The Equivalence Principle is a key element in the development of General Relativity. In one of its formulations, the Equivalence Principle states that a reference frame at rest in a uniform gravitational field is equivalent to a reference frame in uniformly accelerated motion in the absence of any gravitation field. We analyze the spacetime surrounding a non-rotating spherically symmetric charged body, known as Reissner–Nordström geometry, and exhibit a coordinate transformation, which makes explicit its compatibility with the Equivalence Principle. We revisit the Schwarzschild case, previously analyzed in the literature. We also consider second order terms of the relevant expansion parameters in the approximate metric, which is needed for the computed curvature quantities to be correct at zeroth order.

等效原理是广义相对论发展的关键要素。在其公式之一中，等效原理指出，在均匀引力场中静止的参考系等效于在没有任何引力场的情况下匀加速运动的参考系。我们分析了围绕非旋转球对称带电体（称为 Reissner-Nordström 几何）的时空，并展示了坐标变换，这表明它与等效原理的兼容性。我们重新审视了之前在文献中分析过的 Schwarzschild 案例。我们还考虑了近似度量中相关扩展参数的二阶项，这是计算出的曲率量在零阶正确所必需的。