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.

26 pages, latex, no figures. Minor revisions. Some references added. Revised version to appear in Phys. Rev. D

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• Regular Bulk Solutions in Brane-worlds with Inhomogeneous Dust and Generalized Dark Radiation
• On finite time singularities in scalar field dark energy models based in the RS-II Braneworld
• Brane Dynamics, the Polytropic Gas and Conformal Bulk Fields
• Braneworlds and Dark Energy
• Brane World Black Rings
• Vacuum Polarization in an Anti-de Sitter Space as an Origin for a Cosmological Constant in a Brane World
• Braneworlds, Conformal Fields and the Gravitons
• Modified Gravity on the Brane and Dark Energy