Moore General Relativity Workbook Solutions 99%

The equation of motion for a radial geodesic can be derived from the geodesic equation. After some algebra, we find

The geodesic equation is given by

Consider a particle moving in a curved spacetime with metric moore general relativity workbook solutions

Derive the geodesic equation for this metric. The equation of motion for a radial geodesic

Using the conservation of energy, we can simplify this equation to moore general relativity workbook solutions

The gravitational time dilation factor is given by

After some calculations, we find that the geodesic equation becomes