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

The European Physical Journal C, Mar 2014

We explore off-diagonal deformations of ‘prime’ metrics in Einstein gravity (for instance, for wormhole configurations) into ‘target’ exact solutions in \(f(R,T)\)-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.

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

Sergiu I. Vacaru 0 1 0 Theory Division , CERN, 1211 Geneva 23, Switzerland 1 Rector's Office, Alexandru Ioan Cuza University , Alexandru Lapusneanu street, nr. 14, UAIC, Corpus R, office 323, Iasi 700057, Romania We explore off-diagonal deformations of 'prime' metrics in Einstein gravity (for instance, for wormhole configurations) into 'target' exact solutions in f ( R, T )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 ellipsoidde 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. - The bulk of physically important exact solutions in gravity theories (for instance, defining black holes and wormholes) are described by metrics with two Killing symmetries, see for summaries of the results the monographs [1, 2]. For such solutions, there are certain canonical frames of reference, when the coefficients of fundamental geometric/physical objects depend generically on one or two (from maximum four, in four dimensional, 4-d, theories) spacetime coordinates. This class of metrics can be diagonalized by coordinate transformations or contain off-diagonal terms generated by rotations. To construct generic off-diagonal solutions parameterized by metrics with six independent coefficients depending generically on three and/or, in general, on all spacetime coordinates is a very difficult technical and geometric task and the a e-mail: ; b Associated visiting researcher at CERN physical meaning of such generalized/modified, or Einstein, spacetimes is less clear. In our work, see [3, 4] and references therein, we elaborated a geometric method which allows us to deform nonholonomically any prime diagonal metric into various classes of target off-diagonal solutions with one Killing and/or nonKilling symmetries. For deformations on a small parameter, the new classes of target solutions may preserve certain important physical properties of a prime metric (for instance, of a black hole/ring one, or for a wormhole) but may also possess new characteristics related to anisotropic polarizations of constants, nonlinear off-diagonal interactions with new symmetries etc. Wormhole configurations with spacetime handles (shortcuts), non-trivial topology and exotic matter [5] have attracted attention for theoretical probes of foundations of gravity theories and as possible objects of nature (for reviews, see [68] and references therein). Such solutions are determined in reverse direction when some tunneling metrics of prescribed (for instance, spherical and/or conformal) symmetry are considered and then one could try to find some corresponding exotic matter sources. A number of interesting and/or peculiar solutions were found when time-like curves and respective causality violations are allowed, for stressenergy tensors with possible violation of the null energy conditions. The wormhole subjects were revived some times in connection to black hole solutions, coupling with gauge interactions, singularities, generalized/modified gravity theories etc. We studied locally anisotropic wormhole and/or flux tubes in five dimensional (5-d) gravity [911]. Such objects can be determined by extra dimensional or warped/ trapped configurations and/or possible ellipsoidal, toroidal, bipolar, solitonic etc. gravitational polarizations of vacuum and/or gravitational constants. The corresponding spacetime geometries are described by generic off-diagonal metrics1 with coeffi 1 These cannot be diagonalized by coordinate transformations. cients depending on three or four coordinates and various types of (pseudo) Riemannian or non-Riemannian connections. In the present paper, we address the problem of constructing deformations of prime wormhole metrics in general relativity, GR, resulting in generic off-diagonal solutions in modified gravity, MG, and theories with nonholonomically induced torsion, effective masses and bi-metric and bi-connection structures. We shall work with two equivalent connections (the LeviCivita and an auxiliary one) defined by the same metric structure and apply and extend the anholonomic frame deformation method (AFDM, see details in [3, 4], and references therein) of constructing exact solutions in gravity theories. The idea of the AFDM is to find certain classes of nonholonomic (equivalently, anholonomic/ non-integrable) frames with conventional 2 + 2 + , or 3 + 2 + , splitting of dimensions on (pseudo) Riemannian space (...truncated)


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Sergiu I. Vacaru. Exact solutions in modified massive gravity and off-diagonal wormhole deformations, The European Physical Journal C, 2014, pp. 2781, Volume 74, Issue 3, DOI: 10.1140/epjc/s10052-014-2781-y