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Minkowski Space with object

  1. Mar 28, 2009 #1
    Let's say there is a small object heading towards Earth (it will burn up). It is first observed at:
    [tex]x^{\\mu}=[x^{1},x^{2},x^{2},x^{4}]=[x_{0},y_{0},z_{0},t_{0}][/tex]
    with a velocity:
    [tex]V_{v}=[v_{1},v_{2},v_{3},v_{4}][/tex]

    The metric is:
    [tex]ds^{2} = dx^{2} + dy^{2} + dz^{2} -c^{2}*dt^{2}[/tex]
    [tex]g_{\\mu\\v} = \\left(\\begin{array}{cccc}<BR>1 & 0 & 0 & 0\\\\<BR>0 & 1 & 0 & 0\\\\<Br>0 & 0 & 1 & 0\\\\<BR>\\\\<BR>0 & 0 & 0 & 1<BR>\\end{array})\\right[/tex]

    Affinity is:
    [tex]\\Gamma^{\\rho}{\\mu\\v} = 0[/tex]

    Riemann Curvature tensor is:
    [tex]R^{\\rho}{\\mu\\v\\sigma} = 0[/tex]

    Ricci Tensor is:
    [tex]R{\\mu\\sigma} = 0[/tex]

    My Question is how do you make a geodesic path from the metric and initial velocity?

    [tex]V_{v} = x^{\\mu}*g_{\\mu\\v}[/tex] and make incremental steps?
     
    Last edited: Mar 28, 2009
  2. jcsd
  3. Mar 28, 2009 #2
  4. Mar 29, 2009 #3
    Sorry for the abomination. I know that Minkowski Space has no external gravitational forces acting on it.
     
  5. Mar 29, 2009 #4

    Fredrik

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    You can still edit post #1. Looks like you need to remove a lot of \ symbols.
     
  6. Mar 29, 2009 #5
    You indicated an interest in a numerical solution. I did a Scilab solution for the Schwarzschild metric. Unfortunately I compressed the file using bz2 on Linux and my present (vista) decoder has a problem. If you are interested I will have my Linux machine back up in two weeks or perhaps somebody else will separate out the parts; the mash-up is probably my fault.
    I never checked the compression or enhanced the program since nobody ever responded to my scilab post.
    Some orbits are shown in the eps file at:
    http://www.plaidheron.com/ray/temp/ [Broken]
    drdth_f-example.eps
    Ray
     
    Last edited by a moderator: May 4, 2017
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