July 1989; accepted for publication 6 September 1989 Communicated by J.P. Vigier An exact solution of non-vacuum Einstein equations describing the collision of two clouds of null particles and their consequent gravitational interaction is presented. As a result, a source is produced which satisfies the Klein—Gordon equation for massless scalar fields, and a physical singularity finally appears. The gravitational interaction of colliding shells of coupled to the dust, and that a source can be pro- null dust has been recently investigated by duced which behaves, at a macroscopical level, as a Chandrasekhar and Xanthopoulos [1,2], and by fluid with an equation of state different from p = Dray and ‘t Hooft [3]. In refs. [1] and [2], the null and with an anisotropic distribution of pressure, dust flies in flat spacetime following the leading edges being the components orthogonal to the direction of of impulsive gravitational waves, and the collision propagation different from the parallel component. produces a region of interaction where either a mix- The energy—momentum tensor satisfies the strong ture of null dust moving in opposite directions is energy conditions. Unlike the solutions quoted be- present, or a perfect fluid in which the energy density fore, the metric is continuous with its first deriva- ~t is equal to the pressure p. The presence of different tives, therefore no impulsive waves are present on the fluids in the region of interaction, is due, as clarified null hypersurfaces separating different regions. by Taub [4,51, to different assumptions on the en- A physical singularity develops in the region of ergy—momentum tensor, which specify the nature of interaction. the interaction. In ref. [3] the collision of two im- One might ask how is it possible that the gravi- pulsive planar shells of null dust has been considered, tational interaction of null dust can produce a so large with a result similar to that described in ref. [1]. variety of sources, and whether these solutions really One of the most remarkable consequences of the represent the interaction of some fields, and we shall interaction of null dust, is the possibility, shown in try to answer this question. ref. [21, of a gravitationally induced transformation The null dust is defined by the following energy— of massless particles, describing null trajectories, into momentum tensor: a perfect fluid, although with a peculiar equation of T~V — ~ )k~k~ (1) state. We shall show in this paper that a similar transi- where E is a positive function of a null coordinate u tion can occur also when no gravitational waves are representing the energy of the dust, and k’~ is a null vector. This definition presents an intrinsic ambi- Guest of the Department of Physics of the University of Rome. guity, since the energy—momentum tensor (1) can 0375-960l/89/$ 03.50 © Elsevier Science Publishers B.V. 233 (North-Holland Physics Publishing Division)