The possibility of time travel is explored within the framework of first order gravity theory in vacuum. We present explicit solutions (to the field equations), whose geodesics allow the proper clock to run backwards. These four-geometries contain degenerate as well as nondegenerate tetrad fields that are sewn together continuously over different regions of the spacetime. Being devoid of matter and also of torsion by construction, these solutions have no exotic field content.

• Received 9 March 2018
• Revised 21 April 2018

DOI:https://doi.org/10.1103/PhysRevD.97.124038