Equivalence principle in Reissner-Nordstrom geometry

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-Nordstrom 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. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The Equivalence Principle is a key concept in General Relativity, stating that a reference frame at rest in a uniform gravitational field is equivalent to one in uniformly accelerated motion without gravity. The study analyzes the spacetime around a non-rotating spherically symmetric charged body, known as Reissner-Nordstrom geometry, and demonstrates its compatibility with the Equivalence Principle through a coordinate transformation. Revisiting the Schwarzschild case and considering second order terms in the expansion parameters of the approximate metric are necessary for accurate curvature calculations at zeroth order.