Derive the geodesic equation for this metric.
$$\frac{d^2x^\mu}{d\lambda^2} + \Gamma^\mu_{\alpha\beta} \frac{dx^\alpha}{d\lambda} \frac{dx^\beta}{d\lambda} = 0$$
$$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$$
Using the conservation of energy, we can simplify this equation to
where $\lambda$ is a parameter along the geodesic, and $\Gamma^\mu_{\alpha\beta}$ are the Christoffel symbols. moore general relativity workbook solutions
Consider the Schwarzschild metric
Derive the equation of motion for a radial geodesic. Derive the geodesic equation for this metric
$$\frac{d^2t}{d\lambda^2} = 0, \quad \frac{d^2x^i}{d\lambda^2} = 0$$