Thick planar domain wall: its thin wall limit and dynamics

We consider a planar gravitating thick domain wall of the λϕ4 theory as a space–time with finite thickness glued to two vacuum space–times on each side of it. Darmois junction conditions written on the boundaries of the thick wall with the embedding space–times reproduce the Israel junction condition across the wall in the limit of infinitesimal thickness. The thick planar domain wall located at a fixed position is then transformed to a new coordinate system in which its dynamics can be formulated. It is shown that the wall's core expands as if it were a thin wall. The thickness in the new coordinates is not constant anymore and its time dependence is given.

[1]  R. Mansouri,et al.  Dynamics of General Relativistic Spherically Symmetric Dust Thick Shells , 2002, gr-qc/0308025.

[2]  A. Melfo,et al.  Self-gravitating domain walls and the thin-wall limit , 2002, gr-qc/0202011.

[3]  R. Gregory,et al.  Dynamics of curved gravitating walls , 2000, gr-qc/0002063.

[4]  L. Randall,et al.  An Alternative to compactification , 1999, hep-th/9906064.

[5]  L. Randall,et al.  A Large mass hierarchy from a small extra dimension , 1999, hep-ph/9905221.

[6]  R. Gregory,et al.  Thick domain wall universes , 1999, gr-qc/9902081.

[7]  Barrabès,et al.  Gravitational effects on domain walls with curvature corrections. , 1994, Physical review. D, Particles and fields.

[8]  A. Vilenkin,et al.  Topological inflation. , 1994, Physical review letters.

[9]  Larsen,et al.  Dynamics of cylindrical and spherical relativistic domain walls of finite thickness. , 1993, Physical review. D, Particles and fields.

[10]  M. Mukherjee.  Gravitational fields of cosmic membranes , 1993 .

[11]  Guenter Goetz.  The gravitational field of plane symmetric thick domain walls , 1990 .

[12]  Ren,et al.  Multipole expansion of conserved tensor currents and the number of form factors. , 1990, Physical review. D, Particles and fields.

[13]  Widrow.  General-relativistic domain walls. , 1989, Physical review. D, Particles and fields.

[14]  A. Vilenkin.  Gravitational field of vacuum domain walls , 1983 .

[15]  P. Sikivie,et al.  Gravitationally repulsive domain wall , 1983 .

[16]  A. Vilenkin.  Gravitational Field of Vacuum Domain Walls and Strings , 1981 .

[17]  W. Israel.  Singular hypersurfaces and thin shells in general relativity , 1966 .