The gravitational field of plane symmetric thick domain walls

Abstract

Exact solutions of Einstein’s equations for a scalar field with a potential V(Φ) =V0 cos2(1−n) (Φ/f(n)) (0<n<1) are presented describing the gravitational field of thick, plane symmetric domain walls. The scalar field has a time-independent kinklike distribution, whereas the metric depends on a time coordinate. The metric is conformally flat and the hypersurfaces parallel to the wall (z=const) are three-dimensional de-Sitter spaces. A particle horizon exists on which the metric becomes Minkowski space. It is shown that the gravitational field experienced by a test particle is repulsive.

Plane symmetric bulk viscous domain wall in Lyra geometry

“…After the original work by Vilenkin, Ipser and Sikivie [7,8] for thin walls, attempts focused on trying to find a perturbative expansion in the wall thickness [6,10]. With the proposition by Hill, Schramn and Fry [11] of a late phase transition with thick domain walls, there was some effort in finding exact thick solution [12,13]. Recently, Bonjour et al [14] considered gravitating thick domain wall solutions with planar and reflection symmetry in the Goldstone model.…”

“…A thick domain wall can be viewed as a soliton-like solution of the scalar field equation coupled with gravity. In order to determine the gravitational field one has to solve Einstein's equation with an energy momentum tensor T µν describing a scalar field φ with self-interactions contained in a potential V (φ) [6][7][8]12].…”

Plane Symmetric Domain Wall in Lyra Geometry

“…After the original work by Vilenkin, Ipser and Sikivie [7,8] for thin walls, attempts focused on trying to find a perturbative expansion in the wall thickness [10,6]. With the proposition by Hill, Schramn and Fry [11] of a late phase transition with thick domain walls, there was some effort in finding exact thick solution [12,13]. Recently, Bonjour et al [14] considered gravitating thick domain wall solutions with planar and reflection symmetry in the Goldstone model.…”

Exact Solution of a Test Particle in Presence of Thick Domain Walls

“…Many authors [5,6] have discussed non-static solutions of the Einstein scalar field equations for thick domain wall. In these solutions the energy scalar is independent of time while the metric tensor depends on both space and time.…”

“…Solution of equation (9) (11) we can determine A (z) and Φ (z) for a given V (Φ) [5] . For the case of Ricci tensor R ab = 0 we will solve equation's (10) and (11).…”