118,758 research outputs found
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
On the existence of horizons in spacetimes with vanishing curvature invariants
A direct very simple proof that there can be no closed trapped surfaces (ergo
no black hole regions) in spacetimes with all curvature scalar invariants
vanishing is given. Explicit examples of the recently introduced ``dynamical
horizons'' which nevertheless do not enclose any trapped region are presented
too.Comment: 6 pages, no figure
Second-order symmetric Lorentzian manifolds
Lorentzian manifolds with vanishing second covariant derivative of the
Riemann tensor are studied. Their existence, classification and explicit local
expression are considered. Related issues and open questions are briefly
commented.Comment: 8 pages, Contribution to the Proceedings of the XXVIII Spanish
Relativity Meeting, E.R.E.2005 (Oviedo, Spain, 2005
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