pub fn parallel_transport_kernel<T>(
initial_vector: &[T],
path: &[Vec<T>],
christoffel: &CausalTensor<T>,
) -> Result<Vec<T>, PhysicsError>Expand description
Parallel transports a vector along a discrete path using Christoffel symbols.
Solves: $\frac{Dv^\mu}{d\lambda} = \frac{dv^\mu}{d\lambda} + \Gamma^\mu_{\nu\rho} \frac{dx^\nu}{d\lambda} v^\rho = 0$
Uses Euler method for simplicity along discretized path segments.
§Arguments
initial_vector- Vector $v_0^\mu$ to transport.path- List of positions along the path (each position is a slice of coordinates).christoffel- Christoffel symbols $\Gamma^\mu_{\nu\rho}$ (Rank 3 tensor [dim, dim, dim]).
§Returns
Ok(Vec<T>)- The parallel-transported vector at the end of the path.