3
votes
2answers
162 views

Can a curvature in time (and not space) cause acceleration?

I realize that the curvature of space-time causes acceleration (gravity). Is it possible to have a curvature only of space, or a curvature only of time? If so, would a curvature only of space, or a ...
2
votes
1answer
128 views

Trajectory of a photon around a Schwarzschild black hole?

Consider a photon coming from the infinity in a unbounded orbit to a Schwarzschild black hole (Schwarzschild radius $r_{s}$) (see this for illustration). Its impact parameter is $b$ and its distance ...
2
votes
2answers
202 views

Exercise about Lagrange-Euler equations

I'm solving an exercise about the Lagrange-Euler equations, that states the following: Let $\gamma (t) = \{ (t,q) : q = q(t), t_0 \leq t \leq t_1\}$ be a curve in $\mathbb{R} \times \mathbb{R}^2$. ...
5
votes
1answer
2k views

Why is light described by a null geodesic?

I'm trying to wrap my head around how geodesics describe trajectories at the moment. I get that for events to be causally connected, they must be connected by a timelike curve, so free objects must ...