# Tag Info

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### 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 ...
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### 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 ...

### 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 ...

### What is the physical meaning of the affine parameter for null geodesic?

Following David Z's answer, the proof for the last paragraph is: since $t$ is an affine parameter it satisfies: \begin{equation} \frac{\mathrm d^2x^a}{\mathrm dt^2}-\Gamma^a_{bc}\frac{\mathrm dx^b}{\...

### Intuitively, why do attempts to delay hitting a black hole singularity cause you to reach it faster?

Actually, it turns out to be incorrect that the optimal strategy is to free fall. There is an optimal strategy for firing your rocket engine which maximizes your proper time from the event horizon to ...
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### 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 ...

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

It is the least-time path. Fermat's principle was itself built on two earlier observations: on the one hand the Greeks had noticed that in reflections, light traveled along the least-distance path; ...
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### 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 ...

### What is a Null Geodesic?

A null geodesic is a geodesic (that is: with respect to length extremal line in a manifold), whose tangent vector is a light-like vector everywhere on the geodesic (that is $x(s)$ is a geodesic and \$...