how to get the geodesic equation ?

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https://en.wikipedia.org › wiki › Solving_the_geodesic_equations

https://en.wikipedia.org › wiki › Solving_the_geodesic_equations
Solving the geodesic equations – Wikipedia
Solving the geodesic equations is a procedure used in mathematics, particularly Riemannian geometry, and in physics, particularly in general relativity, that results in obtaining geodesics. Physically, these represent the paths of (usually ideal) particles with no proper acceleration, their motion satisfying the geodesic equations. Because the particles are subject to no proper acceleration, the geodesics generally represent the straightest path between two points in a curved …

https://phys.libretexts.org › Bookshelves › Relativity › General_Relativity_(Crowell) › 05:_Curvature › 5.08:_The_Geodesic_Equation

https://phys.libretexts.org › Bookshelves › Relativity › General_Relativity_(Crowell) › 05:_Curvature › 5.08:_The_Geodesic_Equation
5.8: The Geodesic Equation – Physics LibreTexts
The Geodesic Equation Recognizing ∂ κ T μ d x κ d λ as a total non-covariant derivative, we find (5.8.2) ∇ λ T μ = d T μ d λ + Γ κ ν μ T ν d x κ d λ. This is known as the geodesic equation. There is a factor of two that is a common gotcha when applying this equation.

https://phys.libretexts.org › Courses › Skidmore_College › Introduction_to_General_Relativity › 03:_Schwarzschild_Orbits › 3.01:_The_Geodesic_Equation

https://phys.libretexts.org › Courses › Skidmore_College › Introduction_to_General_Relativity › 03:_Schwarzschild_Orbits › 3.01:_The_Geodesic_Equation
3.1: The Geodesic Equation – Physics LibreTexts
The geodesic equation is a way of determining the geodesic that connects two events. You can think of it as an extension of Newton’s First Law to curved spacetimes. Let’s see how this works by applying it to (i.e. the Special Relativity metric). As a reminder, The geodesic equation involves summing over , , and , while is a free index.

https://www.wikihow.com › Find-Geodes

einsteinrelativelyeasy.com › index.php › general-relativity › 97-geodesic-equation-from-the-principle-of-least-action
Geodesic equation from the principle of least action
We get the geodesic equation in its most common form, which is more simple to use than its alternative form with the Christoffel symbol as in this case the metric tensor g αβ get referenced directly. For the sake of it, let us make sure that the two expressions are equivalent. First let us develop the first term of the above equation

https://www.pas.rochester.edu › assets › pdf › undergraduate › solving_geodesic_equation.pdf

https://www.pas.rochester.edu › assets › pdf › undergraduate › solving_geodesic_equation.pdf
PDF Solving the Geodesic Equation – University of Rochester
When the geodesic equation is written in the form of (5), we can identify the Christo el symbols by multiplying that equation by g : g = 1 2 @g @x + @g @x @g @x (14) which is the general relation for the Christo el symbols. This equation can be useful if the metric is diagonal in the coordinate system being used, as then the

https://www.youtube.com › watch?v=PmmU6i0SMic

https://www.youtube.com › watch?v=PmmU6i0SMic
Geodesic Equation Derivation | General Relativity – YouTube
Geodesic Equation Derivation | General Relativity. In this video, I show you how to derive the Geodesic equation via the action approach. Superfluid Helium Resonance Experiment: https://youtu.be …

https://cadabra.science › qa › 1331 › how-to-obtain-the-geodesic-equation-from-the-action

https://cadabra.science › qa › 1331 › how-to-obtain-the-geodesic-equation-from-the-action
How to obtain the geodesic equation from the action? – Cadabra Q&A
However, I’d like to clarify: the geodesic equation can be obtain by extremising (one half of) the Riemannian line element for a given metric, and it is given by the expression stated by @skyfold in the comments of the question. It is, nonetheless, straightforward to obtain the differential equations for the geodesic—once one knows the metric—.

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physicspages.com › pdf › Relativity › Geodesic equation – geodesics on a sphere.pdf
PDF GEODESIC EQUATION – GEODESICS ON A SPHERE – Physicspages
GEODESIC EQUATION – GEODESICS ON A SPHERE 5 tan s R = u p a 2 u (39) Defining s=Rand squaring both sides, we get, using the trig identity 1+tan2 =sec2 = 1 cos2 (40) tan2 = u2 a 2 u (41) a2 tan2 =u2 1+tan2 (42) u=cos = asin (43) Returning to 25, we can now eliminate , since sin2 = 1 cos2 = 1 a2 sin2 1 a2 sin2 d˚ ds = k R (44) d˚ ds = k R 1 a2 sin2 s R (45)

https://cosmo.nyu.edu › yacine › teaching › GR_2019 › lectures › lecture3.pdf

https://cosmo.nyu.edu › yacine › teaching › GR_2019 › lectures › lecture3.pdf
PDF General Relativity Fall 2019 Lecture 3: the geodesic equation
To compute the equation of motion in a general coordinate system, we look for extrema of ˝, again using the Euler-Lagrange equations (2). This time, the right-hand-side is no longer zero, as g (x ) is a priori a function of the non-inertial coordinates. We thus get, for any 2f0;1;2;3g, d d g x_ p g x_ x_ ! = 1 2 @ g ˆ˙ x_ˆx_˙ p g x_ x_ ; notation: @ X @X @x

https://www.physicsforums.com › threads › how-to-read-the-geodesic-equation.990853

https://www.physicsforums.com › threads › how-to-read-the-geodesic-equation.990853
How to read the geodesic equation? | Physics Forums
Your OP in this thread asked about the geodesic equation along a timelike curve; but any timelike curve will have only one point in a spacelike 3-surface, so looking at 3 spatial dimensions tells you nothing at all about the timelike curve except for a single point on it. I suggest keeping this thread focused on the geodesic equation. If you want to ask questions about the EFE you should start a separate thread. But first think carefully about what spacetime is 4-dimensional …

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