爱因斯坦引力、一般解和黑洞的分数动力学
Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
摘要：
研究了非整数维时空的分数引力。我们的建设是基于几何形式主义的分数Caputo导数和积分适应nonolonomic分布。这使我们能够定义一个分数时空几何与基本的几何/物理对象和广义张量演算都是类似于各自的整数维结构。这种分数引力模型模拟了爱因斯坦引力理论和各种拉格朗日-芬斯勒和汉密尔顿-嘉当在非完整变量中的推广。该方法提出了一些新的影响重力和物质场论奇异，随机，动力学，分形，记忆等过程。我们证明了分数阶引力场方程可以用非完整变形方法积分成非常一般的形式。最后，我们研究了分数阶黑洞解、分数阶椭球引力位形和分数阶孤子背景中这类天体的嵌入问题。
英文摘要：
We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange-Finsler and Hamilton-Cartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, fractional ellipsoid gravitational configurations and imbedding of such objects in fractional solitonic backgrounds.
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