# Tag Info

Accepted

### What is really curved, spacetime, or simply the coordinate lines?

Congratulations! You stumbled upon an important question of differential geometry: How can I know whether the curvature is caused by my choice of coordinates or the space I live in? As has been ...
• 1,080
Accepted

### How does a laser from Earth manage to hit the Moon with precision?

Commenters on the first version of this answer (preserved in the edit history) did me the favor of finding the literature that I hadn't read for years, which contains a succinct answer to your ...
• 91.1k
Accepted

### GR and my journey to the centre of the Earth

That is awesome! And it makes complete sense too! (other than a possible misusage of the word "distance"). Let's have a look at the equations of motion of you in Earth's curved spacetime, assuming ...
• 3,613

### In general relativity, why is Earth able to accelerate?

This is quite a common confusion for students new to general relativity, and it's because in GR the term acceleration means something slightly different from its everyday usage. In everyday usage we ...
• 357k

### Is Fermat's principle only an approximation?

In general relativity, it's not entirely clear what "least time" means, since you have to ask "whose time are you talking about"? Are you talking about the time as measured by the emitter? The ...
• 49.5k
Accepted

• 205k

### Least Action in General Relativity

You could ask the same exact thing for the Lagrangian of a nonrelativistic particle. It's an exactly analogous situation. $$L = \frac{1}{2} m \dot x^2$$ Now, if we differentiate the Lagrangian with ...
• 11.5k

### How do geodesics explain two identical balls thrown up at the different speeds?

Two worldlines starting at the same event in spacetime but having different velocities are going in different “directions” in spacetime, even if they are going in the same direction in space. So their ...
• 102k
Accepted

### Difference between Fermi and Riemann normal coordinates

Take a future-directed timelike curve $\gamma= \gamma(\tau)$, $\tau$ being the proper time along $\gamma$ in the spacetime $M$. Assume that $p = \gamma(0)$ is the initial point of $\gamma$. Fermi ...
• 72.6k
Accepted

### Does an electromagnetic field affect neutral particles via the metric because of the EM stress-energy tensor?

The answer to your question is yes, the metric is influenced by the electromagnetic field, and a neutral particle will follow a geodesic of that metric. Thus, this implies that the neutral particle ...
• 7,572

### Trouble understanding Caroll's explanation on why geodesics maximize proper time

I think that all Caroll meant by this remark was that the stationary point has to be a maximum not a minimum of proper time. It can't be a minimum since there are nearby paths with lower (namely, zero)...
• 59.3k
The Schwarzschild radius, $$r_s = \frac{2GM}{c^2}$$ is the natural distance unit to use when discussing black holes. It's convenient to work in units where $r_s=1$. A Schwarzschild black hole is ...