Added caculation of Ricci tensor

GeneralRelativity/CCZ4Geometry.py

@@ -0,0 +1,133 @@
+from typing import Dict
+from GeneralRelativity.DimensionDefinitions import FOR1, FOR2
+from GeneralRelativity.TensorAlgebra import compute_trace
+import torch
+
+
+def compute_ricci_Z(
+    vars: Dict[str, torch.Tensor],
+    d1: Dict[str, torch.Tensor],
+    d2: Dict[str, torch.Tensor],
+    h_UU: torch.Tensor,
+    chris: Dict[str, torch.Tensor],
+    Z_over_chi: torch.Tensor,
+) -> Dict[str, torch.Tensor]:
+    """
+    Compute the Ricci tensor Z using the provided variables, derivatives, and Christoffel symbols.
+
+    Args:
+        vars (dict): Dictionary of tensor variables.
+        d1 (dict): Dictionary of first derivatives of tensor variables.
+        d2 (dict): Dictionary of second derivatives of tensor variables.
+        h_UU (torch.Tensor): Inverse metric tensor.
+        chris (dict): Dictionary containing ULL and LLL Christoffel symbols.
+        Z_over_chi (torch.Tensor): Tensor Z divided by chi.
+
+    Returns:
+        dict: Dictionary containing the components of the Ricci tensor Z.
+    """
+    out = {"LL": torch.zeros_like(vars["h"]), "scalar": 0}
+
+    GR_SPACEDIM = 3
+    boxtildechi = 0
+
+    covdtilde2chi = torch.zeros_like(vars["h"])
+    #    FOR2(k, l)
+    #    {
+    #        covdtilde2chi[k][l] = d2.chi[k][l];
+    #        FOR1(m) { covdtilde2chi[k][l] -= chris.ULL[m][k][l] * d1.chi[m]; }
+    #    }
+    for k, l in FOR2():
+        covdtilde2chi[..., k, l] = d2["chi"][..., k, l]
+        for m in FOR1():
+            covdtilde2chi[..., k, l] -= chris["ULL"][..., m, k, l] * d1["chi"][..., m]
+    #    FOR2(k, l) { boxtildechi += h_UU[k][l] * covdtilde2chi[k][l]; }
+    for k, l in FOR2():
+        boxtildechi += h_UU[..., k, l] * covdtilde2chi[..., k, l]
+    # data_t dchi_dot_dchi = 0;
+    #    {
+    #        FOR2(m, n) { dchi_dot_dchi += h_UU[m][n] * d1.chi[m] * d1.chi[n]; }
+    #    }
+    dchi_dot_dchi = torch.zeros_like(vars["chi"][...])
+    for m, n in FOR2():
+        dchi_dot_dchi += h_UU[..., m, n] * d1["chi"][..., m] * d1["chi"][..., n]
+
+    # FOR2(i, j)
+    # {
+    for i, j in FOR2():
+        #    data_t ricci_tilde = 0;
+        #    FOR1(k)
+        #    {
+        ricci_tilde = 0
+        for k in FOR1():
+            #    ricci_tilde += 0.5 * (vars.h[k][i] * d1.Gamma[k][j] +
+            #                          vars.h[k][j] * d1.Gamma[k][i]);
+            #    ricci_tilde += 0.5 * (vars.Gamma[k] - 2 * Z_over_chi[k]) *
+            #                   (chris.LLL[i][j][k] + chris.LLL[j][i][k]);
+            ricci_tilde += 0.5 * (
+                vars["h"][..., k, i] * d1["Gamma"][..., k, j]
+                + vars["h"][..., k, j] * d1["Gamma"][..., k, i]
+            )
+            ricci_tilde += (
+                0.5
+                * (vars["Gamma"][..., k] - 2 * Z_over_chi[..., k])
+                * (chris["LLL"][..., i, j, k] + chris["LLL"][..., j, i, k])
+            )
+            # FOR1(l)
+            # {
+            for l in FOR1():
+                #  ricci_tilde -= 0.5 * h_UU[k][l] * d2.h[i][j][k][l];
+                ricci_tilde -= 0.5 * h_UU[..., k, l] * d2["h"][..., i, j, k, l]
+                #  FOR1(m)
+                #   {
+                for m in FOR1():
+                    # ricci_tilde +=
+                    #        h_UU[l][m] *
+                    #        (chris.ULL[k][l][i] * chris.LLL[j][k][m] +
+                    #         chris.ULL[k][l][j] * chris.LLL[i][k][m] +
+                    #         chris.ULL[k][i][m] * chris.LLL[k][l][j]);
+                    ricci_tilde += h_UU[..., l, m] * (
+                        chris["ULL"][..., k, l, i] * chris["LLL"][..., j, k, m]
+                        + chris["ULL"][..., k, l, j] * chris["LLL"][..., i, k, m]
+                        + chris["ULL"][..., k, i, m] * chris["LLL"][..., k, l, j]
+                    )
+
+        # data_t ricci_chi =
+        #    0.5 * ((GR_SPACEDIM - 2) * covdtilde2chi[i][j] +
+        #    vars.h[i][j] * boxtildechi -
+        #    ((GR_SPACEDIM - 2) * d1.chi[i] * d1.chi[j] +
+        #    GR_SPACEDIM * vars.h[i][j] * dchi_dot_dchi) /
+        #    (2 * vars.chi));
+        ricci_chi = 0.5 * (
+            (GR_SPACEDIM - 2) * covdtilde2chi[..., i, j]
+            + vars["h"][..., i, j] * boxtildechi
+            - (
+                (GR_SPACEDIM - 2) * d1["chi"][..., i] * d1["chi"][..., j]
+                + GR_SPACEDIM * vars["h"][..., i, j] * dchi_dot_dchi
+            )
+            / (2 * vars["chi"])
+        )
+        # data_t z_terms = 0;
+        # FOR1(k)
+        # {
+        z_terms = 0
+        for k in FOR1():
+            # z_terms +=
+            # Z_over_chi[k] *
+            # (vars.h[i][k] * d1.chi[j] + vars.h[j][k] * d1.chi[i] -
+            # vars.h[i][j] * d1.chi[k] + d1.h[i][j][k] * vars.chi);
+            z_terms += Z_over_chi[..., k] * (
+                vars["h"][..., i, k] * d1["chi"][..., j]
+                + vars["h"][..., j, k] * d1["chi"][..., i]
+                - vars["h"][..., i, j] * d1["chi"][..., k]
+                + d1["h"][..., i, j, k] * vars["chi"]
+            )
+        #     out.LL[i][j] =
+        #        (ricci_chi + vars.chi * ricci_tilde + z_terms) / vars.chi;
+        out["LL"][..., i, j] = (ricci_chi + vars["chi"] * ricci_tilde + z_terms) / vars[
+            "chi"
+        ]
+    # out.scalar = vars.chi * TensorAlgebra::compute_trace(out.LL, h_UU);
+    out["scalar"] = vars["chi"] * compute_trace(out["LL"], h_UU)
+
+    return out