Emergence of the Cotton tensor for describing gravity
Abstract
It is shown that the Cotton tensor can describe the effects of gravity beyond general relativity. Any solution of the Einstein equations with or without the cosmological constant satisfies the field equations described by the Cotton tensor. It implies that the cosmological constant is an integration constant. A vacuum of a theory is represented by the vanishing of the Cotton tensor, rather than the vanishing of the Ricci tensor. An exact Schwarzschildlike solution for a static and spherically symmetric source is discovered. Although the field equations involve the third order of derivative, it is found that they reduce to the secondorder differential equations due to a variational principle.
 Publication:

Physical Review D
 Pub Date:
 June 2021
 DOI:
 10.1103/PhysRevD.103.L121502
 arXiv:
 arXiv:2105.09304
 Bibcode:
 2021PhRvD.103l1502H
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 5 pages, 1 figure, accepted for publication as a Letter in PRD, v2: typos corrected