All Questions
3
questions
3
votes
2
answers
85
views
How does $r$ depend on $\varphi$ in the Schwarzschild metric?
I am confused about the Wikipedia derivation of the equation
for geodesic motion in the Schwarzschild spacetime. The derivation of this equation involves variation with respect to the longitude $\...
- 311
7
votes
1
answer
3k
views
How is the Lagrangian defined in GR?
Reading about the Schwarzschild metric in general relativity I see that sometimes $$L=g_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}$$ and sometimes $$L=\sqrt{g_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}}.$$
Which is ...
- 789
2
votes
0
answers
529
views
Derivation of equations of motion in Nordstrom's theory of scalar gravity?
Nordstrom's theory of a particle moving in the presence of a scalar field $\varphi (x)$ is given by
$$
S = -m\int e^{\varphi (x)}\sqrt{\eta_{\alpha \beta}\frac{dx^{\alpha}}{d \lambda}\frac{dx^{\beta}}{...
- 6,564