Conservative3+1general relativistic Boltzmann equation

Abstract

We present a new derivation of the conservative form of the general relativistic Boltzmann equation and specialize it to the 3+1 metric. The resulting transport equation is intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are lab frame coordinate basis spacetime position components and comoving frame curvilinear momentum space coordinates. With an eye towards astrophysical applicationssuch as core-collapse supernovae and compact object mergers-in which the fluid includes nuclei and/or nuclear matter at finite temperature, and in which the transported particles are neutrinos, we examine the relationship between lepton number and four-momentum exchange between neutrinos and the fluid.

A New Multi-Energy Neutrino Radiation-Hydrodynamics Code in Full General Relativity and Its Application to the Gravitational Collapse of Massive Stars

“…For convenience, we briefly summarize the basic equations of our newly developed code in the following (see Shibata et al 2011 andCardall et al 2013a for the complete derivation).…”

“…Albeit not yet implemented in hydrodynamics simulations, several novel formulations and schemes of the full Boltzmann equation have recently been reported in Cardall et al (2013aCardall et al ( , 2013b, Shibata et al (2014), and Peres et al (2014).…”

GenASiS Basics: Object-oriented utilitarian functionality for large-scale physics simulations

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“…23 https://wci.llnl.gov/codes/visit 24. These access modes are parameter class members of the stream object (see also footnote 9) 25. Depending on the I/O library and hardware, a call to the write method may only buffer the data and not actually write to the file system until the stream is closed.…”

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“…The Boltzmann equation can be written in conservative form with respect to a tetrad field e μ α as follows [9,12]:…”