2013/12/31 by Tamara Gheorghiu, Olivia Vacaru, Sergiu I. Vacaru · 41 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Diagonal #Einstein #General relativity #Geometry #Gravitation #Gravitational field #Linearized gravity #Massive gravity #Mathematical physics #Mathematics #Nonlinear system #Physics #Quantum #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Spacetime #Spacetime symmetries #Theoretical physics #gr-qc #hep-th #msc:83E99 #msc:8C15 #msc:8D99
paper · pdf · doi:10.1140/epjc/s10052-014-3152-4
published in The European Physical Journal C 74(12) (Springer Science+Business Media) · latex 2e, 11pt, 35 pages with table of content; version 2 modified following Editor's requests and accepted to EPJC
arxiv created 2014/10/26 · openalex publication_date 2014/12/01 · arxiv updated 2014/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.