Eur. Phys. J. C (2014) 74: 2781
https://doi.org/10.1140/epjc/s10052-014-2781-y

Regular Article - Theoretical Physics

Exact solutions in modified massive gravity and off-diagonal wormhole deformations

¹ Rector’s Office, Alexandru Ioan Cuza University, Alexandru Lapuşneanu street, nr. 14, UAIC, Corpus R, office 323, Iaşi , 700057, Romania
² Theory Division, CERN, 1211 , Geneva 23, Switzerland

^* e-mail: sergiu.vacaru@uaic.ro
^** e-mail: sergiu.vacaru@cern.ch

Received: 11 September 2013
Accepted: 14 February 2014
Published online: 15 March 2014

Abstract

We explore off-diagonal deformations of ‘prime’ metrics in Einstein gravity (for instance, for wormhole configurations) into ‘target’ exact solutions in -modified and massive/bi-metric gravity theories. The new classes of solutions may, or may not, possess Killing symmetries and can be characterized by effective induced masses, anisotropic polarized interactions, and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small eccentricity rotoid configurations, we can generate wormhole-like objects matching an external black ellipsoid—de Sitter geometries. We conclude that there are nonholonomic transforms and/or non-trivial limits to exact solutions in general relativity when modified/massive gravity effects are modeled by off-diagonal and/or nonholonomic parametric interactions.