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arXiv 1608.01980hep-thmath-phmath.MP
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异质超引力中Kerr椭球和黑椭球的非对角形变

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

Sergiu I. Vacaru, Klee Irwin

摘要:

本文研究了对包含非平凡Yang-Mills扇形和6维6维几乎Kähler内部空间的杂化超引力作用量进行一阶$α^{\prime}$修正的运动方程的精确解的几何构造方法。在10维时空中,一般的非对角度量,非线性和线性连接和物质源,当运动方程解耦在非常一般的形式被认为是一般的参数化。当基本几何/物理对象的系数依赖于所有高维时空坐标时,通过相应的生成函数和积分函数、广义有效源和积分常数,这使我们能够构造各种精确解。这种广义解由通用非对角度量和非线性和/或线性连接确定。特别是,作为配置的翘曲/紧凑化到较低的维度和列维-奇维塔连接。相应的度规可以具有(非)Killing和/或李代数对称性和/或描述(1+2)-d和/或(1+3)-d畴壁构型,可能具有翘曲的几乎Kähler流形,具有非线性真空构型的引力和规范瞬子,以及编码弦引力效应的宇宙学和相互作用常数的有效极化。一系列的例子,精确的解决方案描述通用的非对角超引力修改黑洞/椭球和孤子配置提供和分析。我们证明了在4维空间中再现广义相对论的Kerr解和其它类型的black解(加上某些类型的弦修正)以及将这些解推广到(超)引力/弦论的非真空位形是可能的.

英文摘要:

Geometric methods for constructing exact solutions of motion equations with first order $α^{\prime}$ 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.

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