Difference between revisions of "General Relativity Primer"

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Remember the Lorentz invariant interval, which is conserved between frames:
 
Remember the Lorentz invariant interval, which is conserved between frames:
$$ds^2=c^2dt^2-(dx^2+dy^2+dz^2)$$
+
$$ds^2=-c^2dt^2+(dx^2+dy^2+dz^2)$$
 
Light travels a $ds^2=0$ path.  In tensor form, this equation looks like:
 
Light travels a $ds^2=0$ path.  In tensor form, this equation looks like:
 
$$ds^2=\eta_{\alpha\beta}dx^\alpha dx^\beta$$
 
$$ds^2=\eta_{\alpha\beta}dx^\alpha dx^\beta$$

Revision as of 13:39, 17 January 2017

General Relativity Primer

Lorentz invariance dictates that two inertial frame and , with one moving with respect to the other at velocity , are related by:

where . Note, to give a taste of tensor forms, this all may be written as .

Remember the Lorentz invariant interval, which is conserved between frames:

Light travels a path. In tensor form, this equation looks like:

where , the metric tensor, is given by: