Metric tensor at second perturbation order for spherically symmetric space-times

Abstract

It is shown in this article that if the Einstein Equivalence Principle is valid on a particular metric theory of gravitation in a spherically symmetric space-time, then the time metric component is not equal to the negative of the inverse radial one unless the underlying potential is inversely proportional to the radial coordinate. At the weak field limit of approximation, a general formula is calculated and applied to some useful cases.

arXiv comment5 pages, published in the International Journal of Geometric Methods in Modern Physics

References in corpus (8)

• Extended Theories of Gravity
• The Newtonian Limit of F(R) gravity
• Analysis of the Yukawa gravitational potential in $f(R)$ gravity I: semiclassical periastron advance
• Analysis of the Yukawa gravitational potential in $f(R)$ gravity II: relativistic periastron advance
• Constraining f(R) gravity with PLANCK data on galaxy cluster profiles
• Magnetized discs and photon rings around Yukawa-like black holes
• Gravitational lensing with $f(\chi )={\chi }^{3/2}$ gravity in accordance with astrophysical observations
• Astrophysical constraints and insights on extended relativistic gravity