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Remark on the effective potential of the gravitational perturbation in the black hole background projected on the brane
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.Comment: 12 pages, no figure, CQG accepte
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