Spherically Symmetric Solutions and Dark Matter on the Brane

Abstract

It has recently been suggested that our universe is a three-brane embedded in a higher dimensional spacetime. In this paper I examine static, spherically symmetric solutions that satisfy the effective Einstein field equations on a brane embedded in a five dimensional spacetime. The field equations involve a term depending on the five dimensional Weyl tensor, so that the solutions will not be Schwarzschild in general. This Weyl term is traceless so that any solution of ${}^{(4)}R=0$ is a possible four dimensional spacetime. Different solutions correspond to different five dimensional spacetimes and to different induced energy-momentum tensors on the brane. One interesting possibility is that the Weyl term could be responsible for the observed dark matter in the universe.

5 pages, LATEX

References in corpus (3)

• The Einstein Equations on the 3-Brane World
• Black holes on the brane
• Gravity, Stability and Energy Conservation on the Randall-Sundrum Brane-World

Cited by in corpus (4)

• Dark Matter Detection in the Light of Recent Experimental Results
• Possible wormholes in a brane world
• Schwarzschild Solution on the Brane
• Gravitational Geons on the Brane