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–Nordström 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.

我们详细阐述了非关联和非交换爱因斯坦-狄拉克-麦克斯韦 EDM 模型，该理论由弦理论中的星积 R 通量变形确定。现代物理学中未研究的非关联 EDM 系统和物理特性的解决方案。为了修改四维、4 维爱因斯坦引力，我们研究了建模为星形变形余切洛伦兹丛的传统非关联 8 维相空间。推广非完整框架和连接变形方法，非关联 EDM 方程以精确和参数准稳态形式解耦和积分。相应的通用非对角度量由非线性对称性描述，并根据空间和类动量坐标对非关联有效源和生成函数进行编码。对于各自的非完整参数化，此类解描述了赖斯纳-诺德斯特伦黑洞的非关联变形。还分析了具有各向异性极化质量的费米子的非关联相空间虫洞解的变体。我们得出的结论是，此类相空间物理对象无法使用贝肯斯坦-霍金熵的概念来表征，并展示了如何计算另一种类型（修改后的 G.佩雷尔曼）非关联几何和统计热力学变量。