T2: 5. Geodesics Flashcards
1
Q
What are geodesics?
A
The path of a particle’s free motion in curved spacetime. The ‘straightest possible’ paths.
2
Q
State the geodesic equation? What statement is this equivalent to?
A
V_µ ∇_µ V_ν = 0
3
Q
Define affine parameter
A
The parameter λ which ensures the geodesic equation.
4
Q
Why do we get the full set of Euler-Lagrange in curved space (vs flat space)
A
Since the metric depends on x^µ we have dependence on this and x˙^µ.
5
Q
State the EL equations
A
CHECK NOTES :))
6
Q
Why can we not use the flat space definition of a straight line: V^ν ∂_ν V^μ=0
A
The object ∂_ν V^μ is not a tensor, so the result would not be coordinate independent.
