2,088 research outputs found
Existence of Frequency Modes Coupling Seismic Waves and Vibrating Tall Buildings
We prove in this paper an existence result for frequency modes coupling
seismic waves and vibrating tall buildings. The derivation from physical
principles of a set of equations modeling this phenomenon was done in previous
studies. In this model all vibrations are assumed to be anti plane and time
harmonic so the two dimensional Helmholtz equation can be used. A coupling
frequency mode is obtained once we can determine a wavenumber such that the
solution of the corresponding Helmholtz equation in the lower half plane with
relevant Neumann and Dirichlet at the interface satisfies a specific integral
equation at the base of an idealized tall building. Although numerical
simulations suggest that such wavenumbers should exist, as far as we know, to
date, there is no theoretical proof of existence. This is what this present
study offers to provide.Comment: 20 pages, 3 figure
Giant wormholes in ghost-free bigravity theory
We study Lorentzian wormholes in the ghost-free bigravity theory described by
two metrics, g and f. Wormholes can exist if only the null energy condition is
violated, which happens naturally in the bigravity theory since the graviton
energy-momentum tensors do not apriori fulfill any energy conditions. As a
result, the field equations admit solutions describing wormholes whose throat
size is typically of the order of the inverse graviton mass. Hence, they are as
large as the universe, so that in principle we might all live in a giant
wormhole. The wormholes can be of two different types that we call W1 and W2.
The W1 wormholes interpolate between the AdS spaces and have Killing horizons
shielding the throat. The Fierz-Pauli graviton mass for these solutions becomes
imaginary in the AdS zone, hence the gravitons behave as tachyons, but since
the Breitenlohner-Freedman bound is fulfilled, there should be no tachyon
instability. For the W2 wormholes the g-geometry is globally regular and in the
far field zone it becomes the AdS up to subleading terms, its throat can be
traversed by timelike geodesics, while the f-geometry has a completely
different structure and is not geodesically complete. There is no evidence of
tachyons for these solutions, although a detailed stability analysis remains an
open issue. It is possible that the solutions may admit a holographic
interpretation.Comment: 26 pages, 6 figures, section 8.2 describing the W1b wormhole geometry
is considerably modifie
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