Changed label "ADM" -> "Landau-Lifshitz" for the existing definitions (from

Weinberg); added ADM definitions (from Alcubierre's book).


git-svn-id: https://svn.cct.lsu.edu/repos/numrel/LSUThorns/QuasiLocalMeasures/trunk@9 ef6f4158-a8ee-47d1-ba14-cb73256398e0

2 files changed, 121 insertions, 26 deletions

diff --git a/interface.ccl b/interface.ccl
index 0c01900..050d3d0 100644
--- a/interface.ccl
+++ b/interface.ccl
@@ -177,6 +177,9 @@ REAL qlm_scalars[num_surfaces] TYPE=scalar
   qlm_adm_energy
   qlm_adm_momentum_x qlm_adm_momentum_y qlm_adm_momentum_z
   qlm_adm_angular_momentum_x qlm_adm_angular_momentum_y qlm_adm_angular_momentum_z
+  qlm_ll_energy
+  qlm_ll_momentum_x qlm_ll_momentum_y qlm_ll_momentum_z
+  qlm_ll_angular_momentum_x qlm_ll_angular_momentum_y qlm_ll_angular_momentum_z
 } "Scalar quantities on the surface"
 
 REAL qlm_scalars_p[num_surfaces] TYPE=scalar
diff --git a/src/qlm_analyse.F90 b/src/qlm_analyse.F90
index 44f0cba..887652e 100644
--- a/src/qlm_analyse.F90
+++ b/src/qlm_analyse.F90
@@ -34,7 +34,8 @@ subroutine qlm_analyse (CCTK_ARGUMENTS, hn)
   CCTK_REAL    :: xx(3), ee(3,2)
   CCTK_REAL    :: xi(2), xi1(3)
   CCTK_REAL    :: qq(2,2), dtq
-  CCTK_REAL    :: adm_energy, adm_mom(3), adm_amom(3,3)
+  CCTK_REAL    :: adm_energy, adm_mom(3), adm_amom(3)
+  CCTK_REAL    :: ll_energy, ll_mom(3), ll_amom(3,3)
   CCTK_COMPLEX :: ev
   CCTK_REAL    :: spin
   CCTK_REAL    :: npspin
@@ -95,6 +96,14 @@ subroutine qlm_analyse (CCTK_ARGUMENTS, hn)
   qlm_adm_angular_momentum_y(hn) = 0
   qlm_adm_angular_momentum_z(hn) = 0
 
+  qlm_ll_energy(hn) = 0
+  qlm_ll_momentum_x(hn) = 0
+  qlm_ll_momentum_y(hn) = 0
+  qlm_ll_momentum_z(hn) = 0
+  qlm_ll_angular_momentum_x(hn) = 0
+  qlm_ll_angular_momentum_y(hn) = 0
+  qlm_ll_angular_momentum_z(hn) = 0
+
   ! Compute weights for spherical integration (see Driscoll and Healy).
   ! These are the correct weights in a Gauss-Legendre-Senc.
   ! Also compare qlm_area with AHFinderDirect's area, they are in much
@@ -318,68 +327,137 @@ subroutine qlm_analyse (CCTK_ARGUMENTS, hn)
              + coordspinz * sqrt(dtq) * weights(i)
         
         ! ADM quantities
-        ! Weinberg, chapter 7.6, pp. 165 ff, eqns. (7.6.22) - (7.6.24):
+        ! Alcubierre, Appendix A, p. 402 ff, eqns. (A.5) - (A.7):
         
         ! ADM energy
-        ! E_adm = (-1/16 pi) int_S(r) [h_jj,i - hij,j] n_i r^2 dOmega
+        ! E_adm = (1/16 pi) int_S(r) [delta^jk h_ik,j - (trace(h)),i] n^i r^2 dOmega
         adm_energy = 0
         do a=1,3
            do b=1,3
-              adm_energy = adm_energy + (dh4(b,b,a) - dh4(a,b,b)) * ss(a)
+              do c=1,3
+                 adm_energy = adm_energy + (delta3(a,b) * dh4(a,c,b) &
+             & - gu(a,b) * dh4(a,b,c) - h4(a,b) * dgu(a,b,c) ) * ss(c)
+              end do
            end do
         end do
         qlm_adm_energy(hn) = qlm_adm_energy(hn) &
-             & + adm_energy / (-16*pi) &
-             &   * sqrt(dtq) * weights(i)
+             & + adm_energy / (16*pi) &
+             &   * sqrt(dtq) * qlm_delta_theta(hn) * qlm_delta_phi(hn)
         
         ! ADM momentum
-        ! P_adm^j = (-1/16 pi) int_S(r)
+        ! P_adm^i = (1/8 pi) int_S(r) [K^i_j - K delta^i_j] n^j r^2 dOmega
+        do a=1,3
+           adm_mom(a) = 0
+           do b=1,3
+              do c=1,3
+                 adm_mom(a) = adm_mom(a) &
+             &        + gu(a,c) * kk(c,b) * ss(b) 
+              end do
+              adm_mom(a) = adm_mom(a) &
+                   + delta3(a,b) * trk * ss(b) 
+           end do
+        end do
+        qlm_adm_momentum_x(hn) = qlm_adm_momentum_x(hn) &
+             & + adm_mom(1) / (8*pi) &
+             &   * sqrt(dtq) * qlm_delta_theta(hn) * qlm_delta_phi(hn)
+        qlm_adm_momentum_y(hn) = qlm_adm_momentum_y(hn) &
+             & + adm_mom(2) / (8*pi) &
+             &   * sqrt(dtq) * qlm_delta_theta(hn) * qlm_delta_phi(hn)
+        qlm_adm_momentum_z(hn) = qlm_adm_momentum_z(hn) &
+             & + adm_mom(3) / (8*pi) &
+             &   * sqrt(dtq) * qlm_delta_theta(hn) * qlm_delta_phi(hn)
+        
+        ! ADM angular momentum
+        ! J_adm^i = (1/8 pi) int_S(r)
+        !   epsilon^ijk x_j (K_kl - delta_kl K) * n^l dS 
+        do a=1,3
+           adm_amom(a) = 0
+           do b=1,3
+              do c=1,3
+                 do l=1,3
+                    do m=1,3
+                       adm_amom(a) = adm_amom(a)  &
+                &         + epsilon3(a,b,c) * xx(b) * gu(c,m) * kk(m,l) * ss(l)
+                    end do
+                    adm_amom(a) = adm_amom(a)  &
+                &    - epsilon3(a,b,c) * xx(b) *  delta3(c,l) * trk * ss(l)
+                 end do
+              end do
+           end do
+        end do
+        qlm_adm_angular_momentum_x(hn) = qlm_adm_angular_momentum_x(hn) &
+             & + adm_amom(1) / (8*pi) &
+             &   * sqrt(dtq) * qlm_delta_theta(hn) * qlm_delta_phi(hn)
+        qlm_adm_angular_momentum_y(hn) = qlm_adm_angular_momentum_y(hn) &
+             & + adm_amom(2) / (8*pi) &
+             &   * sqrt(dtq) * qlm_delta_theta(hn) * qlm_delta_phi(hn)
+        qlm_adm_angular_momentum_z(hn) = qlm_adm_angular_momentum_z(hn) &
+             & + adm_amom(3) / (8*pi) &
+             &   * sqrt(dtq) * qlm_delta_theta(hn) * qlm_delta_phi(hn)
+
+        ! Landau-Lifshitz quantities
+        ! Weinberg, chapter 7.6, pp. 165 ff, eqns. (7.6.22) - (7.6.24):
+        
+        ! Landau-Lifshitz energy
+        ! E_ll = (-1/16 pi) int_S(r) [h_jj,i - hij,j] n_i r^2 dOmega
+        ll_energy = 0
+        do a=1,3
+           do b=1,3
+              ll_energy = ll_energy + (dh4(b,b,a) - dh4(a,b,b)) * ss(a)
+           end do
+        end do
+        qlm_ll_energy(hn) = qlm_ll_energy(hn) &
+             & + ll_energy / (-16*pi) &
+             &   * sqrt(dtq) * weights(i)
+        
+        ! Landau-Lifshitz momentum
+        ! P_ll^j = (-1/16 pi) int_S(r)
         !    [- h_kk,0 delta_ij + h_k0,k delta_ij
         !     - h_j0,i + h_ij,0                  ] n_i r^2 dOmega
         ! 
-        ! P_adm^j = (1/8 pi) int_S(r) [K_ij - K delta_ij] n_i r^2 dOmega
+        ! P_ll^j = (1/8 pi) int_S(r) [K_ij - K delta_ij] n_i r^2 dOmega
         do a=1,3
-           adm_mom(a) = 0
+           ll_mom(a) = 0
            do b=1,3
-              adm_mom(a) = adm_mom(a) &
+              ll_mom(a) = ll_mom(a) &
                    + (- dh4(b,b,0) + dh4(b,0,b)) * ss(a) &
                    + (- dh4(a,0,b) + dh4(b,a,0)) * ss(b)
            end do
         end do
-        qlm_adm_momentum_x(hn) = qlm_adm_momentum_x(hn) &
-             & + adm_mom(1) / (-16*pi) &
+        qlm_ll_momentum_x(hn) = qlm_ll_momentum_x(hn) &
+             & + ll_mom(1) / (-16*pi) &
              &   * sqrt(dtq) * weights(i)
-        qlm_adm_momentum_y(hn) = qlm_adm_momentum_y(hn) &
-             & + adm_mom(2) / (-16*pi) &
+        qlm_ll_momentum_y(hn) = qlm_ll_momentum_y(hn) &
+             & + ll_mom(2) / (-16*pi) &
              &   * sqrt(dtq) * weights(i)
-        qlm_adm_momentum_z(hn) = qlm_adm_momentum_z(hn) &
-             & + adm_mom(3) / (-16*pi) &
+        qlm_ll_momentum_z(hn) = qlm_ll_momentum_z(hn) &
+             & + ll_mom(3) / (-16*pi) &
              &   * sqrt(dtq) * weights(i)
         
-        ! ADM angular momentum
-        ! J_adm^jk = (-1/16 pi) int_S(r)
+        ! Landau-Lifshitz angular momentum
+        ! J_ll^jk = (-1/16 pi) int_S(r)
         !    [- x_j h_0k,i + x_k h_0j,i
         !     + x_j h_ki,0 - x_k h_ji,0
         !     + h_0k delta_ij - h_0j delta_ik] n_i r^2 dOmega
         do a=1,3
            do b=1,3
-              adm_amom(a,b) = 0
+              ll_amom(a,b) = 0
               do c=1,3
-                 adm_amom(a,b) = adm_amom(a,b) + ss(c) * ( &
+                 ll_amom(a,b) = ll_amom(a,b) + ss(c) * ( &
                       + (- xx(a) * dh4(0,b,c) + xx(b) * dh4(0,a,c)) &
                       + (+ xx(a) * dh4(b,c,0) - xx(b) * dh4(a,c,0)) &
                       + (h4(0,b) * delta4(c,a) - h4(0,a) * delta4(c,b)))
               end do
            end do
         end do
-        qlm_adm_angular_momentum_x(hn) = qlm_adm_angular_momentum_x(hn) &
-             & + adm_amom(2,3) / (-16*pi) &
+        qlm_ll_angular_momentum_x(hn) = qlm_ll_angular_momentum_x(hn) &
+             & + ll_amom(2,3) / (-16*pi) &
              &   * sqrt(dtq) * weights(i)
-        qlm_adm_angular_momentum_y(hn) = qlm_adm_angular_momentum_y(hn) &
-             & + adm_amom(3,1) / (-16*pi) &
+        qlm_ll_angular_momentum_y(hn) = qlm_ll_angular_momentum_y(hn) &
+             & + ll_amom(3,1) / (-16*pi) &
              &   * sqrt(dtq) * weights(i)
-        qlm_adm_angular_momentum_z(hn) = qlm_adm_angular_momentum_z(hn) &
-             & + adm_amom(1,2) / (-16*pi) &
+        qlm_ll_angular_momentum_z(hn) = qlm_ll_angular_momentum_z(hn) &
+             & + ll_amom(1,2) / (-16*pi) &
              &   * sqrt(dtq) * weights(i)
         
      end do
@@ -483,6 +561,20 @@ subroutine qlm_analyse (CCTK_ARGUMENTS, hn)
      call CCTK_INFO (msg)
      write (msg, '("   ADM angular momentum z: ",g16.6)') qlm_adm_angular_momentum_z(hn)
      call CCTK_INFO (msg)
+     write (msg, '("   Landau-Lifshitz energy:             ",g16.6)') qlm_ll_energy(hn)
+     call CCTK_INFO (msg)
+     write (msg, '("   Landau-Lifshitz momentum x:         ",g16.6)') qlm_ll_momentum_x(hn)
+     call CCTK_INFO (msg)
+     write (msg, '("   Landau-Lifshitz momentum y:         ",g16.6)') qlm_ll_momentum_y(hn)
+     call CCTK_INFO (msg)
+     write (msg, '("   Landau-Lifshitz momentum z:         ",g16.6)') qlm_ll_momentum_z(hn)
+     call CCTK_INFO (msg)
+     write (msg, '("   Landau-Lifshitz angular momentum x: ",g16.6)') qlm_ll_angular_momentum_x(hn)
+     call CCTK_INFO (msg)
+     write (msg, '("   Landau-Lifshitz angular momentum y: ",g16.6)') qlm_ll_angular_momentum_y(hn)
+     call CCTK_INFO (msg)
+     write (msg, '("   Landau-Lifshitz angular momentum z: ",g16.6)') qlm_ll_angular_momentum_z(hn)
+     call CCTK_INFO (msg)
      
   end if