Speaker
Description
The Einstein field equations are known to follow from a variational principle based on the Einstein-Hilbert action. In this work, we investigate actions formulated in non-Riemannian geometry that produce the metric dynamics of general relativity. We classify these actions into two broad categories: (i) those whose equivalence with general relativity holds only \textit{on-shell}, and (ii) those whose equivalence holds already \textit{off-shell}. We clarify that the standard teleparallel equivalents of general relativity belong to the first category, and we emphasise the role of the teleparallel constraint in establishing this equivalence. We then introduce an action belonging to the second category, differing from the Einstein-Hilbert action only by a boundary term. We show that imposing on-shell constraints can modify this pre-arranged, off-shell equivalence. We derive general conditions under which a connection constraint preserves the equivalence with general relativity and illustrate them with two explicit examples.
| Topic | Modified theories of gravity |
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