Questions tagged [geodesics]

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).

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With north and south poles fixed, do all geodesics have constant $\theta$ and $\phi$?

I was going thorough reading Kolb and Turner's The Early Universe where in Section 2.2 it starts by asking the following question. For a comoving observer with coordinates $(r_0,\theta_0,\phi_0)$, ...
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Inertial frame and its transformation in anti-de Sitter spacetime

From the wikipedia, I learned and was able to follow mathematically the definition of anti-de Sitter space. As the maximally symmetric solution to field equations with negative cosmological constant, ...
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Why is the Christoffel symbol in the geodesic equation for a test particle negative?

The geodesic equation is $${d^2 x^\mu \over {ds}^2}+\Gamma^\mu {}_{\alpha \beta}{d x^\alpha \over ds}{d x^\beta \over ds}=0\$$ for some scalar parameter of motion s and connection coefficients of ...
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How does spatial curvature apply to the planets' orbits?

We all know that in the presence of large, massive objects, spacetime is positively curved, more so the more massive it is. This means that the path of an object without any forces on it is a straight ...
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Some aspect of covariant derivative of point particle energy-momentum tensor

My question is related to Derivation of the geodesic equation from the continuity equation for the energy momentum tensor I need to understand one step in derivation. Let's consider the Energy-...
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Is there a known mechanism for mass-energy distorting spacetime?

I’ve been really interested in learning about the mechanisms behind physical phenomena that go beyond just learning to manipulate the equations and give a physical intuition about HOW something ...
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How to compute Kerr geodesics?

How would I start to numerically compute trajectories of Kerr geodesics with constants of motion like in this wikipedia page. I want to recreate trajectories like in this picture in Matlab.
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Rotationally invariant metrics and conservation of angular momentum

This was prompted by an exam question, though the questions are more general: A 2D Riemannian space has the metric: $ds^2=dr^2 + \gamma^2 r^4 d\phi^2$ State what conserved quantity ...
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Proving that test particles in GR, follow spacetime geodesics

My question is pretty much in the title. According to this paper, this is not exactly proven rigorously yet. What I dont understand is what exactly is not proven. If I'm not too wrong, a test particle ...
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Radial infall in Schwarzschild

In Straumann's book on general relativity, one finds the following solution to the question of geodesic radial infall into the black hole: $$d\tau=(\frac{2m}{r}-\frac{2m}{R})^{-\frac{1}{2}}dr$$ To ...
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Why can we parameterize a null geodesic such that its velocity is four-momentum? [duplicate]

One principle in general relativity is that the wordlines of massless particles are null geodesics. It also seem to be a commonly stated fact (for instance see eq. (3.62) in Section 3.4 of Carroll's ...
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Fundamental Principle of Dynamics and equations of geodesics with proper time

I just wanted to have a little precision. In the expression below translating the PFD (Fundamental Principle of Dynamics) in tensor calculus (or more precisely the inertial principle) : a^{\nu}=\...
In one of my lecture, it is said: Let us use the freedom of the choice of parametrization to demand that the variation of $\lambda$ after a small displacement along the curve is proportional to the ...