Remark on the effective potential of the gravitational perturbation in the black hole background projected on the brane
arXiv:hep-th/0603028 · doi:10.1088/0264-9381/23/23/010
Abstract
The polar perturbation is examined when the spacetime is expressed by a 4d metric induced from higher-dimensional Schwarzschild geometry. Since the spacetime background is not a vacuum solution of 4d Einstein equation, the various general principles are used to understand the behavior of the energy-momentum tensor under the perturbation. It is found that although the general principles fix many components, they cannot fix two components of the energy-momentum tensor. Choosing two components suitably, we derive the effective potential which has a correct 4d limit.
12 pages, no figure, CQG accepted