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fix geodesics transformation #57

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Kwasniok opened this issue Oct 4, 2021 · 0 comments
Open

fix geodesics transformation #57

Kwasniok opened this issue Oct 4, 2021 · 0 comments
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Kwasniok commented Oct 4, 2021

The Christoffel symbols do not transform like tensors. This leads to a correction term when dealing with a covariant derivative.

- {\Gamma^\prime}^i_{ab} {u^\prime}^a {u^\prime}^b = \frac{\partial {x^\prime}^i}{\partial x^ j} \left ( -\Gamma^j_{cd} u^c u^d  - \frac{\partial^2 x^j}{\partial x^c \partial {x^\prime}^e} \frac{{x^\prime}^e}{\partial x^d}  u^c u^d\right )

christoffel_correction_term

@Kwasniok Kwasniok added bug Something isn't working priority-high high priority labels Oct 4, 2021
@Kwasniok Kwasniok added this to the v5 milestone Oct 4, 2021
@Kwasniok Kwasniok self-assigned this Oct 4, 2021
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