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|
/*
* Methods of class Black_hole to compute global quantities
*
* (see file blackhole.h for documentation).
*
*/
/*
* Copyright (c) 2005-2007 Keisuke Taniguchi
*
* This file is part of LORENE.
*
* LORENE is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2
* as published by the Free Software Foundation.
*
* LORENE is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
char blackhole_global_C[] = "$Header: /cvsroot/Lorene/C++/Source/Black_hole/blackhole_global.C,v 1.5 2014/10/13 08:52:46 j_novak Exp $" ;
/*
* $Id: blackhole_global.C,v 1.5 2014/10/13 08:52:46 j_novak Exp $
* $Log: blackhole_global.C,v $
* Revision 1.5 2014/10/13 08:52:46 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.4 2014/10/06 15:13:02 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.3 2008/07/02 20:45:58 k_taniguchi
* Addition of routines to compute angular momentum.
*
* Revision 1.2 2008/05/15 19:28:03 k_taniguchi
* Change of some parameters.
*
* Revision 1.1 2007/06/22 01:19:51 k_taniguchi
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Source/Black_hole/blackhole_global.C,v 1.5 2014/10/13 08:52:46 j_novak Exp $
*
*/
// C++ headers
//#include <>
// C headers
#include <cmath>
// Lorene headers
#include "blackhole.h"
#include "unites.h"
#include "utilitaires.h"
//-----------------------------------------//
// Irreducible mass of BH //
//-----------------------------------------//
namespace Lorene {
double Black_hole::mass_irr() const {
// Fundamental constants and units
// -------------------------------
using namespace Unites ;
if (p_mass_irr == 0x0) { // a new computation is required
Scalar psi4(mp) ;
psi4 = pow(confo, 4.) ;
psi4.std_spectral_base() ;
psi4.annule_domain(0) ;
psi4.raccord(1) ;
double radius_ah = mp.val_r(1,-1.,M_PI/2.,0.) ;
Map_af mp_aff(mp) ;
double a_ah = mp_aff.integrale_surface(psi4, radius_ah) ;
double mirr = sqrt(a_ah/16./M_PI) / ggrav ;
p_mass_irr = new double( mirr ) ;
}
return *p_mass_irr ;
}
//---------------------------//
// ADM mass //
//---------------------------//
double Black_hole::mass_adm() const {
// Fundamental constants and units
// -------------------------------
using namespace Unites ;
if (p_mass_adm == 0x0) { // a new computation is required
double madm ;
double integ_s ;
double integ_v ;
double radius_ah = mp.val_r(1,-1.,M_PI/2.,0.) ;
Map_af mp_aff(mp) ;
Scalar source_surf(mp) ;
source_surf.set_etat_qcq() ;
Scalar source_volm(mp) ;
source_volm.set_etat_qcq() ;
Scalar rr(mp) ;
rr = mp.r ;
rr.std_spectral_base() ;
Scalar st(mp) ;
st = mp.sint ;
st.std_spectral_base() ;
Scalar ct(mp) ;
ct = mp.cost ;
ct.std_spectral_base() ;
Scalar sp(mp) ;
sp = mp.sinp ;
sp.std_spectral_base() ;
Scalar cp(mp) ;
cp = mp.cosp ;
cp.std_spectral_base() ;
Vector ll(mp, CON, mp.get_bvect_cart()) ;
ll.set_etat_qcq() ;
ll.set(1) = st * cp ;
ll.set(2) = st * sp ;
ll.set(3) = ct ;
ll.std_spectral_base() ;
Scalar lldconf = confo.dsdr() ;
lldconf.std_spectral_base() ;
if (kerrschild) {
cout << "!!!!! WARNING: Not yet available !!!!!" << endl ;
abort() ;
/*
Scalar divshf(mp) ;
divshf = shift_rs(1).deriv(1) + shift_rs(2).deriv(2)
+ shift_rs(3).deriv(3) ;
divshf.std_spectral_base() ;
divshf.dec_dzpuis(2) ;
Scalar llshift(mp) ;
llshift = ll(1)%shift_rs(1) + ll(2)%shift_rs(2)
+ ll(3)%shift_rs(3) ;
llshift.std_spectral_base() ;
Scalar lldllsh = llshift.dsdr() ;
lldllsh.std_spectral_base() ;
lldllsh.dec_dzpuis(2) ;
double mass = ggrav * mass_bh ;
// Surface integral
// ----------------
source_surf = confo/rr - 2.*pow(confo,3.)*lapse_bh*mass/lapse/rr/rr
- pow(confo,3.)*(divshf - 3.*lldllsh
+ 2.*mass*lapse_bh%lapse_bh%llshift/rr/rr
+ 4.*mass*pow(lapse_bh,3.)*lapse_rs
*(1.+3.*mass/rr)/rr/rr)
/6./lapse/lapse_bh ;
source_surf.std_spectral_base() ;
source_surf.annule_domain(0) ;
source_surf.raccord(1) ;
integ_s = mp_aff.integrale_surface(source_surf, radius_ah) ;
// Volume integral
// ---------------
Scalar lldlldco = lldconf.dsdr() ;
lldlldco.std_spectral_base() ;
Scalar tmp1 = 2.*mass*mass*pow(lapse_bh,4.)*confo/pow(rr,4.) ;
tmp1.std_spectral_base() ;
tmp1.inc_dzpuis(4) ;
Scalar tmp2 = 2.*mass*mass*pow(lapse_bh,6.)
*(1.+3.*mass/rr)*(1.+3.*mass/rr)*pow(confo,5.)/3./pow(rr,4.) ;
tmp2.std_spectral_base() ;
tmp2.inc_dzpuis(4) ;
Scalar tmp3 = 4.*mass*lapse_bh*lapse_bh*lldlldco/rr ;
tmp3.std_spectral_base() ;
tmp3.inc_dzpuis(1) ;
Scalar tmp4 = 2.*mass*pow(lapse_bh,4.)*lldconf
*(3.+8.*mass/rr)/rr/rr ;
tmp4.std_spectral_base() ;
tmp4.inc_dzpuis(2) ;
source_volm = 0.25 * taij_quad / pow(confo,7.) - tmp1 - tmp2
- tmp3 - tmp4 ;
source_volm.annule_domain(0) ;
source_volm.std_spectral_base() ;
integ_v = source_volm.integrale() ;
// ADM mass
// --------
madm = mass_bh + integ_s / qpig + integ_v / qpig ;
// Another ADM mass
// ----------------
double mmm = mass_bh
- 2.*(mp_aff.integrale_surface_infini(lldconf))/qpig ;
cout << "Another ADM mass : " << mmm / msol << endl ;
*/
}
else { // Isotropic coordinates with the maximal slicing
Scalar divshf(mp) ;
divshf = shift(1).deriv(1) + shift(2).deriv(2)
+ shift(3).deriv(3) ;
divshf.std_spectral_base() ;
divshf.dec_dzpuis(2) ;
Scalar llshift(mp) ;
llshift = ll(1)%shift(1) + ll(2)%shift(2) + ll(3)%shift(3) ;
llshift.std_spectral_base() ;
Scalar lldllsh = llshift.dsdr() ;
lldllsh.std_spectral_base() ;
lldllsh.dec_dzpuis(2) ;
// Surface integral
// ----------------
source_surf = confo/rr
- pow(confo,4.) * (divshf - 3.*lldllsh) / lapconf / 6. ;
source_surf.std_spectral_base() ;
source_surf.annule_domain(0) ;
source_surf.raccord(1) ;
integ_s = mp_aff.integrale_surface(source_surf, radius_ah) ;
// Volume integral
// ---------------
source_volm = 0.25 * taij_quad / pow(confo,7.) ;
source_volm.std_spectral_base() ;
source_volm.annule_domain(0) ;
integ_v = source_volm.integrale() ;
// ADM mass
// --------
madm = integ_s / qpig + integ_v / qpig ;
// Another ADM mass
// ----------------
double mmm = - 2.*(mp_aff.integrale_surface_infini(lldconf))/qpig ;
cout << "Another ADM mass : " << mmm / msol << endl ;
}
p_mass_adm = new double( madm ) ;
}
return *p_mass_adm ;
}
//-----------------------------//
// Komar mass //
//-----------------------------//
double Black_hole::mass_kom() const {
// Fundamental constants and units
// -------------------------------
using namespace Unites ;
if (p_mass_kom == 0x0) { // a new computation is required
double mkom ;
double integ_s ;
double integ_v ;
double radius_ah = mp.val_r(1,-1.,M_PI/2.,0.) ;
Map_af mp_aff(mp) ;
Scalar source_surf(mp) ;
source_surf.set_etat_qcq() ;
Scalar source_volm(mp) ;
source_volm.set_etat_qcq() ;
Scalar rr(mp) ;
rr = mp.r ;
rr.std_spectral_base() ;
Scalar st(mp) ;
st = mp.sint ;
st.std_spectral_base() ;
Scalar ct(mp) ;
ct = mp.cost ;
ct.std_spectral_base() ;
Scalar sp(mp) ;
sp = mp.sinp ;
sp.std_spectral_base() ;
Scalar cp(mp) ;
cp = mp.cosp ;
cp.std_spectral_base() ;
Vector ll(mp, CON, mp.get_bvect_cart()) ;
ll.set_etat_qcq() ;
ll.set(1) = st * cp ;
ll.set(2) = st * sp ;
ll.set(3) = ct ;
ll.std_spectral_base() ;
Vector dlcnf(mp, CON, mp.get_bvect_cart()) ;
dlcnf.set_etat_qcq() ;
for (int i=1; i<=3; i++)
dlcnf.set(i) = confo.deriv(i) / confo ;
dlcnf.std_spectral_base() ;
if (kerrschild) {
cout << "!!!!! WARNING: Not yet available !!!!!" << endl ;
abort() ;
/*
Scalar llshift(mp) ;
llshift = ll(1)%shift_rs(1) + ll(2)%shift_rs(2)
+ ll(3)%shift_rs(3) ;
llshift.std_spectral_base() ;
Vector dlap(mp, CON, mp.get_bvect_cart()) ;
dlap.set_etat_qcq() ;
for (int i=1; i<=3; i++)
dlap.set(i) = lapse_rs.deriv(i) ;
dlap.std_spectral_base() ;
double mass = ggrav * mass_bh ;
// Surface integral
// ----------------
Scalar lldlap_bh(mp) ;
lldlap_bh = pow(lapse_bh,3.) * mass / rr / rr ;
lldlap_bh.std_spectral_base() ;
lldlap_bh.annule_domain(0) ;
lldlap_bh.inc_dzpuis(2) ;
Scalar lldlap_rs = lapse_rs.dsdr() ;
lldlap_rs.std_spectral_base() ;
source_surf = lldlap_rs + lldlap_bh ;
source_surf.std_spectral_base() ;
source_surf.dec_dzpuis(2) ;
source_surf.annule_domain(0) ;
source_surf.raccord(1) ;
integ_s = mp_aff.integrale_surface(source_surf, radius_ah) ;
// Volume integral
// ---------------
Scalar lldlldlap = lldlap_rs.dsdr() ;
lldlldlap.std_spectral_base() ;
Scalar lldlcnf = lconfo.dsdr() ;
lldlcnf.std_spectral_base() ;
Scalar tmp1(mp) ;
tmp1 = dlap(1)%dlcnf(1) + dlap(2)%dlcnf(2) + dlap(3)%dlcnf(3)
-2.*mass*lapse_bh%lapse_bh%lldlap_rs%lldlcnf/rr ;
tmp1.std_spectral_base() ;
Scalar tmp2(mp) ;
tmp2 = 4.*mass*mass*pow(lapse_bh,6.)*(1.+3.*mass/rr)*(1.+3.*mass/rr)
*lapse_rs*pow(confo,4.)/3./pow(rr,4.) ;
tmp2.std_spectral_base() ;
tmp2.inc_dzpuis(4) ;
Scalar tmp3(mp) ;
tmp3 = -2.*mass*pow(lapse_bh,5.)*llshift
*(2.+10.*mass/rr+9.*mass*mass/rr/rr)*pow(confo,4.)/pow(rr,3.) ;
tmp3.std_spectral_base() ;
tmp3.inc_dzpuis(4) ;
Scalar tmp4(mp) ;
tmp4 = 2.*mass*lapse_bh%lapse_bh%lldlldlap/rr ;
tmp4.std_spectral_base() ;
tmp4.inc_dzpuis(1) ;
Scalar tmp5(mp) ;
tmp5 = mass*pow(lapse_bh,4.)*lldlap_rs*(3.+8.*mass/rr)/rr/rr ;
tmp5.std_spectral_base() ;
tmp5.inc_dzpuis(2) ;
Scalar tmp6(mp) ;
tmp6 = -2.*pow(lapse_bh,5.)*mass*lldlcnf/rr/rr ;
tmp6.std_spectral_base() ;
tmp6.inc_dzpuis(2) ;
Scalar tmp_bh(mp) ;
tmp_bh = -pow(lapse_bh,7.)*mass*mass
*( 4.*(5.+24.*mass/rr+18.*mass*mass/rr/rr)*pow(confo,4.)/3.
+ 1. - 6.*mass/rr) / pow(rr, 4.) ;
tmp_bh.std_spectral_base() ;
tmp_bh.inc_dzpuis(4) ;
source_volm = lapse % taij_quad / pow(confo,8.) - 2.*tmp1
+ tmp2 + tmp3 + tmp4 + tmp5 + tmp6 + tmp_bh ;
source_volm.annule_domain(0) ;
source_volm.std_spectral_base() ;
integ_v = source_volm.integrale() ;
// Komar mass
// ----------
mkom = integ_s / qpig + integ_v / qpig ;
// Another Komar mass
// ------------------
double mmm = (mp_aff.integrale_surface_infini(lldlap_rs+lldlap_bh))
/ qpig ;
cout << "Another Komar mass : " << mmm / msol << endl ;
*/
}
else { // Isotropic coordinates with the maximal slicing
// Surface integral
// ----------------
Scalar lldlap = lapconf.dsdr() / confo
- lapconf * confo.dsdr() / confo / confo ;
lldlap.std_spectral_base() ;
source_surf = lldlap ;
source_surf.std_spectral_base() ;
source_surf.dec_dzpuis(2) ;
source_surf.annule_domain(0) ;
source_surf.raccord(1) ;
integ_s = mp_aff.integrale_surface(source_surf, radius_ah) ;
// Volume integral
// ---------------
Vector dlap(mp, CON, mp.get_bvect_cart()) ;
dlap.set_etat_qcq() ;
for (int i=1; i<=3; i++)
dlap.set(i) = lapconf.deriv(i) / confo
- lapconf * confo.deriv(i) / confo / confo ;
dlap.std_spectral_base() ;
source_volm = lapconf % taij_quad / pow(confo,9.)
- 2.*(dlap(1)%dlcnf(1) + dlap(2)%dlcnf(2) + dlap(3)%dlcnf(3)) ;
source_volm.std_spectral_base() ;
source_volm.annule_domain(0) ;
integ_v = source_volm.integrale() ;
// Komar mass
// ----------
mkom = integ_s / qpig + integ_v / qpig ;
// Another Komar mass
double mmm = (mp_aff.integrale_surface_infini(lldlap)) / qpig ;
cout << "Another Komar mass : " << mmm / msol << endl ;
}
p_mass_kom = new double( mkom ) ;
}
return *p_mass_kom ;
}
//------------------------------------//
// Apparent horizon //
//------------------------------------//
double Black_hole::rad_ah() const {
if (p_rad_ah == 0x0) { // a new computation is required
Scalar rr(mp) ;
rr = mp.r ;
rr.std_spectral_base() ;
double rad = rr.val_grid_point(1,0,0,0) ;
p_rad_ah = new double( rad ) ;
}
return *p_rad_ah ;
}
//-------------------------------------------//
// Quasi-local spin angular momentum //
//-------------------------------------------//
double Black_hole::spin_am_bh(bool bclapconf_nd, bool bclapconf_fs,
const Tbl& xi_i, const double& phi_i,
const double& theta_i, const int& nrk_phi,
const int& nrk_theta) const {
// Fundamental constants and units
// -------------------------------
using namespace Unites ;
if (p_spin_am_bh == 0x0) { // a new computation is required
Scalar st(mp) ;
st = mp.sint ;
st.std_spectral_base() ;
Scalar ct(mp) ;
ct = mp.cost ;
ct.std_spectral_base() ;
Scalar sp(mp) ;
sp = mp.sinp ;
sp.std_spectral_base() ;
Scalar cp(mp) ;
cp = mp.cosp ;
cp.std_spectral_base() ;
Vector ll(mp, CON, mp.get_bvect_cart()) ;
ll.set_etat_qcq() ;
ll.set(1) = st % cp ;
ll.set(2) = st % sp ;
ll.set(3) = ct ;
ll.std_spectral_base() ;
double radius_ah = mp.val_r(1,-1.,M_PI/2.,0.) ;
if (kerrschild) {
cout << "Not yet prepared!!!" << endl ;
abort() ;
}
else { // Isotropic coordinates
// Killing vector of the spherical components
Vector killing_spher(mp, COV, mp.get_bvect_spher()) ;
killing_spher.set_etat_qcq() ;
killing_spher = killing_vect_bh(xi_i, phi_i, theta_i,
nrk_phi, nrk_theta) ;
killing_spher.std_spectral_base() ;
killing_spher.set(2) = confo * confo * radius_ah * killing_spher(2) ;
killing_spher.set(3) = confo * confo * radius_ah * killing_spher(3) ;
// killing_spher(3) is already divided by sin(theta)
killing_spher.std_spectral_base() ;
// Killing vector of the Cartesian components
Vector killing(mp, COV, mp.get_bvect_cart()) ;
killing.set_etat_qcq() ;
killing.set(1) = (killing_spher(2) * ct * cp - killing_spher(3) * sp)
/ radius_ah ;
killing.set(2) = (killing_spher(2) * ct * sp + killing_spher(3) * cp)
/ radius_ah ;
killing.set(3) = - killing_spher(2) * st / radius_ah ;
killing.std_spectral_base() ;
// Surface integral <- dzpuis should be 0
// --------------------------------------
// Source terms in the surface integral
Scalar source_1(mp) ;
source_1 = (ll(1) * (taij(1,1) * killing(1)
+ taij(1,2) * killing(2)
+ taij(1,3) * killing(3))
+ ll(2) * (taij(2,1) * killing(1)
+ taij(2,2) * killing(2)
+ taij(2,3) * killing(3))
+ ll(3) * (taij(3,1) * killing(1)
+ taij(3,2) * killing(2)
+ taij(3,3) * killing(3)))
/ pow(confo, 4.) ;
source_1.std_spectral_base() ;
source_1.dec_dzpuis(2) ; // dzpuis : 2 -> 0
Scalar source_surf(mp) ;
source_surf = source_1 ;
source_surf.std_spectral_base() ;
source_surf.annule_domain(0) ;
source_surf.raccord(1) ;
Map_af mp_aff(mp) ;
double spin = mp_aff.integrale_surface(source_surf, radius_ah) ;
double spin_angmom = 0.5 * spin / qpig ;
p_spin_am_bh = new double( spin_angmom ) ;
}
}
return *p_spin_am_bh ;
}
//------------------------------------------//
// Total angular momentum //
//------------------------------------------//
const Tbl& Black_hole::angu_mom_bh() const {
// Fundamental constants and units
// -------------------------------
using namespace Unites ;
if (p_angu_mom_bh == 0x0) { // a new computation is required
p_angu_mom_bh = new Tbl(3) ;
p_angu_mom_bh->annule_hard() ; // fills the double array with zeros
double integ_bh_s_x ;
double integ_bh_s_y ;
double integ_bh_s_z ;
double radius_ah = mp.val_r(1,-1.,M_PI/2.,0.) ;
Map_af mp_aff(mp) ;
Scalar xx(mp) ;
xx = mp.x ;
xx.std_spectral_base() ;
Scalar yy(mp) ;
yy = mp.y ;
yy.std_spectral_base() ;
Scalar zz(mp) ;
zz = mp.z ;
zz.std_spectral_base() ;
Scalar st(mp) ;
st = mp.sint ;
st.std_spectral_base() ;
Scalar ct(mp) ;
ct = mp.cost ;
ct.std_spectral_base() ;
Scalar sp(mp) ;
sp = mp.sinp ;
sp.std_spectral_base() ;
Scalar cp(mp) ;
cp = mp.cosp ;
cp.std_spectral_base() ;
Vector ll(mp, CON, mp.get_bvect_cart()) ;
ll.set_etat_qcq() ;
ll.set(1) = st % cp ;
ll.set(2) = st % sp ;
ll.set(3) = ct ;
ll.std_spectral_base() ;
Vector jbh_x(mp, CON, mp.get_bvect_cart()) ;
jbh_x.set_etat_qcq() ;
for (int i=1; i<=3; i++)
jbh_x.set(i) = yy * taij(3,i) - zz * taij(2,i) ;
jbh_x.std_spectral_base() ;
Vector jbh_y(mp, CON, mp.get_bvect_cart()) ;
jbh_y.set_etat_qcq() ;
for (int i=1; i<=3; i++)
jbh_y.set(i) = zz * taij(1,i) - xx * taij(3,i) ;
jbh_y.std_spectral_base() ;
Vector jbh_z(mp, CON, mp.get_bvect_cart()) ;
jbh_z.set_etat_qcq() ;
for (int i=1; i<=3; i++)
jbh_z.set(i) = xx * taij(2,i) - yy * taij(1,i) ;
jbh_z.std_spectral_base() ;
/*
if (kerrschild) {
cout << "Not yet prepared!!!" << endl ;
abort() ;
}
else { // Isotropic coordinates
// Sets C/M^2 for each case of the lapse boundary condition
// --------------------------------------------------------
double cc ;
if (bclapconf_nd) { // Neumann boundary condition
if (bclapconf_fs) { // First condition
// d(\alpha \psi)/dr = 0
// ---------------------
cc = 2. * (sqrt(13.) - 1.) / 3. ;
}
else { // Second condition
// d(\alpha \psi)/dr = (\alpha \psi)/(2 rah)
// -----------------------------------------
cc = 4. / 3. ;
}
}
else { // Dirichlet boundary condition
if (bclapconf_fs) { // First condition
// (\alpha \psi) = 1/2
// -------------------
cout << "!!!!! WARNING: Not yet prepared !!!!!" << endl ;
abort() ;
}
else { // Second condition
// (\alpha \psi) = 1/sqrt(2.) \psi_KS
// ----------------------------------
cout << "!!!!! WARNING: Not yet prepared !!!!!" << endl ;
abort() ;
}
}
Scalar r_are(mp) ;
r_are = r_coord(bclapconf_nd, bclapconf_fs) ;
r_are.std_spectral_base() ;
}
*/
//-------------//
// X component //
//-------------//
//-------------------------------------
// Integration over the BH map
//-------------------------------------
// Surface integral <- dzpuis should be 0
// --------------------------------------
Scalar sou_bh_sx(mp) ;
sou_bh_sx = jbh_x(1)%ll(1) + jbh_x(2)%ll(2) + jbh_x(3)%ll(3) ;
sou_bh_sx.std_spectral_base() ;
sou_bh_sx.dec_dzpuis(2) ; // dzpuis : 2 -> 0
sou_bh_sx.annule_domain(0) ;
sou_bh_sx.raccord(1) ;
integ_bh_s_x = mp_aff.integrale_surface(sou_bh_sx, radius_ah) ;
p_angu_mom_bh->set(0) = 0.5 * integ_bh_s_x / qpig ;
//-------------//
// Y component //
//-------------//
//-------------------------------------
// Integration over the BH map
//-------------------------------------
// Surface integral <- dzpuis should be 0
// --------------------------------------
Scalar sou_bh_sy(mp) ;
sou_bh_sy = jbh_y(1)%ll(1) + jbh_y(2)%ll(2) + jbh_y(3)%ll(3) ;
sou_bh_sy.std_spectral_base() ;
sou_bh_sy.dec_dzpuis(2) ; // dzpuis : 2 -> 0
sou_bh_sy.annule_domain(0) ;
sou_bh_sy.raccord(1) ;
integ_bh_s_y = mp_aff.integrale_surface(sou_bh_sy, radius_ah) ;
p_angu_mom_bh->set(1) = 0.5 * integ_bh_s_y / qpig ;
//-------------//
// Z component //
//-------------//
//-------------------------------------
// Integration over the BH map
//-------------------------------------
// Surface integral <- dzpuis should be 0
// --------------------------------------
Scalar sou_bh_sz(mp) ;
sou_bh_sz = jbh_z(1)%ll(1) + jbh_z(2)%ll(2) + jbh_z(3)%ll(3) ;
sou_bh_sz.std_spectral_base() ;
sou_bh_sz.dec_dzpuis(2) ; // dzpuis : 2 -> 0
sou_bh_sz.annule_domain(0) ;
sou_bh_sz.raccord(1) ;
integ_bh_s_z = mp_aff.integrale_surface(sou_bh_sz, radius_ah) ;
p_angu_mom_bh->set(2) = 0.5 * integ_bh_s_z / qpig ;
}
return *p_angu_mom_bh ;
}
}
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