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Covariant theory of gravitation in the framework of special relativity

机译：特殊相对论框架中的协调性引力理论

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In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a magnetic-like force must be present whenever two or more bodies are in motion. The exact expression for this gravitomagnetic force is then derived purely from special relativity and the consequences of such a covariant theory are developed. For instance, we show that the gravitomagnetic fields satisfy a system of differential equations similar to the Maxwell equations of electrodynamics. This implies that the gravitational waves spread out with the speed of light in a flat spacetime, which is in agreement with the recent results concerning the gravitational waves detection. We also propose that the vector potential can be associated with the interaction momentum in the same way as the scalar potential is usually associated with the interaction energy. Other topics are also discussed, for example, the transformation laws for the fields, the energy and momentum stored in the gravitomagnetic fields, the invariance of the gravitational mass and so on. We remark that is not our intention here to propose an alternative theory of gravitation but, rather, only a first approximation for the gravitational phenomena, so that it can be applied whenever the gravitational force can be regarded as an ordinary effective force field and special relativity can be used with safety. To make this point clear we present briefly a comparison between our approach and that based on the (linearized) Einstein's theory. Finally, we remark that although we have assumed nothing from the electromagnetic theory, we found that gravity and electricity share many properties in common -these similarities, in fact, are just a requirement of special relativity that must apply to any physically acceptable force field.
机译：在这项工作中，我们研究了重力在特殊相对论框架中的磁效应。从洛伦兹转化施加重力的协方差，我们从思想实验表明，每当两个或更多个体在运动时必须存在磁性样力。然后纯粹来自特殊的相对性，产生这种协助理论的后果的确切表达。例如，我们表明，Gragitomagnic磁场满足与电动麦克风方程类似的微分方程系统。这意味着引力波以平坦时空的光速散布，这与关于引力波检测的最近结果一致。我们还提出，随着标量电位通常与相互作用能量相关联，向量电位可以与相互作用动量相关联。例如，还讨论了其他主题，例如，磁场的变换法，存储在重力场中的能量和动量，引力质量的不变性等。我们备注的是，这不是我们在这里提出一种替代的着心理论，而是，而是只有引力现象的第一近似，从而可以在重力被视为普通的有效力场和特殊相对性时应用它可以安全使用。为了使这一点清楚地清楚我们简要介绍了我们的方法和基于（线性化）爱因斯坦理论的比较。最后，虽然我们从电磁理论中没有假设任何东西，但我们发现重力和电力分享了许多共同的性质 - 事实上，实际上只是必须适用于任何身体上可接受的力场的特殊相对性的要求。

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