On the Collision of Impulsive Gravitational Waves when Coupled with Fluid Motions

• Published in: Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1985-12, Vol.402 (1822), p.37-65
• Main Authors: Chandrasekhar, Subrahmanyan, Xanthopoulos, Basilis C.
• Format: Article
• Language: English
• Subjects: Coordinate systems; Equations of state; Exact sciences and technology; General relativity and gravitation; Gravitational waves; Mathematical constants; Mathematical discontinuity; Mathematical expressions; Physics; Scalars; Self-graviting systems; continuous media and classical fields in curved spacetime; Sound waves; Spacetime; Tensors
• ISSN: 1364-5021; 0080-4630; 1471-2946; 2053-9169
• DOI: 10.1098/rspa.1985.0107

An exact solution of Einstein’s equations, with a source derived from a perfect fluid in which the energy density, ε, is equal to the pressure, p, is obtained. The solution describes the space–time following the collision of plane impulsive gravitational waves and is the natural generalization of the Nutku─Halil solution of the vacuum equations, in the region of interaction under similar basic conditions. A consistent extension of the solution, prior to the instant of collision, requires that the fluid in the region of interaction is the direct result of a transformation of incident null-dust (i. e. of massless particles describing null trajectories). The ultimate result of the collision is the development of a space─time singularity, the nature of which is strongly dependent on the amplitude and the character of the sound waves that are present. The distribution of ε that follows the collision has many intriguing features. The solution obtained in this paper provides the first example of an induced transformation of a massless into a massive particle.