Homogeneous plane-wave spacetimes and their stability

We consider the stability of spatially homogeneous plane-wave spacetimes. We carry out a full analysis for plane-wave spacetimes in (4 + 1) dimensions, and find there are two cases to consider, which we call non-exceptional and exceptional. In the non-exceptional case the plane waves are stable to (spatially homogeneous) vacuum perturbations as well as a restricted set of matter perturbations. In the exceptional case we always find an instability. Also we consider the Milne universe in arbitrary dimensions and find it is also stable provided the strong energy condition is satisfied. This implies that there exists an open set of stable plane-wave solutions in arbitrary dimensions.

[1]  J. Barrow,et al.  The future of tilted Bianchi universes , 2003, gr-qc/0304050.

[2]  C. G. Hewitt,et al.  Asymptotic dynamics of the exceptional Bianchi cosmologies , 2002, gr-qc/0211071.

[3]  D. Marolf,et al.  On the Singularity Structure and Stability of Plane Waves , 2002, hep-th/0210309.

[4]  P. Saffin,et al.  String theory and the classical stability of plane waves , 2002, hep-th/0210308.

[5]  S. Hervik.  Vacuum plane waves in 4+1 D and exact solutions to Einstein's equations in 3+1 D , 2002, gr-qc/0210080.

[6]  M. Hancock,et al.  Late-time asymptotic dynamics of Bianchi VIII cosmologies , 2002, gr-qc/0210031.

[7]  S. Hervik.  Multidimensional cosmology: spatially homogeneous models of dimension 4 + 1 , 2002, gr-qc/0207079.

[8]  R. R. Metsaev.  Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background , 2002 .

[9]  J. Maldacena,et al.  Strings in flat space and pp waves from ${\cal N}=4$ Super Yang Mills , 2002, hep-th/0202021.

[10]  R. D'Aoust.  Reports , 2002 .

[11]  L. Bianchi.  On the Three-Dimensional Spaces Which Admit a Continuous Group of Motions , 2001 .

[12]  G. Papadopoulos,et al.  A new maximally supersymmetric background of IIB superstring theory , 2001, hep-th/0110242.

[13]  A. Coley.  Dynamical Systems in Cosmology , 1999, gr-qc/9910074.

[14]  C. G. Hewitt.  An investigation of the dynamical evolution of a class of Bianchi VI−1/9 cosmological models , 1991 .

[15]  J. Barrow,et al.  Asymptotic stability of Bianchi type universes , 1986 .

[16]  J. Barrow,et al.  Stability of certain spatially homogeneous cosmological models , 1985 .

[17]  Jiří Patera,et al.  Subalgebras of real three‐ and four‐dimensional Lie algebras , 1977 .

[18]  R. T. Sharp,et al.  Invariants of real low dimension Lie algebras , 1976 .

[19]  A. Taub.  Empty Space-Times Admitting a Three Parameter Group of Motions , 1951 .

[20]  M. MacCallum.  On the Classification of the Real Four-Dimensional Lie Algebras , 1999 .

[21]  E. Schucking,et al.  On Einstein's path : essays in honor of Engelbert Schucking , 1998 .

[22]  G. Ellis,et al.  A class of homogeneous cosmological models , 1969 .