Brane world dynamics and conformal bulk fields

Abstract

In the Randall-Sundrum scenario we investigate the dynamics of a spherically symmetric 3-brane world when matter fields are present in the bulk. To analyze the 5-dimensional Einstein equations we employ a global conformal transformation whose factor characterizes the Z 2 symmetric warp. We find a new set of exact dynamical collapse solutions which localize gravity in the vicinity of the brane for a stress-energy tensor of conformal weight -4 and a warp factor that depends only on the coordinate of the fifth dimension. Geometries which describe the dynamics of inhomogeneous dust and generalized dark radiation on the brane are shown to belong to this set. The conditions for singular or globally regular behavior and the static marginally bound limits are discussed for these examples. Also explicitly demonstrated is complete consistency with the effective point of view of a 4-dimensional observer who is confined to the brane and makes the same assumptions about the bulk degrees of freedom.

Braneworlds, Conformal Fields and Dark Energy

“…For inhomogeneous dust, generalized dark radiation and homogeneous polytropic matter such solutions were determined in Refs. [16] and [23]. The latter describes the dynamics on the brane of dark energy in the form of a polytropic fluid.…”

“…In the RS1 model this is only possible if the radion mode is stabilized using for example a bulk scalar field [3,6,9,10]. Gravitational collapse was also analyzed in the RS scenario [11]- [16]. However, an exact 5D solution representing a stable black hole localized on a 3-brane has not yet been discovered.…”

“…So far, the only known static black holes localized on a brane remain to be those found for a 2-brane in a 4D AdS space [12]. A solution to this problem requires the non-singular localization of both gravity and matter [11,13]- [16] and could be connected to quantum black holes on the brane [15]. This is an extra motivation to look for 5D collapse solutions localized on a brane.…”

“…In our previous work [16,23] we have found a new class of exact 5D dynamical solutions for which gravity is localized near the brane by the exponential RS warp. These solutions were shown to describe on the brane the dynamics of inhomogeneous dust, generalized dark radiation and homogeneous polytropic matter.…”

“…In this paper we continue the research on the dynamics of a spherically symmetric RS 3-brane when 5D conformal matter fields propagate in the bulk [16,23] (see also [24]). In our previous work [16,23] we have found a new class of exact 5D dynamical solutions for which gravity is localized near the brane by the exponential RS warp.…”