arXiv subjects

William Lesame

Publications and source records attributed to William Lesame.

3 recordsLinked to original sources

arXiv1999

Nonperturbative gravito-magnetic fields

In a cold matter universe, the linearized gravito-magnetic tensor field satisfies a transverse condition (vanishing divergence) when it is purely radiative. We show that in the nonlinear theory, it is no longer possible to maintain the transverse condition, since it leads to a non-terminating chain of integrability conditions. These conditions are highly restrictive, and are likely to hold only in models with special symmetries, such as the known Bianchi and $G_2$ examples. In models with realistic inhomogeneity, the gravito-magnetic field is necessarily non-transverse at second and higher order.

gr-qc↗

arXiv1998

Newtonian-like and anti-Newtonian universes

In an irrotational dust universe, the locally free gravitational field is covariantly described by the gravito-electric and gravito-magnetic tensors $E_{ab}$ and $H_{ab}$. In Newtonian theory, $H_{ab}=0$ and $E_{ab}$ is the tidal tensor. Newtonian-like dust universes in general relativity (i.e. with $H_{ab}=0$, often called `silent') have been shown to be inconsistent in general and unlikely to extend beyond the known spatially homogeneous or Szekeres examples. Furthermore, they are subject to a linearization instability. Here we show that `anti-Newtonian' universes, i.e. with purely gravito-magnetic field, so that $E_{ab} = 0\neq H_{ab}$, are also subject to severe integrability conditions. Thus these models are inconsistent in general. We show also that there are no anti-Newtonian spacetimes that are linearized perturbations of Robertson-Walker universes. The only $E_{ab}=0\neq H_{ab}$ solution known to us is not a dust solution, and we show that it is kinematically Gödel-like but dynamically unphysical.

gr-qc↗

arXiv1997

Consistency of dust solutions with div H=0

One of the necessary covariant conditions for gravitational radiation is the vanishing of the divergence of the magnetic Weyl tensor H_{ab}, while H_{ab} itself is nonzero. We complete a recent analysis by showing that in irrotational dust spacetimes, the condition div H=0 evolves consistently in the exact nonlinear theory.

gr-qc↗