Let's say there is a small object heading towards Earth (it will burn up). It is first observed at:(adsbygoogle = window.adsbygoogle || []).push({});

[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?

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# Minkowski Space with object

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