3,484 research outputs found
Smooth metrics can hide thin shells
In this note, I consider a class of metric tensors with smooth components
that naively appear to describe dynamical wormholes with vanishing spacetime
curvature. I point out that the smoothness of the metric tensor components is
deceptive, and that in general relativity, such metrics must be sourced by
exotic thin shells.Comment: 2 pages, fixed typ
Linearised conformal Einstein field equations
The linearisation of a second-order formulation of the conformal Einstein
field equations (CEFEs) in Generalised Harmonic Gauge (GHG), with trace-free
matter is derived. The linearised equations are obtained for a general
background and then particularised for the study linear perturbations around a
flat background -- the inversion (conformal) representation of the Minkowski
spacetime -- and the solutions discussed. We show that the generalised Lorenz
gauge (defined as the linear analogue of the GHG-gauge) propagates. Moreover,
the equation for the conformal factor can be trivialised with an appropriate
choice for the gauge source functions; this permits a scri-fixing strategy
using gauge source functions for the linearised wave-like CEFE-GHG, which can
in principle be generalised to the nonlinear case. As a particular application
of the linearised equations, the far-field and compact source approximation is
employed to derive quadrupole-like formulae for various conformal fields such
as the perturbation of the rescaled Weyl tensor.Comment: 31 pages, 2 figures. Matches published versio
- …