Merge pull request sxs-collaboration#5688 from nikwit/KS-christoffel

Add spacetime Christoffel symbols to Kerr-Schild spacetime
jyoo1042 · Jan 4, 2024 · 10c0957 · 10c0957
2 parents 44798f9 + b3621ed
commit 10c0957
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Showing 4 changed files with 44 additions and 3 deletions.
diff --git a/src/PointwiseFunctions/AnalyticSolutions/GeneralRelativity/KerrSchild.cpp b/src/PointwiseFunctions/AnalyticSolutions/GeneralRelativity/KerrSchild.cpp
@@ -16,7 +16,9 @@
 #include "DataStructures/Tensor/EagerMath/Trace.hpp"
 #include "Options/ParseError.hpp"
 #include "PointwiseFunctions/GeneralRelativity/Christoffel.hpp"
+#include "PointwiseFunctions/GeneralRelativity/DerivativesOfSpacetimeMetric.hpp"
 #include "PointwiseFunctions/GeneralRelativity/ExtrinsicCurvature.hpp"
+#include "PointwiseFunctions/GeneralRelativity/InverseSpacetimeMetric.hpp"
 #include "PointwiseFunctions/GeneralRelativity/Tags.hpp"
 #include "Utilities/ConstantExpressions.hpp"
 #include "Utilities/ContainerHelpers.hpp"
@@ -756,6 +758,41 @@ KerrSchild::IntermediateVars<DataType, Frame>::get_var(
       spatial_christoffel_second_kind, inverse_spatial_metric);
 }
 
+template <typename DataType, typename Frame>
+tnsr::Abb<DataType, 3, Frame>
+KerrSchild::IntermediateVars<DataType, Frame>::get_var(
+    const IntermediateComputer<DataType, Frame>& computer,
+    gr::Tags::SpacetimeChristoffelSecondKind<DataType, 3, Frame> /*meta*/) {
+  const auto& lapse = get_var(computer, gr::Tags::Lapse<DataType>{});
+  const auto& shift = get_var(computer, gr::Tags::Shift<DataType, 3, Frame>{});
+  const auto& spatial_metric =
+      get_var(computer, gr::Tags::SpatialMetric<DataType, 3, Frame>{});
+  const auto& inverse_spatial_metric =
+      get_var(computer, gr::Tags::InverseSpatialMetric<DataType, 3, Frame>{});
+  const auto& dt_lapse =
+      get_var(computer, ::Tags::dt<gr::Tags::Lapse<DataType>>{});
+  const auto& di_lapse = get_var(
+      computer,
+      ::Tags::deriv<gr::Tags::Lapse<DataType>, tmpl::size_t<3>, Frame>{});
+  const auto& dt_shift =
+      get_var(computer, ::Tags::dt<gr::Tags::Shift<DataType, 3, Frame>>{});
+  const auto& di_shift =
+      get_var(computer, ::Tags::deriv<gr::Tags::Shift<DataType, 3, Frame>,
+                                      tmpl::size_t<3>, Frame>{});
+  const auto& dt_spatial_metric = get_var(
+      computer, ::Tags::dt<gr::Tags::SpatialMetric<DataType, 3, Frame>>{});
+  const auto& di_spatial_metric = get_var(
+      computer, ::Tags::deriv<gr::Tags::SpatialMetric<DataType, 3, Frame>,
+                              tmpl::size_t<3>, Frame>{});
+  const auto inverse_spacetime_metric =
+      gr::inverse_spacetime_metric(lapse, shift, inverse_spatial_metric);
+  const auto d_spacetime_metric = gr::derivatives_of_spacetime_metric(
+      lapse, dt_lapse, di_lapse, shift, dt_shift, di_shift, spatial_metric,
+      dt_spatial_metric, di_spatial_metric);
+  return gr::christoffel_second_kind(d_spacetime_metric,
+                                     inverse_spacetime_metric);
+}
+
 #define DTYPE(data) BOOST_PP_TUPLE_ELEM(0, data)
 #define FRAME(data) BOOST_PP_TUPLE_ELEM(1, data)
 

diff --git a/src/PointwiseFunctions/AnalyticSolutions/GeneralRelativity/KerrSchild.hpp b/src/PointwiseFunctions/AnalyticSolutions/GeneralRelativity/KerrSchild.hpp
@@ -250,7 +250,8 @@ class KerrSchild : public AnalyticSolution<3_st>,
       gr::Tags::TraceExtrinsicCurvature<DataType>,
       gr::Tags::SpatialChristoffelFirstKind<DataType, 3, Frame>,
       gr::Tags::SpatialChristoffelSecondKind<DataType, 3, Frame>,
-      gr::Tags::TraceSpatialChristoffelSecondKind<DataType, 3, Frame>>>;
+      gr::Tags::TraceSpatialChristoffelSecondKind<DataType, 3, Frame>,
+      gr::Tags::SpacetimeChristoffelSecondKind<DataType, 3, Frame>>>;
 
   KerrSchild() = default;
   KerrSchild(const KerrSchild& /*rhs*/) = default;
@@ -552,6 +553,9 @@ class KerrSchild : public AnalyticSolution<3_st>,
         const IntermediateComputer<DataType, Frame>& computer,
         gr::Tags::TraceSpatialChristoffelSecondKind<DataType, 3,
                                                     Frame> /*meta*/);
+    tnsr::Abb<DataType, 3, Frame> get_var(
+        const IntermediateComputer<DataType, Frame>& computer,
+        gr::Tags::SpacetimeChristoffelSecondKind<DataType, 3, Frame> /*meta*/);
 
    private:
     // Here null_vector_0 is simply -1, but if you have a boosted solution,

diff --git a/src/PointwiseFunctions/GeneralRelativity/DerivativesOfSpacetimeMetric.cpp b/src/PointwiseFunctions/GeneralRelativity/DerivativesOfSpacetimeMetric.cpp
@@ -126,7 +126,7 @@ void derivatives_of_spacetime_metric(
 }  // namespace gr
 
 GENERATE_INSTANTIATIONS(INSTANTIATE, (1, 2, 3), (double, DataVector),
-                        (Frame::Grid, Frame::Inertial))
+                        (Frame::Grid, Frame::Distorted, Frame::Inertial))
 
 #undef DIM
 #undef DTYPE

diff --git a/src/PointwiseFunctions/GeneralRelativity/InverseSpacetimeMetric.cpp b/src/PointwiseFunctions/GeneralRelativity/InverseSpacetimeMetric.cpp
@@ -68,7 +68,7 @@ void inverse_spacetime_metric(
           inverse_spatial_metric);
 
 GENERATE_INSTANTIATIONS(INSTANTIATE, (1, 2, 3), (double, DataVector),
-                        (Frame::Grid, Frame::Inertial))
+                        (Frame::Grid, Frame::Distorted, Frame::Inertial))
 
 #undef DIM
 #undef DTYPE