On the equivalence between different canonical forms of F(R) theory of gravity

Abstract

Classical equivalence between Jordan's and Einstein's frame counterparts of F(R) theory of gravity has recently been questioned, since the two produce different Noether symmetries, which couldn't be translated back and forth using transformation relations. Here we add the Hamiltonian constraint equation, which is essentially the time-time component of Einstein's equation, through a Lagrange multiplier to the existence condition for Noether symmetry to show that all the three different canonical structures of F(R) theory of gravity, including the one which follows from Lagrange multiplier technique, admit each and every available symmetry independently. This establishes classical equivalence amongst all the three.

10 pages, o figures

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Cited by in corpus (8)

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• Degenerate Hamiltonian operator in higher-order canonical gravity -- the problem and a remedy
• A viable form of the metric Teleparallel F(T) theory of gravity
• Black branes in four-dimensional conformal equivalent theories
• Conformal and kinetic couplings as two Jordan frames of the same theory
• Some aspects of modified theory of gravity in Palatini formalism unveiled
• Cosmological Lorentzian Wormholes via Noether symmetry approach
• Analyzing Conserved Currents in F(R) theory of gravity