Xcts::Solutions Namespace Reference

Analytic solutions of the XCTS equations. More...

Classes
class	AnalyticSolution
	Base class for analytic solutions of the XCTS equations. More...
struct	CommonVariables
	Implementations for variables that solutions can share. More...
class	ConstantDensityStar
	A constant density star in general relativity. More...
class	Flatness
	Flat spacetime in general relativity. Useful as initial guess. More...
class	Kerr
	Kerr spacetime in general relativity. More...
class	Schwarzschild
	Schwarzschild spacetime in general relativity. More...

Typedefs
template<typename DataType >
using	common_tags = tmpl::push_back< AnalyticData::common_tags< DataType >, ::Tags::Flux< Tags::ConformalFactor< DataType >, tmpl::size_t< 3 >, Frame::Inertial >, ::Tags::Flux< Tags::LapseTimesConformalFactor< DataType >, tmpl::size_t< 3 >, Frame::Inertial >, Tags::LongitudinalShiftExcess< DataType, 3, Frame::Inertial >, gr::Tags::Shift< 3, Frame::Inertial, DataType >, Tags::LongitudinalShiftMinusDtConformalMetricSquare< DataType >, Tags::LongitudinalShiftMinusDtConformalMetricOverLapseSquare< DataType >, Tags::ShiftDotDerivExtrinsicCurvatureTrace< DataType > >
	Tags for variables that solutions can share.

Enumerations
enum class	SchwarzschildCoordinates { Isotropic }
	Various coordinate systems in which to express the Schwarzschild solution. More...

Functions
bool	operator== (const ConstantDensityStar &, const ConstantDensityStar &) noexcept
bool	operator!= (const ConstantDensityStar &lhs, const ConstantDensityStar &rhs) noexcept
template<typename Registrars >
bool	operator== (const Flatness< Registrars > &, const Flatness< Registrars > &) noexcept
template<typename Registrars >
bool	operator!= (const Flatness< Registrars > &lhs, const Flatness< Registrars > &rhs) noexcept
std::ostream &	operator<< (std::ostream &os, SchwarzschildCoordinates coords) noexcept

Detailed Description

Analytic solutions of the XCTS equations.

Enumeration Type Documentation

SchwarzschildCoordinates

enum class Xcts::Solutions::SchwarzschildCoordinates

strong

Various coordinate systems in which to express the Schwarzschild solution.

Enumerator

Isotropic

Isotropic Schwarzschild coordinates. These arise from the canonical Schwarzschild coordinates by the radial transformation \begin{equation} r = \bar{r}\left(1+\frac{M}{2\bar{r}}\right)^2 \end{equation} (Eq. (1.61) in [8]) where \(r\) is the canonical Schwarzschild radius, also referred to as "areal" radius because it is defined such that spheres with constant \(r\) have the area \(4\pi r^2\), and \(\bar{r}\) is the "isotropic" radius. In the isotropic radius the Schwarzschild spatial metric is conformally flat: \begin{equation} \gamma_{ij}=\psi^4\eta_{ij} \quad \text{with conformal factor} \quad \psi=1+\frac{M}{2\bar{r}} \end{equation} (Table 2.1 in [8]). Its lapse transforms to \begin{equation} \alpha=\frac{1-M/(2\bar{r})}{1+M/(2\bar{r})} \end{equation} and the shift vanishes ( \(\beta^i=0\)) as it does in areal Schwarzschild coordinates. The solution also remains maximally sliced, i.e. \(K=0\). The Schwarzschild horizon in these coordinates is at \(\bar{r}=\frac{M}{2}\) due to the radial transformation from \(r=2M\).