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authorAnton Khirnov <anton@khirnov.net>2023-04-04 21:23:44 +0200
committerAnton Khirnov <anton@khirnov.net>2023-04-04 21:23:44 +0200
commit49fb496527a3557ee44cc0ac210eba2ca8dd7bc6 (patch)
treea7a55049e15cd826fbf82e82d3d65885108eb74c
parent564b1ce9d104c2b25b1a2aff719327efddc26bb3 (diff)
null: update documentation
-rw-r--r--null.py4
1 files changed, 3 insertions, 1 deletions
diff --git a/null.py b/null.py
index 1bdc5ab..2ba59f0 100644
--- a/null.py
+++ b/null.py
@@ -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