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.

arXiv comment4 pages, to appear in PRD, a reference added

References in corpus (14)

• Coincident General Relativity
• f(T) Gravity and local Lorentz invariance
• The covariant formulation of f(T) gravity
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Generalizations of teleparallel gravity and local Lorentz symmetry
• On the covariance of teleparallel gravity theories
• Nonmetricity formulation of general relativity and its scalar-tensor extension
• Symmetric teleparallel general relativity
• Modified teleparallel theories of gravity in symmetric spacetimes
• General Teleparallel Quadratic Gravity
• 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
• Teleparallelism: A New Insight Into Gravity

Cited by in corpus (12)

• Spherically symmetric configuration in $f(Q)$ gravity
• Exploring physical properties of minimally deformed strange star model and constraints on maximum mass limit in $f(\mathcal{Q})$ gravity
• Realistic neutron star models in $f(T)$ gravity
• Neutron Star in Covariant $f(Q)$ gravity
• Interaction of divergence-free deceleration parameter in Weyl-type $f(Q,T)$ gravity
• Weiss variation for general boundaries
• Projective and amplified symmetries in metric-affine theories
• 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)