139 research outputs found
Equations for general shells
The complete set of (field) equations for shells of arbitrary, even changing,
causal character are derived in arbitrary dimension. New equations that seem to
have never been considered in the literature emerge, even in the traditional
cases of everywhere non-null, or everywhere null, shells. In the latter case
there arise field equations for some degrees of freedom encoded exclusively in
the distributional part of the Weyl tensor. For non-null shells the standard
Israel equations are recovered but not only, the additional relations
containing also relevant information. The results are applicable to a
widespread literature on domain walls, branes and braneworlds, gravitational
layers, impulsive gravitational waves, and the like. Moreover, they are of a
geometric nature, and thus they can be used in any theory based on a Lorentzian
manifold.Comment: 32 pages, no figures. New paragraph and new footnote, plus some added
references. Version to be publishe
The universal 'energy' operator
The "positive square" of any tensor is presented in a universal and unified
manner, valid in Lorentzian manifolds of arbitrary dimension, and independently
of any (anti)-symmetry properties of the tensor. For rank-m tensors, the
positive square has rank 2m. Positive here means future, that is to say,
satisfying the dominant property. The standard energy-momentum and super-energy
tensors are recovered as appropriate parts of the general square. A richer
structure of principal null directions arises.Comment: 13 pages, no figures; minor improvements and corrections. This is a
larger, expanded version, containing proofs and explanations not available in
the short Note to be published in CQ
Double layers in gravity theories
Gravitational double layers, unlike their classical electromagnetic
counterparts, are thought to be forbidden in gravity theories. It has been
recently shown, however, that they are feasible in, for instance, gravity
theories with a Lagrangian quadratic in the curvature. This is surprising with
many potential consequences and the possibility of new physical behaviours.
While a clear interpretation seems elusive, several lines of research are open.
I present the field equations for double layers, the new physical quantities
arising, and several explicit examples.Comment: 11 pages, no figures. Invited talk at the Spanish Relativity Meeting
2014 (ERE-2014), submitted to its Proceeding
- …