119,398 research outputs found
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
Eta invariants with spectral boundary conditions
We study the asymptotics of the heat trace \Tr\{fPe^{-tP^2}\} where is
an operator of Dirac type, where is an auxiliary smooth smearing function
which is used to localize the problem, and where we impose spectral boundary
conditions. Using functorial techniques and special case calculations, the
boundary part of the leading coefficients in the asymptotic expansion is found.Comment: 19 pages, LaTeX, extended Introductio
Universal curvature identities
We study scalar and symmetric 2-form valued universal curvature identities.
We use this to establish the Gauss-Bonnet theorem using heat equation methods,
to give a new proof of a result of Kuz'mina and Labbi concerning the
Euler-Lagrange equations of the Gauss-Bonnet integral, and to give a new
derivation of the Euh-Park-Sekigawa identity.Comment: 11 page
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