Other
Scientific paper
May 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988phrvd..37.2803y&link_type=abstract
Physical Review D (Particles and Fields), Volume 37, Issue 10, 15 May 1988, pp.2803-2817
Other
25
Scientific paper
It is well known that when two precisely plane-symmetric gravitational waves propagating in an otherwise flat background collide, they focus each other so strongly as to produce a curvature singularity. This paper is the first of several devoted to almost-plane gravitational waves and their collisions. Such waves are more realistic than plane waves in having a finite but very large transverse size. In this paper we review some crucial features of the well-known exact solutions for colliding plane waves and we argue that one of these features, the breakdown of ``local inextendibility'' can be regarded as nongeneric. We then introduce a new framework for analyzing general colliding plane-wave spacetimes; we give an alternative proof of a theorem due to Tipler implying the existence of singularities in all generic colliding plane-wave solutions; and we discuss the fact that the recently constructed Chandrasekhar-Xanthopoulos colliding plane-wave solutions are not strictly plane symmetric and thus do not satisfy the conditions and the conclusion of Tipler's theorem. Our alternative proof of Tipler's theorem emphasizes the role and the necessity of strict plane symmetry in establishing the existence of singularities in colliding plane-wave spacetimes. However, we argue on the basis of previous work that the breakdown of strict plane symmetry as exhibited in the Chandrasekhar-Xanthopoulos solutions is a nongeneric phenomenon. We then propose a definition of general gravitational-wave spacetimes, of which almost-plane waves are a special case; and we develop some mathematical tools for studying them. An old result of Dautcourt implies that the only gravitational-wave spacetimes with a Killing propagation direction are plane fronted waves with parallel rays (PP waves); and we prove a new, related result, that only the gravitational-wave spacetimes with a precisely sandwiched curvature distribution are PP waves. These properties imply that almost-plane waves cannot propagate without diffraction, and that as opposed to the case for precisely plane waves, the curvature in an almost-plane-wave spacetime cannot be precisely sandwiched between two null surfaces (i.e., the wave must have tails). We also prove a ``peeling theorem'' for components of the Weyl curvature in general gravitational-wave spacetimes.
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