5 research outputs found
Electromagnetic duality in general relativity
By resolving the Riemann curvature relative to a unit timelike vector into
electric and magnetic parts, we consider duality relations analogous to the
electromagnetic theory. It turns out that the duality symmetry of the Einstein
action implies the Einstein vacuum equation without the cosmological term. The
vacuum equation is invariant under interchange of active and passive electric
parts giving rise to the same vacuum solutions but the gravitational constant
changes sign. Further by modifying the equation it is possible to construct
interesting dual solutions to vacuum as well as to flat spacetimes.Comment: 18 pages, LaTEX versio
Gravito-electromagnetism
We develop and apply a fully covariant 1+3 electromagnetic analogy for
gravity. The free gravitational field is covariantly characterized by the Weyl
gravito-electric and gravito-magnetic spatial tensor fields, whose dynamical
equations are the Bianchi identities. Using a covariant generalization of
spatial vector algebra and calculus to spatial tensor fields, we exhibit the
covariant analogy between the tensor Bianchi equations and the vector Maxwell
equations. We identify gravitational source terms, couplings and potentials
with and without electromagnetic analogues. The nonlinear vacuum Bianchi
equations are shown to be invariant under covariant spatial duality rotation of
the gravito-electric and gravito-magnetic tensor fields. We construct the
super-energy density and super-Poynting vector of the gravitational field as
natural U(1) group invariants, and derive their super-energy conservation
equation. A covariant approach to gravito-electric/magnetic monopoles is also
presented.Comment: 14 pages. Version to appear in Class. Quant. Gra
Gravito-electromagnetic analogies
We reexamine and further develop different gravito-electromagnetic (GEM)
analogies found in the literature, and clarify the connection between them.
Special emphasis is placed in two exact physical analogies: the analogy based
on inertial fields from the so-called "1+3 formalism", and the analogy based on
tidal tensors. Both are reformulated, extended and generalized. We write in
both formalisms the Maxwell and the full exact Einstein field equations with
sources, plus the algebraic Bianchi identities, which are cast as the
source-free equations for the gravitational field. New results within each
approach are unveiled. The well known analogy between linearized gravity and
electromagnetism in Lorentz frames is obtained as a limiting case of the exact
ones. The formal analogies between the Maxwell and Weyl tensors are also
discussed, and, together with insight from the other approaches, used to
physically interpret gravitational radiation. The precise conditions under
which a similarity between gravity and electromagnetism occurs are discussed,
and we conclude by summarizing the main outcome of each approach.Comment: 60 pages, 2 figures. Improved version (compared to v2) with some
re-write, notation improvements and a new figure that match the published
version; expanded compared to the published version to include Secs. 2.3 and