2 research outputs found
Rigorous Formulation of Duality in Gravitational Theories
In this paper we evince a rigorous formulation of duality in gravitational
theories where an Einstein like equation is valid, by providing the conditions
under which the Hodge duals (with respect to the metric tensor g) of T^a and
R_b^a may be considered as the torsion and curvature 2-forms associated with a
connection D', part of a Riemann-Cartan structure (M,g',D'), in the cases g =
g' and g does not equal g', once T^a and R_b^a are the torsion and curvature
2-forms associated with a connection D part of a Riemann-Cartan structure
(M,g,D). A new form for the Einstein equation involving the dual of the Riemann
tensor of D is also provided, and the result is compared with others appearing
in the literature.Comment: 15 page
Relaxing the Parity Conditions of Asymptotically Flat Gravity
Four-dimensional asymptotically flat spacetimes at spatial infinity are
defined from first principles without imposing parity conditions or
restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a
correct variational principle when it is supplemented by an anomalous
counter-term which breaks asymptotic translation, supertranslation and
logarithmic translation invariance. Poincar\'e transformations as well as
supertranslations and logarithmic translations are associated with finite and
conserved charges which represent the asymptotic symmetry group. Lorentz
charges as well as logarithmic translations transform anomalously under a
change of regulator. Lorentz charges are generally non-linear functionals of
the asymptotic fields but reduce to well-known linear expressions when parity
conditions hold. We also define a covariant phase space of asymptotically flat
spacetimes with parity conditions but without restrictions on the Weyl tensor.
In this phase space, the anomaly plays classically no dynamical role.
Supertranslations are pure gauge and the asymptotic symmetry group is the
expected Poincar\'e group.Comment: Four equations corrected. Two references adde