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Merged
alisagk merged 2 commits into from
Jan 14, 2026
Merged

Dev/polar #167

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a3354d2
small-angle approximation for polar area in GR, replicates SR
alisagk Jan 14, 2026
99c21ee
added definition of small_angle to ks metric
alisagk Jan 14, 2026
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21 changes: 16 additions & 5 deletions src/metrics/kerr_schild.h
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Original file line number Diff line number Diff line change
Expand Up @@ -40,6 +40,7 @@ namespace metric {

const real_t dr, dtheta, dphi;
const real_t dr_inv, dtheta_inv, dphi_inv;
const bool small_angle;

Inline auto Delta(real_t r) const -> real_t {
return SQR(r) - TWO * r + SQR(a);
Expand Down Expand Up @@ -85,7 +86,8 @@ namespace metric {
, dphi { (x3_max - x3_min) / nx3 }
, dr_inv { ONE / dr }
, dtheta_inv { ONE / dtheta }
, dphi_inv { ONE / dphi } {
, dphi_inv { ONE / dphi }
, small_angle { HALF * dtheta < constant::SMALL_ANGLE } {
set_dxMin(find_dxMin());
}

Expand Down Expand Up @@ -443,12 +445,21 @@ namespace metric {
/**
* differential area at the pole (used in axisymmetric solvers)
* @param x1 radial coordinate along the axis (code units)
* @note uses small-angle approximation when the resolution is too high
*/
Inline auto polar_area(real_t x1) const -> real_t {
return dr * (SQR(x1 * dr + x1_min) + SQR(a)) *
math::sqrt(ONE + TWO * (x1 * dr + x1_min) /
(SQR(x1 * dr + x1_min) + SQR(a))) *
(ONE - math::cos(HALF * dtheta));
if (small_angle) {
return dr * (SQR(x1 * dr + x1_min) + SQR(a)) *
math::sqrt(ONE + TWO * (x1 * dr + x1_min) /
(SQR(x1 * dr + x1_min) + SQR(a))) *
(static_cast<real_t>(48) - SQR(dtheta)) * SQR(dtheta) /
static_cast<real_t>(384);
} else {
return dr * (SQR(x1 * dr + x1_min) + SQR(a)) *
math::sqrt(ONE + TWO * (x1 * dr + x1_min) /
(SQR(x1 * dr + x1_min) + SQR(a))) *
(ONE - math::cos(HALF * dtheta));
}
}

/**
Expand Down
28 changes: 21 additions & 7 deletions src/metrics/qkerr_schild.h
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Original file line number Diff line number Diff line change
Expand Up @@ -39,6 +39,7 @@ namespace metric {
const real_t chi_min, eta_min, phi_min;
const real_t dchi, deta, dphi;
const real_t dchi_inv, deta_inv, dphi_inv;
const bool small_angle;

Inline auto Delta(real_t r) const -> real_t {
return SQR(r) - TWO * r + SQR(a);
Expand Down Expand Up @@ -89,7 +90,8 @@ namespace metric {
, dphi { (x3_max - phi_min) / nx3 }
, dchi_inv { ONE / dchi }
, deta_inv { ONE / deta }
, dphi_inv { ONE / dphi } {
, dphi_inv { ONE / dphi }
, small_angle { eta2theta(HALF * deta) < constant::SMALL_ANGLE } {
set_dxMin(find_dxMin());
}

Expand Down Expand Up @@ -503,15 +505,27 @@ namespace metric {
* differential area at the pole (used in axisymmetric solvers)
* @note approximate solution for the polar area
* @param x1 radial coordinate along the axis (code units)
* @note uses small-angle approximation when the resolution is too high
*/
Inline auto polar_area(real_t x1) const -> real_t {
if constexpr (D != Dim::_1D) {
return dchi * math::exp(x1 * dchi + chi_min) *
(SQR(r0 + math::exp(x1 * dchi + chi_min)) + SQR(a)) *
math::sqrt(
ONE + TWO * (r0 + math::exp(x1 * dchi + chi_min)) /
(SQR(r0 + math::exp(x1 * dchi + chi_min)) + SQR(a))) *
(ONE - math::cos(eta2theta(HALF * deta)));
if (small_angle) {
const real_t dtheta = eta2theta(HALF * deta);
return dchi * math::exp(x1 * dchi + chi_min) *
(SQR(r0 + math::exp(x1 * dchi + chi_min)) + SQR(a)) *
math::sqrt(
ONE + TWO * (r0 + math::exp(x1 * dchi + chi_min)) /
(SQR(r0 + math::exp(x1 * dchi + chi_min)) + SQR(a))) *
(static_cast<real_t>(48) - SQR(dtheta)) * SQR(dtheta) /
static_cast<real_t>(384);
} else {
return dchi * math::exp(x1 * dchi + chi_min) *
(SQR(r0 + math::exp(x1 * dchi + chi_min)) + SQR(a)) *
math::sqrt(
ONE + TWO * (r0 + math::exp(x1 * dchi + chi_min)) /
(SQR(r0 + math::exp(x1 * dchi + chi_min)) + SQR(a))) *
(ONE - math::cos(eta2theta(HALF * deta)));
}
}
}

Expand Down