English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We work out the most general theory for the interaction of spacetime geometryand matter fields -- commonly referred to as geometrodynamics -- for spin-$0$and spin-$1$ particles. The minimum set of postulates to be introduced is that(i) the action principle should apply and that(ii) the total action should byform-invariant under the (local) diffeomorphism group. The second postulatethus implements the Principle of General Relativity. According to Noether'stheorem, this physical symmetry gives rise to a conserved Noether current, fromwhich the complete set of theories compatible with both postulates can bededuced. This finally results in a new generic Einstein-type equation, whichcan be interpreted as an energy-momentum balance equation emerging from theLagrangian $L_{R}$ for the source-free dynamics of gravitation and theenergy-momentum tensor of the source system $L_{0}$. Provided that the systemhas no other symmetries -- such as SU$(N)$ -- the canonical energy-momentumtensor turns out to be the correct source term of gravitation. For the case ofmassive spin particles, this entails an increased weighting of the kineticenergy over the mass in their roles as the source of gravity as compared to themetric energy momentum tensor, which constitutes the source of gravity inEinstein's General Relativity. We furthermore confirm that a massive vectorfield necessarily acts as a source for torsion of spacetime. Thus, from theviewpoint of our generic Einstein-type equation, Einstein's General Relativityconstitutes the particular case for spin-$0$ and massless spin particle fields,and the Hilbert Lagrangian $L_{R,H}$ as the model for the source-free dynamicsof gravitation.

Generic Theory of Geometrodynamics from Noether's theorem for the Diff(M) symmetry group