Analytic extension in colliding waves with NUT parameter, Yang-Mills fields and extra dimen.pdf

a r X i v : 0 7 0 7 .1 9 4 5 v 1 [ g r - q c ] 1 3 J u l 2 0 0 7 Analytic extension in colliding waves with NUT parameter, Yang-Mills fields and extra dimensions Ozay Gurtug? and Mustafa Halilsoy? Department of Physics, Eastern Mediterranean University, G. Magusa, north Cyprus, via Mersin 10, Turkey. Abstract The Cauchy horizon forming colliding wave solution due to Chandrasekhar and Xanthopoulos (CX) has been generalized by inclusion of the NUT ( Newman - Unti - Tamburino) parameter. This is done by transforming the part of the inner horizon region of a Kerr-Newman-NUT black hole into the space of colliding waves. By taking appropriate combination of Killing vectors and analytically extending beyond the Cauchy horizon the time-like hyperbolic sigularities are resolved as well. This provides another example of its kind among the type - D metrics with special emphasis on the role of the NUT parameter. By applying a non-Abelian gauge transformation we show that the same CX metric describes also collision of Einstein-Yang-Mills (EYM) plane waves with cross polarization. Finally, it is shown that horizons of colliding higher dimensional plane waves obtained from the black p-branes undergoes a similar procedure of analytic extension. ?Electronic address: ozay.gurtug@emu.edu.tr ?Electronic address: mustafa.halilsoy@emu.edu.tr 1 I. INTRODUCTION Colliding gravitational waves (CGW) in general relativity constitutes one of the out- standing subjects that nonlinear effects of the Einstein’s theory of relativity are manifestly displayed. The prototype exact solutions suggested that when two plane gravitational waves collide, they focus each other in a way that after a finite time from the instant of the collision, a space-time singularity develops [1]. In contrast to this view, exceptional solutions were found which do not exhibit curvature singularities; instead, they develop Killing - Cauchy horizons [2]. Under what conditions the collision of waves produce a space-ti