Parametric nonholonomic frame transforms and exact solutions in gravity
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In this paper, a generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations, and five classes of exact off-diagonal solutions are constructed in vacuum Einstein and in string gravity describing solitonic pp-wave interactions.Abstract:
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for nonholonomic manifolds and Finsler spaces) when the gravitational field equations transform into systems of nonlinear partial differential equations which can be integrated in general form. The new classes of solutions are defined by generic off-diagonal metrics depending on integration functions on one, two and three (or three and four) variables if we consider four (or five) dimensional spacetimes. Second, we use a general scheme when one (two) parameter families of exact solutions are defined by any source-free solutions of Einstein's equations with one (two) Killing vector field(s). A successive iteration procedure results in new classes of solutions characterized by an infinite number of parameters for a non-Abelian group involving arbitrary functions on one variable. Five classes of exact off-diagonal solutions are constructed in vacuum Einstein and in string gravity describing solitonic pp-wave interactions. We explore possible physical consequences of such solutions derived from primary Schwarzschild or pp-wave metrics.read more
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Finsler and Lagrange Geometries in Einstein and String Gravity
TL;DR: In this paper, the current status of Finsler-Lagrange geometry and generalizations is reviewed and a canonical scheme for geometrical objects on a (pseudo) Riemannian space are nonholonomically deformed into generalized Lagrange configurations on the same manifold.
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Modified Dispersion Relations in Horava-Lifshitz Gravity and Finsler Brane Models
TL;DR: In this article, the authors studied possible links between quantum gravity phenomenology encoding Lorentz violations as nonlinear dispersions, the Einstein-Finsler gravity models, EFG, and nonholonomic (nonintegrable) deformations to Hořava-Lifshitz, HL, and/or Einstein's general relativity, GR, theories.
Journal ArticleDOI
Finsler and Lagrange Geometries in Einstein and String Gravity
TL;DR: In this article, the current status of Finsler-Lagrange geometry and generalizations is reviewed and a canonical scheme for geometrical objects on a (pseudo) Riemannian space are nonholonomically deformed into generalized Lagrange-Finsler configurations on the same manifold.
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Principles of einstein–finsler gravity and perspectives in modern cosmology
TL;DR: In this article, the geometric and physical foundations of Finsler gravity theories with metric compatible connections defined on tangent bundles, or (pseudo) Riemannian manifolds, endowed with nonholonomic frame structure are studied.
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Spectral functionals, nonholonomic Dirac operators, and noncommutative Ricci flows
TL;DR: In this article, a non-commutative generalization of the Ricci flow theory in the framework of spectral action approach to non-holonomic Riemannian geometry is formulated.
References
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Book
Exact Solutions of Einstein's Field Equations
TL;DR: A survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources can be found in this paper, where the solutions are ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties.
Journal ArticleDOI
String theory
TL;DR: The standard model of particle physics is valid to distances as small as 10−16 cm, and there is some evidence (such as that obtained by extrapolating the strengths of the four forces to determine the distance scale at which they might become indistinguishable) that the next level of structure will be detected only at a distance scale of roughly 10−32 cm as discussed by the authors.
Journal ArticleDOI
Strings in flat space and pp waves from Script N = 4 Super Yang Mills
TL;DR: In this paper, the string spectrum in flat space and pp-waves arises from the large-N limit, at fixed g2YM, of U(N) = 4 super Yang Mills.
MonographDOI
String theory. Vol. 2: Superstring theory and beyond
TL;DR: A comprehensive and pedagogic account of superstring theory can be found in this article, which includes a detailed treatment of D-branes and their dynamics, and covering string duality, M-theory, and black hole entropy.
Journal ArticleDOI
Black holes in general relativity
TL;DR: In this paper, it is shown that a stationary black hole must have topologically spherical boundary and must be axisymmetric if it is rotating, and these results together with those of Israel and Carter go most of the way towards establishing the conjecture that any stationary blackhole is a Kerr solution.