For questions involving consideration of the shortest (or longest) path between two points in a curved space (e.g. a straight line between two points on the surface of a sphere such as the earth).
Questions tagged [geodesics]
1025 questions
72
votes
7 answers
Does gravity bend gravity?
Let's say that there is a large mass $M$ a light-year or so away from a black hole merger, which causes a very large gravitational wave to be produced. When the gravitational wave reaches $M$, does it bend like light bends when it comes into a…
Tachyon
- 2,120
61
votes
5 answers
What is really curved, spacetime, or simply the coordinate lines?
It is often said that, according to general relativity, spacetime is curved by the presence of matter/energy.
But isn't it simply the coordinate lines of the coordinate system that are curved?
Bob
- 943
- 9
- 14
55
votes
4 answers
GR and my journey to the centre of the Earth
[General Relativity] basically says that the reason you are sticking to the floor right now is that the shortest distance between today and tomorrow is through the center of the Earth.
I love this, not the least because it sounds…
Lloeki
- 643
40
votes
6 answers
To which extent is general relativity a gauge theory?
In quantum mechanics, we know that a change of frame -- a gauge transform -- leaves the probability of an outcome measurement invariant (well, the square modulus of the wave-function, i.e. the probability), because it is just a multiplication by a…
FraSchelle
- 11,033
38
votes
5 answers
What is the physical meaning of the affine parameter for null geodesic?
For time-like geodesic, the affine parameter is the proper time $\tau$ or its linear transform, and the geodesic equation is
$$\frac{\mathrm d^{2}x^{\mu}}{\mathrm d\tau^{2}}+\Gamma_{\rho\sigma}^{\mu}\frac{\mathrm dx^{\rho}}{\mathrm…
Siyuan Ren
- 5,132
35
votes
11 answers
Why do objects follow geodesics in spacetime?
Trying to teach myself general relativity. I sort of understand the derivation of the geodesic equation $$\frac{d^{2}x^{\alpha}}{d\tau^{2}}+\Gamma_{\gamma\beta}^{\alpha}\frac{dx^{\beta}}{d\tau}\frac{dx^{\gamma}}{d\tau}=0.$$ which describes "how"…
Peter4075
- 3,109
33
votes
5 answers
Can Lagrangian be thought of as a metric?
My question is, can the (classical) Lagrangian be thought of as a metric? That is, is there a meaningful sense in which we can think of the least-action path from the initial to the final configuration as being the shortest one? Then the equations…
N. Virgo
- 35,274
29
votes
2 answers
How does a laser from Earth manage to hit the Moon with precision?
A question I've been asked is how a laser, fired from earth, would hit the moon without "leading it" (or hit it with precision). When firing a laser at the moon, it takes about 3 seconds to reach it. Given the combined effects of orbit, rotation,…
Omnivore
- 475
28
votes
2 answers
Do light waves precisely follow null geodesic paths in General Relativity?
In special relativity one may show that a plane wave solution of Maxwell's equations (in a vacuum), of the form $A^a=C^a\mathrm{e}^{\mathrm{i}\psi}$ has the following properties: The normal $k:=\mathrm{d}\psi$ to the surfaces of constant $\psi$ is a…
Ryan Unger
- 9,011
27
votes
4 answers
What does this depiction of a black hole in the movie Interstellar mean?
I was expecting a whirlpool in 3D and the matter glowing from friction as it nears the center, as I expected a event horizon to be negligible visually.
How does this depiction work? How big is the central sphere? I am puzzled by the perpendicular…
Jesvin Jose
- 657
24
votes
11 answers
Can we bend a light ray into any closed loop?
Suppose we have a medium with varying refractive index and a source of light inside that medium emitting rays. Is it possible to bend the ray into any closed loop?
As the medium has varying refractive index, is it possible?
And if possible, how will…
The Space Guy
- 1,741
- 7
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24
votes
5 answers
Is Fermat's principle only an approximation?
Fermat's principle says that the path taken between two points by a ray of light is the path that can be traversed in the least time.
It occurred to me today that maybe the path is actually the one that covers the smallest distance through…
Mark Dominus
- 2,727
24
votes
4 answers
Geodesic Equation from variation: Is the squared lagrangian equivalent?
It is well known that geodesics on some manifold $M$, covered by some coordinates ${x_\mu}$, say with a Riemannian metric can be obtained by an action principle . Let $C$ be curve $\mathbb{R} \to M$, $x^\mu(s)$ be an affine parametrization of $C$.…
zzz
- 2,987
20
votes
4 answers
Intuitively, why do attempts to delay hitting a black hole singularity cause you to reach it faster?
In general relativity, proper time is maximized along geodesics. Inside of a black hole, all future-oriented timelike trajectories end at the singularity. Putting these two facts together, we find that any deviation from geodesic free fall decreases…
tparker
- 51,104
20
votes
2 answers
Chasing someone who has fallen into a black hole
Assume that my friend and I decided to explore a black hole. I parked the spaceship in a circular orbit safely away from the horizon. He puts on his spacesuit with a jet pack and carefully travels towards the horizon. We communicate by…
Curiosa
- 437