Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity

Abstract

Geometric methods for constructing exact solutions of motion equations with first order ${\alpha }^{\prime }$ corrections to the heterotic supergravity action implying a non-trivial Yang-Mills sector and six dimensional, 6-d, almost-Kähler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics, nonlinear and linear connections and matter sources, when the equations of motion decouple in very general forms are considered. This allows us to construct a variety of exact solutions when the coefficients of fundamental geometric/physical objects depend on all higher dimensional spacetime coordinates via corresponding classes of generating and integration functions, generalized effective sources and integration constants. Such generalized solutions are determined by generic off-diagonal metrics and nonlinear and/or linear connections. In particular, as configurations which are warped/compactified to lower dimensions and for Levi-Civita connections. The corresponding metrics can have (non) Killing and/or Lie algebra symmetries and/or describe (1+2)-d and/or (1+3)-d domain wall configurations, with possible warping nearly almost-Kähler manifolds, with gravitational and gauge instantons for nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants encoding string gravity effects. A series of examples of exact solutions describing generic off-diagonal supergravity modifications to black hole/ ellipsoid and solitonic configurations are provided and analyzed. We prove that it is possible to reproduce the Kerr and other type black solutions in general relativity (with certain types of string corrections) in 4-d and to generalize the solutions to non-vacuum configurations in (super) gravity/ string theories.

latex2e, 44 pages with table of content, v2 accepted to EJPC with minor typos modifications requested by editor and referee and up-dated references

References in corpus (12)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Flux Compactification
• Lectures on Gauged Supergravity and Flux Compactifications
• Exact Schwarzschild-de Sitter black holes in a family of massive gravity models
• Torsional Heterotic Geometries
• Lectures on Nongeometric Flux Compactifications
• The Imaginary Starobinsky Model
• Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
• Parametric Nonholonomic Frame Transforms and Exact Solutions in Gravity
• G-structures and Domain Walls in Heterotic Theories
• Equivalent off-diagonal cosmological models and ekpyrotic scenarios in f(R)-modified, massive and Einstein gravity
• Order ${\alpha }^{\prime }$ heterotic domain walls with warped nearly Kähler geometry

Cited by in corpus (5)

• Heterotic Supergravity with Internal Almost-Kähler Spaces, Instantons for $SO(32)$, or $E_8\times E_8$, Gauge Groups, and Deformed Black Holes with Soliton, Quasiperiodic and/or Pattern-forming Structures
• Nonassociative black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks
• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
• Off-diagonal deformations of regular Schwarzschild black holes and general relativistic G. Perelman thermodynamics
• The fundamental physical importance of generic off-diagonal solutions and Grigori Perelman entropy in the Einstein gravity theory