Eur. Phys. J. C (2014) 74: 3152
https://doi.org/10.1140/epjc/s10052-014-3152-4

Regular Article - Theoretical Physics

Off-diagonal deformations of kerr black holes in Einstein and modified massive gravity and higher dimensions

¹ University “Al. I. Cuza” Iaşi, Project IDEI, 14 Alexadnru Lapuşneanu street, Corpus R, UAIC, office 323, Iaşi, 700057, Romania
² Faculty of Medicine, University of Medicine and Pharmacy “Gr. T. Popa” Iaşi, 16 University street, Iaşi, 700115, Romania
³ National College of Iaşi, 4 Arcu street, Iaşi, 700125, Romania
⁴ Theory Division, CERN, 1211, Geneva 23, Switzerland
⁵ University “Al. I. Cuza” Iaşi, Rector’s Office, 14 Alexadnru Lapuşneanu street, Corpus R, UAIC, office 323, Iaşi, 700057, Romania

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

Received: 27 February 2014
Accepted: 24 October 2014
Published online: 23 December 2014

Abstract

We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and modified gravity theories when the field equations decouple with respect to certain types of nonholonomic frames of reference. This allows us to construct various classes of exact solutions when the coefficients of the fundamental geometric/physical objects depend on all spacetime coordinates via corresponding classes of generating and integration functions and/or constants. Such (modified) spacetimes display Killing and non-Killing symmetries, describe nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants. Our method can be extended to higher dimensions which simplifies some proofs for embedded and nonholonomically constrained four-dimensional configurations. We reproduce the Kerr solution and show how to deform it nonholonomically into new classes of generic off-diagonal solutions depending on 3–8 spacetime coordinates. Certain examples of exact solutions are analyzed and they are determined by contributions of a new type of interactions with sources in massive gravity and/or modified f(R,T) gravity. We conclude that by considering generic off-diagonal nonlinear parametric interactions in GR it is possible to mimic various effects in massive and/or modified gravity, or to distinguish certain classes of “generic” modified gravity solutions which cannot be encoded in GR.