This has come up in a few threads that I have participated in, so it seems convenient to post here for reference some general equations relating to the metric and the Einstein Field Equation for static, spherically symmetric spacetimes.

First, we are talking about spacetimes which can be described by the following line element, written in standard Schwarzschild coordinates (i.e., coordinates in which a 2-sphere at radial coordinate [itex]r[/itex] has area [itex]4 \pi r^2[/itex]):...

Deformation of EM wave signals
14 August 2012

Electromagnetic wave carries signals emitted by antenna into space. The EM field of a wave is mathematically defined by the EM wave equation whose monochromatic solution is the equation (1). A signal is a time varying EM field that can be expressed by Fourier series which is the sum of monochromatic wave functions, that is, a sum of equation (1) of different amplitudes and wave lengths.

We notice that the amplitude...