Title: Nonassociative Einstein-Dirac-Maxwell systems and R-flux modified Reissner-Nordström black holes and wormholes Show Chinese title

Title: 非结合爱因斯坦-狄拉克-麦克斯韦系统和R通量修正的Reissner-Nordström黑洞和虫洞

Abstract: We elaborate on a model of nonassociative and noncommutative Einstein--Dirac-Maxwell, EDM, theory determined by star product R-flux deformations in string theory. Solutions for nonassociative EDM systems and physical properties not studied in modern physics. For modifications of the four-dimensional, 4-d, Einstein gravity, we work on conventional nonassociative 8-d phase spaces modelled as star-deformed co-tangent Lorentz bundles. Generalizing the anholonomic frame and connection deformation method, the nonassociative EDM equations are decoupled and integrated in exact and parametric quasi-stationary forms. Corresponding generic off-diagonal metrics are described by nonlinear symmetries and encode nonassociative effective sources and generating functions depending on space and momentum-like coordinates. For respective nonholonomic parameterizations, such solutions describe nonassociative deformations of the Reissner-Nordstr\"{o}m black holes. A variant of nonassociative phase space wormhole solution with fermions possessing anisotropic polarized masses is also analyzed. We conclude that such phase space physical objects can't be characterized using the concept of Bekenstein-Hawking entropy and show how to compute another type (modified G. Perelman ones) nonassociative geometric and statistical thermodynamic variables. Show Chinese abstract

Abstract: 我们详细探讨了一种由弦理论中的星积R通量形变确定的非结合性和非交换性爱因斯坦-狄拉克-麦克斯韦（EDM）理论模型。研究了非结合性EDM系统的解及其在现代物理学中未被研究的物理性质。对于四维爱因斯坦引力的修正，我们在传统的八维非结合性相空间模型中工作，该模型被建模为星形变形的余切洛伦兹丛。通过推广全各向异性框架和连接变形方法，非结合性EDM方程被解耦并以精确和参数化准稳态形式积分。相应的非对角度规由非线性对称性描述，并编码依赖于空间和动量类坐标的非结合性有效源和生成函数。对于相应的非完整参数化，这些解描述了雷斯勒-诺斯特罗姆黑洞的非结合性形变。还分析了一种具有各向异性极化质量的费米子的非结合性相空间虫洞解的变体。我们得出结论，这种相空间物理对象不能用贝肯斯坦-霍金熵的概念来表征，并展示了如何计算另一种类型的（修改后的G.佩雷尔曼的）非结合性几何和统计热力学变量。