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equations:geodesic_equation [2018/04/14 11:09]
aresmarrero [Intuitive]
equations:geodesic_equation [2018/12/19 11:01] (current)
jakobadmin ↷ Links adapted because of a move operation
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 Solutions of the geodesic equations are called geodesics. ​ Solutions of the geodesic equations are called geodesics. ​
  
-Geodesics are the straightest path between two points in a curved spacetime.  ​+Geodesics are the "​shortest"​ paths between two points in a flat spacetime and the straightest path between two points in a curved spacetime.  ​
   ​   ​
 +On a sphere the geodesics are "great circles"​. ​
 <tabbox Concrete> ​ <tabbox Concrete> ​
  
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 \end{align*} \end{align*}
 where the last line follows since $g_{ik}=g_{ki}$. where the last line follows since $g_{ik}=g_{ki}$.
-Now we define the so-called [[advanced_notions:general_relativity:christoffel_symbols|Christoffel symbols]]+Now we define the so-called [[advanced_tools:connections:levi_civita_connection|Christoffel symbols]]
 \[ \[
  ​\Gamma_{ijk} \equiv -\bigl(\partial_{i}g_{jk}-\partial_{k}g_{ij}-\partial_{j}g_{ki}\bigr)  ​\Gamma_{ijk} \equiv -\bigl(\partial_{i}g_{jk}-\partial_{k}g_{ij}-\partial_{j}g_{ki}\bigr)
equations/geodesic_equation.1523696990.txt.gz · Last modified: 2018/04/14 09:09 (external edit)