Correspondence between the first and second order formalism by a metricity constraint
Abstract
A way to obtain a correspondence between the first order and second order formalism is studied. By introducing a Lagrange multiplier coupled to the covariant derivative of the metric, a metricity constraint is implemented. The new contributions which comes from the variation of the Lagrange multiplier transforms the field equations from the first order to the second order formalism, yet the action is formulated in the first order. In this way all the higher derivatives terms in the second order formalism appear as derivatives of the Lagrange multiplier. Using the same method for breaking metricity condition and building conformal invariant theory is briefly discussed, so the method goes beyond just the study of first order or second formulations of gravity, in fact vast new possible theories of gravity are envisioned this way.
 Publication:

Physical Review D
 Pub Date:
 August 2018
 DOI:
 10.1103/PhysRevD.98.044023
 arXiv:
 arXiv:1805.09667
 Bibcode:
 2018PhRvD..98d4023B
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 5 pages. Accepted for publication in Phys Rev D