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| struct | CartesianCoords |
| | CartesianCoords(i) is \(x_{\rm surf}^i\), the vector of \((x,y,z)\) coordinates of each point on the surface. More...
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| struct | CartesianCoordsCompute |
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| struct | D2xRadius |
| | D2xRadius(i,j) is \(\partial^2 r_{\rm surf}/\partial x^i\partial x^j\). Here \(r_{\rm surf}=r_{\rm surf}(\theta,\phi)\) is the function describing the surface, which is considered a function of Cartesian coordinates \(r_{\rm surf}=r_{\rm surf}(\theta(x,y,z),\phi(x,y,z))\) for this operation. More...
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| struct | D2xRadiusCompute |
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| struct | DimensionfulSpinVector |
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| struct | DimensionfulSpinVectorCompute |
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| struct | DxRadius |
| | DxRadius(i) is \(\partial r_{\rm surf}/\partial x^i\). Here \(r_{\rm surf}=r_{\rm surf}(\theta,\phi)\) is the function describing the surface, which is considered a function of Cartesian coordinates \(r_{\rm surf}=r_{\rm surf}(\theta(x,y,z),\phi(x,y,z))\) for this operation. More...
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| struct | DxRadiusCompute |
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| struct | EuclideanAreaElement |
| | Computes the Euclidean area element on a Strahlkorper. Useful for flat space integrals. More...
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| struct | EuclideanAreaElementCompute |
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| struct | EuclideanSurfaceIntegral |
| | Computes the flat-space integral of a scalar over a Strahlkorper. More...
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| struct | EuclideanSurfaceIntegralCompute |
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| struct | EuclideanSurfaceIntegralVector |
| | Computes the Euclidean-space integral of a vector over a Strahlkorper, \(\oint V^i s_i (s_j s_k \delta^{jk})^{-1/2} d^2 S\), where \(s_i\) is the Strahlkorper surface unit normal and \(\delta^{ij}\) is the Kronecker delta. Note that \(s_i\) is not assumed to be normalized; the denominator of the integrand effectively normalizes it using the Euclidean metric. More...
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| struct | EuclideanSurfaceIntegralVectorCompute |
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| struct | ExtrinsicCurvature |
| | Extrinsic curvature of a 2D Strahlkorper embedded in a 3D space. More...
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| struct | ExtrinsicCurvatureCompute |
| | Calculates the Extrinsic curvature of a 2D Strahlkorper embedded in a 3D space. More...
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| struct | GradUnitNormalOneForm |
| | The 3-covariant gradient \(D_i S_j\) of a Strahlkorper's normal. More...
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| struct | GradUnitNormalOneFormCompute |
| | Computes 3-covariant gradient \(D_i S_j\) of a Strahlkorper's normal. More...
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| struct | InvHessian |
| | InvHessian(k,i,j) is \(\partial (J^{-1}){}^k_j/\partial x^i\), where \((J^{-1}){}^k_j\) is the inverse Jacobian. InvHessian is not symmetric because the Jacobians are Pfaffian. InvHessian doesn't depend on the shape of the surface. More...
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| struct | InvHessianCompute |
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| struct | InvJacobian |
| | InvJacobian(0,i) is \(r\partial\theta/\partial x^i\), and InvJacobian(1,i) is \(r\sin\theta\partial\phi/\partial x^i\). Here \(r\) means \(\sqrt{x^2+y^2+z^2}\). InvJacobian doesn't depend on the shape of the surface. More...
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| struct | InvJacobianCompute |
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| struct | Jacobian |
| | Jacobian(i,0) is \(\frac{1}{r}\partial x^i/\partial\theta\), and Jacobian(i,1) is \(\frac{1}{r\sin\theta}\partial x^i/\partial\phi\). Here \(r\) means \(\sqrt{x^2+y^2+z^2}\). Jacobian doesn't depend on the shape of the surface. More...
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| struct | JacobianCompute |
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| struct | LaplacianRadius |
| | \(\nabla^2 r_{\rm surf}\), the flat Laplacian of the surface. This is \(\eta^{ij}\partial^2 r_{\rm surf}/\partial x^i\partial x^j\), where \(r_{\rm surf}=r_{\rm surf}(\theta(x,y,z),\phi(x,y,z))\). More...
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| struct | LaplacianRadiusCompute |
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| struct | MaxRicciScalar |
| | The pointwise maximum of the Strahlkorper's intrinsic Ricci scalar curvature. More...
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| struct | MaxRicciScalarCompute |
| | Computes the pointwise maximum of the Strahlkorper's intrinsic Ricci scalar curvature. More...
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| struct | MinRicciScalar |
| | The pointwise minimum of the Strahlkorper’s intrinsic Ricci scalar curvature. More...
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| struct | MinRicciScalarCompute |
| | Computes the pointwise minimum of the Strahlkorper’s intrinsic Ricci scalar curvature. More...
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| struct | NormalOneForm |
| | NormalOneForm(i) is \(s_i\), the (unnormalized) normal one-form to the surface, expressed in Cartesian components. This is computed by \(x_i/r-\partial r_{\rm surf}/\partial x^i\), where \(x_i/r\) is Rhat and \(\partial r_{\rm surf}/\partial x^i\) is DxRadius. See Eq. (8) of [14]. Note on the word "normal": \(s_i\) points in the correct direction (it is "normal" to the surface), but it does not have unit length (it is not "normalized"; normalization requires a metric). More...
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| struct | NormalOneFormCompute |
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| struct | OneOverOneFormMagnitude |
| | The OneOverOneFormMagnitude is the reciprocal of the magnitude of the one-form perpendicular to the horizon. More...
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| struct | OneOverOneFormMagnitudeCompute |
| | Computes the reciprocal of the magnitude of the one form perpendicular to the horizon. More...
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| struct | PhysicalCenter |
| | The geometrical center of the surface. Uses ylm::Strahlkorper::physical_center. More...
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| struct | PhysicalCenterCompute |
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| struct | PreviousStrahlkorpers |
| | Tag for holding the previously-found values of a Strahlkorper, which are saved for extrapolation for future initial guesses and for computing the time deriv of a Strahlkorper. More...
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| struct | Radius |
| | (Euclidean) distance \(r_{\rm surf}(\theta,\phi)\) from the center to each point of the surface. More...
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| struct | RadiusCompute |
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| struct | Rhat |
| | Rhat(i) is \(\hat{r}^i = x_i/\sqrt{x^2+y^2+z^2}\) on the grid. Doesn't depend on the shape of the surface. More...
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| struct | RhatCompute |
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| struct | RicciScalar |
| | Ricci scalar is the two-dimensional intrinsic Ricci scalar curvature of a Strahlkorper. More...
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| struct | RicciScalarCompute |
| | Computes the two-dimensional intrinsic Ricci scalar of a Strahlkorper. More...
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| struct | Strahlkorper |
| | Tag referring to a ylm::Strahlkorper More...
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| struct | Tangents |
| | Tangents(i,j) is \(\partial x_{\rm surf}^i/\partial q^j\), where \(x_{\rm surf}^i\) are the Cartesian coordinates of the surface (i.e. CartesianCoords) and are considered functions of \((\theta,\phi)\). More...
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| struct | TangentsCompute |
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| struct | ThetaPhi |
| | \((\theta,\phi)\) on the grid. Doesn't depend on the shape of the surface. More...
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| struct | ThetaPhiCompute |
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| struct | TimeDerivStrahlkorper |
| | Tag to compute the time derivative of the coefficients of a Strahlkorper from a number of previous Strahlkorpers. More...
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| struct | TimeDerivStrahlkorperCompute |
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| struct | UnitNormalOneForm |
| | The unit normal one-form \(s_j\) to the horizon. More...
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| struct | UnitNormalOneFormCompute |
| | Computes the unit one-form perpendicular to the horizon. More...
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| struct | UnitNormalVector |
| | UnitNormalVector is defined as \(S^i = \gamma^{ij} S_j\), where \(S_j\) is the unit normal one form and \(\gamma^{ij}\) is the inverse spatial metric. More...
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| struct | UnitNormalVectorCompute |
| | Computes the UnitNormalVector perpendicular to the horizon. More...
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Holds tags and ComputeItems associated with a ylm::Strahlkorper.