diff options
| -rw-r--r-- | null.py | 4 |
1 files changed, 3 insertions, 1 deletions
@@ -27,7 +27,9 @@ def _null_geodesic_axis_rhs(Lambda, f, As p^μ should be null, it also holds 0 = g_μν p^μ p^ν = g_tt (p^t)^2 + 2 g_tx p^t p^x + g_xx (p^x)^2 - -> p^t = (-g_tx p^x ± √((g_tx p^x)^2 - g_tt g_xx (p^x)^2)) / g_tt + -> p^x = (-g_tx p^t ± √((g_tx p^t)^2 - g_tt g_xx (p^t)^2)) / g_xx + This constraint needs to be enforced at runtime to ensure the curve remains + null. With zero shift, it can be easily computed that Γ^t_tt = 0.5 g^tt g_tt,t |