The paper presents a theory of gravitation as a continuum dynamical theory, i.e. the equations of motion are first order in the time derivatives. The theory satisfies the laws of conservation of total energy, momentum and mass in the standard sense, i.e. as applications of Stokes’ theorem. A model in this theory is defined by the specification of an energy density function that accounts for the total mechanical and gravitational energy of the system and which in turn defines an action function. The derivation of the equations of motion is based on Hamilton’s principle of least action with the “same” action function as used for the derivation of the Einstein equation of the theory of general relativity, however, not with respect to variations of the metric but with respect to variations induced by local displacements of space, i.e. variations of the conjugate variable of the momentum and variations of the momentum density. Entropy density is introduced as a variable. This makes it possible to determine the thermodynamic equilibrium conditions for a model. Solutions of the equilibrium conditions are the Schwarzschild and Minkowski metrics on space-time, and the metrics defining the spherical and hyper spherical spaces.

中文翻译：

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万有引力理论

论文提出了一种作为连续介质动力学理论的引力理论，即运动方程是时间导数的一阶。该理论满足标准意义上的总能量、动量和质量守恒定律，即作为斯托克斯定理的应用。该理论中的模型由能量密度函数的规范定义，该函数解释了系统的总机械能和重力能量，进而定义了动作函数。运动方程的推导基于哈密顿的最小作用原理，其作用函数与推导广义相对论的爱因斯坦方程所用的“相同”作用函数，然而，不是关于度量的变化，而是与关于空间局部位移引起的变化，即 动量共轭变量的变化和动量密度的变化。熵密度作为变量被引入。这使得确定模型的热力学平衡条件成为可能。平衡条件的解是 Schwarzschild 和 Minkowski 时空度量，以及定义球形和超球形空间的度量。