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SpECTRE
v2024.04.12
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The vector \(J^i\) in \(\dot{M} = -\int J^i s_i d^2S\), representing the mass flux through a surface with normal \(s_i\). More...
#include <Tags.hpp>
Public Types | |
| using | type = tnsr::I< DataType, Dim, Fr > |
Static Public Member Functions | |
| static std::string | name () |
The vector \(J^i\) in \(\dot{M} = -\int J^i s_i d^2S\), representing the mass flux through a surface with normal \(s_i\).
Note that the integral is understood as a flat-space integral: all metric factors are included in \(J^i\). In particular, if the integral is done over a Strahlkorper, the gr::surfaces::euclidean_area_element of the Strahlkorper should be used, and \(s_i\) is the normal one-form to the Strahlkorper normalized with the flat metric, \(s_is_j\delta^{ij}=1\).
The formula is \( J^i = \rho W \sqrt{\gamma}(\alpha v^i-\beta^i)\), where \(\rho\) is the mass density, \(W\) is the Lorentz factor, \(v^i\) is the spatial velocity of the fluid, \(\gamma\) is the determinant of the 3-metric \(\gamma_{ij}\), \(\alpha\) is the lapse, and \(\beta^i\) is the shift.