## Conservative $3+1$ general relativistic variable Eddington tensor radiation transport equations

## Abstract

We present conservative 3+1 general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These equations are intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are the lab frame coordinate basis spacetime position coordinates and the particle energy measured in the comoving frame. With an eye towards astrophysical applications—such 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 pay special attention to the consistency of four-momentum and lepton number exchange between neutrinos and the fluid, showing the term-by-term cancellations that must occur for this consistency to be achieved.

- Authors:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1408677

- Alternate Identifier(s):
- OSTI ID: 1102211

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review. D, Particles, Fields, Gravitation and Cosmology

- Additional Journal Information:
- Journal Volume: 87; Journal Issue: 10; Journal ID: ISSN 1550-7998

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Cardall, Christian Y., Endeve, Eirik, and Mezzacappa, Anthony. Conservative 3+1 general relativistic variable Eddington tensor radiation transport equations. United States: N. p., 2013.
Web. doi:10.1103/PhysRevD.87.103004.
```

```
Cardall, Christian Y., Endeve, Eirik, & Mezzacappa, Anthony. Conservative 3+1 general relativistic variable Eddington tensor radiation transport equations. United States. doi:10.1103/PhysRevD.87.103004.
```

```
Cardall, Christian Y., Endeve, Eirik, and Mezzacappa, Anthony. Tue .
"Conservative 3+1 general relativistic variable Eddington tensor radiation transport equations". United States. doi:10.1103/PhysRevD.87.103004. https://www.osti.gov/servlets/purl/1408677.
```

```
@article{osti_1408677,
```

title = {Conservative 3+1 general relativistic variable Eddington tensor radiation transport equations},

author = {Cardall, Christian Y. and Endeve, Eirik and Mezzacappa, Anthony},

abstractNote = {We present conservative 3+1 general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These equations are intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are the lab frame coordinate basis spacetime position coordinates and the particle energy measured in the comoving frame. With an eye towards astrophysical applications—such 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 pay special attention to the consistency of four-momentum and lepton number exchange between neutrinos and the fluid, showing the term-by-term cancellations that must occur for this consistency to be achieved.},

doi = {10.1103/PhysRevD.87.103004},

journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},

number = 10,

volume = 87,

place = {United States},

year = {2013},

month = {5}

}

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