Connection independent formulation of general relativity

Abstract

A connection-independent formulation of general relativity is presented, in which the dynamics does not depend on the choice of connection. The gravity action in this formulation includes one additional scalar term in addition to the Einstein-Hilbert action. No conditions on the connection are imposed. Nevertheless, this formulation yields the Einstein equations, without adding the Gibbons-Hawking-York term even when a manifold has a boundary. Furthermore, this formulation yields a unified description of general relativity, teleparallel gravity, and symmetric teleparallel gravity.

4 pages, to appear in PRD, a reference added

References in corpus (4)

• Generalizations of teleparallel gravity and local Lorentz symmetry
• Translation of Einstein's Attempt of a Unified Field Theory with Teleparallelism
• Gauge Structure of Teleparallel Gravity
• Role of spacetime boundaries in Einstein's other gravity

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• Einstein gravity from the Einstein action: Counterterms and covariance
• Junction conditions in a general field theory
• Static plane symmetric solutions in $f(Q)$ gravity
• Bayesian Inference of Neutron Star Properties in $f(Q)$ Gravity Using NICER Observations
• Lost in translation: the Abelian affine connection (in the coincident gauge)