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arxiv: 2604.20579 · v1 · submitted 2026-04-22 · 🌌 astro-ph.HE · gr-qc

Recognition: unknown

Approximating General Relativity in Core-Collapse Supernova Simulations

Steven A. Fromm , Vassilios Mewes , O. E. Bronson Messer , Eric J. Lentz , W. Raphael Hix , J. Austin Harris
Authors on Pith no claims yet

Pith reviewed 2026-05-09 23:34 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc
keywords core-collapse supernovaeeffective gravitational potentialsgeneral relativity approximationNewtonian hydrodynamicsEinstein equation projectionsneutrino stress-energyspherical symmetryshock dynamics
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The pith

New effective potentials derived from Einstein equation projections approximate full general relativity in core-collapse supernova simulations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops two effective gravitational potentials by taking Eulerian and Lagrangian projections of the Einstein equations under the assumption of spherical symmetry, with the stress-energy tensor including both fluid and neutrino contributions. These potentials supply general relativistic corrections to the Newtonian gravitational potential and are implemented inside the Chimera and Flash-X simulation codes. Adiabatic and full core-collapse runs are compared against Newtonian, full general relativistic, and earlier effective-potential calculations from multiple independent codes. The new potentials produce density profiles, shock trajectories, and neutrino luminosities that lie close to the fully relativistic benchmarks. This matters because full general relativity remains expensive for three-dimensional supernova modeling, so a reliable Newtonian correction can make realistic simulations feasible while preserving the dominant relativistic effects.

Core claim

We present formulations of effective potentials suitable for approximating general relativistic effects in Newtonian simulations of core-collapse supernovae. Assuming a spherically symmetric spacetime and a stress-energy tensor that includes both fluid and neutrino contributions, Eulerian and Lagrangian projections of the Einstein equations are made to determine general relativistic corrections to the Newtonian gravitational potential. We implement the effective potentials in both the Chimera and Flash-X codes, and perform a series of adiabatic and core collapse simulations. The results are compared to Newtonian and fully general relativistic simulations, as well as another widely used effec

What carries the argument

Effective gravitational potentials obtained from Eulerian and Lagrangian projections of the Einstein equations that correct the Newtonian potential while incorporating fluid and neutrino stress-energy.

If this is right

  • Newtonian supernova codes can incorporate general relativistic gravity corrections without solving the full Einstein equations.
  • Including the neutrino contribution to the stress-energy tensor in the projection improves agreement with full general relativity.
  • The same potentials can be used across different Newtonian frameworks such as Chimera and Flash-X.
  • Adiabatic test problems confirm that the potentials recover the correct relativistic structure before collapse begins.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method may be adapted to other spherically symmetric relativistic flows where full general relativity is costly.
  • Because the potentials are derived directly from the Einstein equations, they provide a controlled way to test which relativistic effects matter most in supernova dynamics.
  • Extending the projection technique to include rotation or magnetic fields would require dropping spherical symmetry but could be checked against existing axisymmetric general relativistic simulations.

Load-bearing premise

The spacetime remains spherically symmetric and the stress-energy tensor can be split into fluid plus neutrino pieces so that the projections of the Einstein equations produce usable corrections to the Newtonian potential.

What would settle it

A one-dimensional core-collapse run in which the shock radius or central density evolution deviates by more than a few percent from the results of multiple independent full general relativistic codes would show the approximation has failed.

Figures

Figures reproduced from arXiv: 2604.20579 by Eric J. Lentz, J. Austin Harris, O. E. Bronson Messer, Steven A. Fromm, Vassilios Mewes, W. Raphael Hix.

Figure 2
Figure 2. Figure 2: Central density evolution near bounce from the Chimera adiabatic collapse simulations of the 15M⊙ progen￾itor from S. E. Woosley & A. Heger (2007). GREP (solid blue line) reaches a post-bounce central density comparable to the full GR simulation in GR1D (dashed yellow line). The Newto￾nian potential (solid purple line) produces a marginally lower post-bounce central density, and the new effective potential… view at source ↗
Figure 3
Figure 3. Figure 3: , while the central densities near bounce are shown in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Shock and PNS radius results from Chimera CCSN simulations of the 15M⊙ progenitor from S. E. Woosley & A. Heger (2007). With the new effective poten￾tial Φ¯ L (solid red line) the shock expands more slowly than with the Newtonian potential (solid purple line), but faster than GREP (solid blue line). A similar ordering is observed in the PNS radius (dashed-dotted lines). The results from full GR simulations… view at source ↗
Figure 6
Figure 6. Figure 6: Central density evolution near bounce from Chimera CCSN simulations of the 15M⊙ progenitor from S. E. Woosley & A. Heger (2007). GREP (blue line) reaches the highest post-bounce central density, slightly above the GR1D result (yellow dashed line). The new effective potential Φ¯ L (red line) and the Newtonian potential (purple line) are consecutively lower, with the AGILE-BOLTZTRAN (AB, black dotted line) f… view at source ↗
Figure 8
Figure 8. Figure 8: Flash-X frequency spectrum of the central den￾sity oscillations for the isolated neutron star simulations. The new effective potential Φ¯ E (red solid line) and the GR re￾sults from SphericalNR (gray dashed line) oscillate at about ∼1.2 kHz around their migrated central densities, while the GREP (blue solid line) result reaches a central density that oscillates at ∼2 kHz. tions used in some GR codes, e.g.,… view at source ↗
read the original abstract

We present formulations of effective potentials suitable for approximating general relativistic effects in Newtonian simulations of core-collapse supernovae. Assuming a spherically symmetric spacetime and a stress-energy tensor that includes both fluid and neutrino contributions, Eulerian and Lagrangian projections of the Einstein equations are made to determine general relativistic corrections to the Newtonian gravitational potential. We implement the effective potentials in both the Chimera and Flash-X codes, and perform a series of adiabatic and core collapse simulations. The results are compared to Newtonian and fully general relativistic simulations, as well as another widely used effective potential formulation. We find close agreement between our new effective potentials and the fully general relativistic results from multiple other codes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript derives effective gravitational potentials by performing Eulerian and Lagrangian projections of the Einstein equations under spherical symmetry, with a stress-energy tensor that includes both fluid and neutrino contributions. These potentials are implemented in the Chimera and Flash-X Newtonian codes and tested via adiabatic and core-collapse supernova simulations, with results compared against Newtonian runs, full GR simulations from multiple codes, and an existing effective-potential formulation; the central claim is close agreement with the full GR results.

Significance. If the agreement is robust, the work supplies a practical, computationally inexpensive route to incorporate leading GR corrections into widely used Newtonian CCSN codes. The parameter-free derivation from the Einstein equations and the multi-code validation (including two Newtonian implementations) are notable strengths that would make the method immediately usable by the community.

major comments (2)
  1. [§2] §2 (projections of the Einstein equations): the Eulerian and Lagrangian projections are performed under the assumption of spherical symmetry and a fixed form for the stress-energy tensor; it is not shown that all leading time-dependent metric corrections are retained in the high-compactness regime near core bounce, which is the regime where the claimed agreement with full GR is most load-bearing.
  2. [Results section] Results section (comparison plots and tables): quantitative error metrics (e.g., L2 norms or fractional differences in central density and shock radius) between the new potentials and the full-GR reference runs are not reported; without these, the statement of “close agreement” cannot be assessed for systematic bias or post-hoc tuning.
minor comments (2)
  1. Notation for the two new potentials (Eulerian vs. Lagrangian) is introduced without a compact summary table relating each to the corresponding GR correction term; this would aid readability.
  2. The abstract states agreement “across codes” but the text does not list the specific GR codes and resolutions used in the comparison; adding this information would strengthen reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of the work's significance and for the constructive comments. We address each major point below and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: §2 (projections of the Einstein equations): the Eulerian and Lagrangian projections are performed under the assumption of spherical symmetry and a fixed form for the stress-energy tensor; it is not shown that all leading time-dependent metric corrections are retained in the high-compactness regime near core bounce, which is the regime where the claimed agreement with full GR is most load-bearing.

    Authors: The projections are performed directly from the Einstein equations under the stated assumptions of spherical symmetry and a stress-energy tensor that includes both fluid and neutrino contributions; this is the standard approach for deriving effective potentials in this context. By construction, the Eulerian and Lagrangian forms retain the leading GR corrections to the Newtonian potential that arise from the metric components in the 3+1 decomposition. Time-dependent effects enter through the evolving matter and neutrino fields that source the projections at each time step. We acknowledge that an explicit order-of-magnitude analysis of neglected higher-order time-dependent metric terms near core bounce is not provided in the current §2. In the revised manuscript we will add a short subsection discussing the validity of the approximation in the high-compactness regime, including estimates showing that the retained terms dominate over the neglected ones under spherical symmetry. revision: partial

  2. Referee: Results section (comparison plots and tables): quantitative error metrics (e.g., L2 norms or fractional differences in central density and shock radius) between the new potentials and the full-GR reference runs are not reported; without these, the statement of “close agreement” cannot be assessed for systematic bias or post-hoc tuning.

    Authors: We agree that quantitative error metrics are needed to allow readers to evaluate the level of agreement rigorously. In the revised manuscript we will add a new table (and corresponding text in the Results section) reporting L2 norms and time-averaged fractional differences for central density, shock radius, and other key diagnostics, computed against the full-GR reference runs from the multiple codes already cited. These metrics will be shown for both the adiabatic and core-collapse suites. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation from Einstein projections with external GR comparisons

full rationale

The paper derives effective potentials directly from Eulerian and Lagrangian projections of the Einstein equations under spherical symmetry with a fluid-plus-neutrino stress-energy tensor. These potentials are implemented in Newtonian hydro codes and compared to independent fully general-relativistic simulations from other codes as well as to Newtonian and alternative effective-potential runs. No step reduces a prediction to a fitted parameter by construction, no load-bearing claim rests on self-citation, and no ansatz is smuggled in; the central agreement result is externally validated rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of spherical symmetry and the inclusion of fluid plus neutrino stress-energy in the projections; no free parameters or invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Spherically symmetric spacetime
    Invoked to enable Eulerian and Lagrangian projections of the Einstein equations
  • domain assumption Stress-energy tensor includes both fluid and neutrino contributions
    Used when determining general relativistic corrections to the Newtonian gravitational potential

pith-pipeline@v0.9.0 · 5430 in / 1158 out tokens · 51713 ms · 2026-05-09T23:34:13.788783+00:00 · methodology

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Reference graph

Works this paper leans on

56 extracted references · 51 canonical work pages

  1. [2]

    and Shapiro, Stuart L

    Baumgarte, Thomas W. and Shapiro, Stuart L. , year =. Numerical Relativity: Solving Einstein's Equations on the Computer , doi =

  2. [3]

    Bruenn, S. W. , year =. Stellar core collapse - Numerical model and infall epoch , volume =. doi:10.1086/191056 , journal =

    work page doi:10.1086/191056

  3. [4]

    , keywords =

    General Relativistic Effects in the Core Collapse Supernova Mechanism. , keywords =. doi:10.1086/322319 , archiveprefix =. astro-ph/0101400 , primaryclass =

    work page doi:10.1086/322319

  4. [5]

    W., Blondin , J

    , keywords =. 2020 , month = may, volume =. doi:10.3847/1538-4365/ab7aff , archiveprefix =. 1809.05608 , primaryclass =

    work page doi:10.3847/1538-4365/ab7aff 2020

  5. [6]

    Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport. I. Numerical method and results for a 15 M star. , keywords =. doi:10.1051/0004-6361:20053783 , archiveprefix =. astro-ph/0507135 , primaryclass =

    work page doi:10.1051/0004-6361:20053783

  6. [7]

    2022 , month = jul, volume =

    SoftwareX , keywords =. 2022 , month = jul, volume =. doi:10.1016/j.softx.2022.101168 , archiveprefix =. 2208.11630 , primaryclass =

    work page doi:10.1016/j.softx.2022.101168 2022

  7. [8]

    arXiv e-prints , keywords =

    thornado+Flash-X: A Hybrid DG-IMEX and Finite-Volume Framework for Neutrino-Radiation Hydrodynamics in Core-Collapse Supernovae. arXiv e-prints , keywords =

  8. [9]

    1998, Astrophys

    Hannestad, Steen and Raffelt, Georg , year =. Supernova Neutrino Opacity from Nucleon‐Nucleon Bremsstrahlung and Related Processes , volume =. , publisher =. doi:10.1086/306303 , number =

    work page doi:10.1086/306303

  9. [10]

    R., Millman, K

    Array programming with NumPy. , keywords =. doi:10.1038/s41586-020-2649-2 , archiveprefix =. 2006.10256 , primaryclass =

    work page doi:10.1038/s41586-020-2649-2 2006

  10. [11]

    D., 2007, @doi [Computing in Science Engineering] 10.1109/MCSE.2007.55 , 9, 90

    Matplotlib: A 2D Graphics Environment. Computing in Science and Engineering , keywords =. doi:10.1109/MCSE.2007.55 , adsurl =

    work page doi:10.1109/mcse.2007.55 2007

  11. [12]

    , keywords =

    Impact of Neutrino Opacities on Core-collapse Supernova Simulations. , keywords =. doi:10.3847/1538-4357/aaa716 , archiveprefix =. 1801.02703 , primaryclass =

    work page doi:10.3847/1538-4357/aaa716

  12. [13]

    doi:10.1088/1742-6596/1623/1/012013 , adsurl =

    Journal of Physics Conference Series , year =. doi:10.1088/1742-6596/1623/1/012013 , adsurl =

    work page doi:10.1088/1742-6596/1623/1/012013

  13. [14]

    2004 , month = jan, volume =

    , keywords =. 2004 , month = jan, volume =. doi:10.1086/380191 , archiveprefix =. astro-ph/0207036 , primaryclass =

    work page doi:10.1086/380191 2004

  14. [15]

    doi:10.1051/0004-6361:20052840 , archiveprefix =

    , keywords =. doi:10.1051/0004-6361:20052840 , archiveprefix =. astro-ph/0502161 , primaryclass =

    work page doi:10.1051/0004-6361:20052840

  15. [16]

    PeerJ Computer Science , issn =

    SymPy: symbolic computing in Python , author =. PeerJ Computer Science , issn =

  16. [17]

    , keywords =

    Numerical relativity in spherical coordinates with the Einstein Toolkit. , keywords =. doi:10.1103/PhysRevD.97.084059 , archiveprefix =. 1802.09625 , primaryclass =

    work page doi:10.1103/physrevd.97.084059

  17. [18]

    , keywords =

    Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit. , keywords =. doi:10.1103/PhysRevD.101.104007 , archiveprefix =. 2002.06225 , primaryclass =

    work page doi:10.1103/physrevd.101.104007 2002

  18. [19]

    Relativistic equations for adiabatic, spher- ically symmetric gravitational collapse,

    Physical Review , year = 1964, month = oct, volume =. doi:10.1103/PhysRev.136.B571 , adsurl =

    work page doi:10.1103/physrev.136.b571 1964

  19. [20]

    2017 , publisher =

    Gravitation. 2017 , publisher =

    2017

  20. [21]

    A New Multi-dimensional General Relativistic Neutrino Hydrodynamics Code for Core-collapse Supernovae. II. Relativistic Explosion Models of Core-collapse Supernovae. , keywords =. doi:10.1088/0004-637X/756/1/84 , archiveprefix =. 1202.0815 , primaryclass =

    work page doi:10.1088/0004-637x/756/1/84

  21. [22]

    2010 , month = jun, volume =

    Classical and Quantum Gravity , keywords =. 2010 , month = jun, volume =. doi:10.1088/0264-9381/27/11/114103 , archiveprefix =. 0912.2393 , primaryclass =

    work page doi:10.1088/0264-9381/27/11/114103 2010

  22. [23]

    2015 , month = aug, volume =

    , keywords =. 2015 , month = aug, volume =. doi:10.1088/0067-0049/219/2/24 , archiveprefix =. 1411.7058 , primaryclass =

    work page doi:10.1088/0067-0049/219/2/24 2015

  23. [24]

    , keywords =

    Two-dimensional Core-collapse Supernova Explosions Aided by General Relativity with Multidimensional Neutrino Transport. , keywords =. doi:10.3847/1538-4357/aaa893 , archiveprefix =. 1511.07443 , primaryclass =

    work page doi:10.3847/1538-4357/aaa893

  24. [25]

    Journal of Physics G Nuclear Physics , keywords =

    Global comparison of core-collapse supernova simulations in spherical symmetry. Journal of Physics G Nuclear Physics , keywords =. doi:10.1088/1361-6471/aadeae , archiveprefix =. 1806.04175 , primaryclass =

    work page doi:10.1088/1361-6471/aadeae

  25. [26]

    R., & Volkoff, G

    On Massive Neutron Cores. Physical Review , year = 1939, month = feb, volume =. doi:10.1103/PhysRev.55.374 , adsurl =

    work page doi:10.1103/physrev.55.374 1939

  26. [27]

    doi:10.1051/0004-6361:20021398 , archiveprefix =

    , keywords =. doi:10.1051/0004-6361:20021398 , archiveprefix =. astro-ph/0203101 , primaryclass =

    work page doi:10.1051/0004-6361:20021398

  27. [28]

    , keywords =

    Should One Use the Ray-by-Ray Approximation in Core-collapse Supernova Simulations?. , keywords =. doi:10.3847/0004-637X/831/1/81 , archiveprefix =. 1512.00113 , primaryclass =

    work page doi:10.3847/0004-637x/831/1/81

  28. [29]

    W., Hempel , M., & Fischer , T

    , keywords =. 2013 , month = sep, volume =. doi:10.1088/0004-637X/774/1/17 , archiveprefix =. 1207.2184 , primaryclass =

    work page doi:10.1088/0004-637x/774/1/17 2013

  29. [30]

    Physical Review , year = 1939, month = feb, volume =

    Static Solutions of Einstein's Field Equations for Spheres of Fluid. Physical Review , year = 1939, month = feb, volume =. doi:10.1103/PhysRev.55.364 , adsurl =

    work page doi:10.1103/physrev.55.364 1939

  30. [31]

    2007 , month = apr, volume =

    , keywords =. 2007 , month = apr, volume =. doi:10.1016/j.physrep.2007.02.009 , archiveprefix =. astro-ph/0702176 , primaryclass =

    work page doi:10.1016/j.physrep.2007.02.009 2007

  31. [32]

    Classical and Quantum Gravity , keywords =

    The Einstein Toolkit: a community computational infrastructure for relativistic astrophysics. Classical and Quantum Gravity , keywords =. doi:10.1088/0264-9381/29/11/115001 , archivePrefix =. 1111.3344 , primaryClass =

    work page doi:10.1088/0264-9381/29/11/115001

  32. [33]

    Maxwell Rizzo and Roland Haas and Steven R. Brandt and Zachariah Etienne and Deborah Ferguson and Lucas Timotheo Sanches and Bing-Jyun Tsao and Leonardo Werneck and David Boyer and Gabriele Bozzola and Cheng-Hsin Cheng and Samuel Cupp and Peter Diener and Terrence Pierre Jacques and Liwei Ji and Hayley Macpherson and Ivan Markin and Erik Schnetter and Wol...

    work page doi:10.5281/zenodo.15520463

  33. [34]

    Darmois, Georges , journal=. Les. doi:http://www.numdam.org/item/MSM_1927__25__1_0 , year=

  34. [35]

    , keywords =

    Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes. , keywords =. doi:10.1103/PhysRevD.108.104005 , archivePrefix =. 2305.01537 , primaryClass =

    work page doi:10.1103/physrevd.108.104005

  35. [36]

    Three-dimensional numerical general relativistic hydrodynamics. II. Long-term dynamics of single relativistic stars. , keywords =. doi:10.1103/PhysRevD.65.084024 , archivePrefix =. gr-qc/0110047 , primaryClass =

    work page doi:10.1103/physrevd.65.084024

  36. [37]

    , keywords =

    Improved constrained scheme for the Einstein equations: An approach to the uniqueness issue. , keywords =. doi:10.1103/PhysRevD.79.024017 , archivePrefix =. 0809.2325 , primaryClass =

    work page doi:10.1103/physrevd.79.024017

  37. [38]

    , keywords =

    Comparing Models of Rapidly Rotating Relativistic Stars Constructed by Two Numerical Methods. , keywords =. doi:10.1086/175605 , archivePrefix =. astro-ph/9411032 , primaryClass =

    work page doi:10.1086/175605

  38. [39]

    Annual Review of Nuclear and Particle Science , keywords =

    Long-Term Multidimensional Models of Core-Collapse Supernovae: Progress and Challenges. Annual Review of Nuclear and Particle Science , keywords =. doi:10.1146/annurev-nucl-121423-100945 , archivePrefix =. 2502.14836 , primaryClass =

    work page doi:10.1146/annurev-nucl-121423-100945

  39. [40]

    Living Reviews in Computational Astrophysics , keywords =

    Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae. Living Reviews in Computational Astrophysics , keywords =. doi:10.1007/s41115-020-00010-8 , archivePrefix =. 2010.09013 , primaryClass =

    work page doi:10.1007/s41115-020-00010-8 2010

  40. [41]

    2005, title Ascertaining The Core Collapse Supernova Mechanism: The State of the Art and the Road Ahead , Annu

    ASCERTAINING THE CORE COLLAPSE SUPERNOVA MECHANISM: The State of the Art and the Road Ahead. Annual Review of Nuclear and Particle Science , year = 2005, month = dec, volume =. doi:10.1146/annurev.nucl.55.090704.151608 , adsurl =

    work page doi:10.1146/annurev.nucl.55.090704.151608 2005

  41. [42]

    T., Langanke, K., Marek, A., Mart \'i nez-Pinedo , G., & M \"u ller, B

    Theory of core-collapse supernovae. , keywords =. doi:10.1016/j.physrep.2007.02.002 , archivePrefix =. astro-ph/0612072 , primaryClass =

    work page doi:10.1016/j.physrep.2007.02.002 2007

  42. [43]

    , keywords =

    Magnetorotational Explosion of a Massive Star Supported by Neutrino Heating in General Relativistic Three-dimensional Simulations. , keywords =. doi:10.3847/1538-4357/ab9308 , archivePrefix =. 2003.02004 , primaryClass =

    work page doi:10.3847/1538-4357/ab9308 2003

  43. [44]

    A New Multi-dimensional General Relativistic Neutrino Hydrodynamic Code for Core-collapse Supernovae. I. Method and Code Tests in Spherical Symmetry. , keywords =. doi:10.1088/0067-0049/189/1/104 , archivePrefix =. 1001.4841 , primaryClass =

    work page doi:10.1088/0067-0049/189/1/104

  44. [45]

    , keywords =

    Multidimensional Boltzmann Neutrino Transport Code in Full General Relativity for Core-collapse Simulations. , keywords =. doi:10.3847/1538-4357/abe1bf , archivePrefix =. 2010.10780 , primaryClass =

    work page doi:10.3847/1538-4357/abe1bf 2010

  45. [46]

    , keywords =

    General-Relativistic Three-Dimensional Multi-group Neutrino Radiation-Hydrodynamics Simulations of Core-Collapse Supernovae. , keywords =. doi:10.3847/0004-637X/831/1/98 , archivePrefix =. 1604.07848 , primaryClass =

    work page doi:10.3847/0004-637x/831/1/98

  46. [47]

    , keywords =

    A New Multi-energy Neutrino Radiation-Hydrodynamics Code in Full General Relativity and Its Application to the Gravitational Collapse of Massive Stars. , keywords =. doi:10.3847/0067-0049/222/2/20 , archivePrefix =. 1501.06330 , primaryClass =

    work page doi:10.3847/0067-0049/222/2/20

  47. [48]

    , keywords =

    NADA-FLD: a general relativistic, multidimensional neutrino-hydrodynamics code employing flux-limited diffusion. , keywords =. doi:10.1093/mnras/stz2791 , archivePrefix =. 1901.10523 , primaryClass =

    work page doi:10.1093/mnras/stz2791 1901

  48. [49]

    A., Dolence , J

    FORNAX: A Flexible Code for Multiphysics Astrophysical Simulations. , keywords =. doi:10.3847/1538-4365/ab007f , archivePrefix =. 1806.07390 , primaryClass =

    work page doi:10.3847/1538-4365/ab007f

  49. [50]

    2020, title Hydrodynamics of Core-Collapse Supernovae and Their Progenitors, Living Reviews in Computational Astrophysics, 6, 3, 10.1007/s41115-020-0008-5

    Hydrodynamics of core-collapse supernovae and their progenitors. Living Reviews in Computational Astrophysics , keywords =. doi:10.1007/s41115-020-0008-5 , archivePrefix =. 2006.05083 , primaryClass =

    work page doi:10.1007/s41115-020-0008-5 2006

  50. [51]

    Reviews of Modern Physics , keywords =

    Colloquium: Perspectives on core-collapse supernova theory. Reviews of Modern Physics , keywords =. doi:10.1103/RevModPhys.85.245 , archivePrefix =. 1210.4921 , primaryClass =

    work page doi:10.1103/revmodphys.85.245

  51. [52]

    Philosophical Transactions of the Royal Society of London Series A , year = 2017, month = sep, volume =

    The mechanism(s) of core-collapse supernovae. Philosophical Transactions of the Royal Society of London Series A , year = 2017, month = sep, volume =. doi:10.1098/rsta.2016.0271 , adsurl =

    work page doi:10.1098/rsta.2016.0271 2017

  52. [53]

    , keywords =

    The Explosion Mechanism of Core-Collapse Supernovae: Progress in Supernova Theory and Experiments. , keywords =. doi:10.1017/pasa.2015.9 , archivePrefix =. 1501.01334 , primaryClass =

    work page doi:10.1017/pasa.2015.9 2015

  53. [54]

    Universe , keywords =

    The Physics of Core-Collapse Supernovae: Explosion Mechanism and Explosive Nucleosynthesis. Universe , keywords =. doi:10.3390/universe10030148 , archivePrefix =. 2403.12942 , primaryClass =

    work page doi:10.3390/universe10030148

  54. [55]

    , keywords =

    An Adaptive Grid, Implicit Code for Spherically Symmetric, General Relativistic Hydrodynamics in Comoving Coordinates. , keywords =. doi:10.1086/339872 , archivePrefix =. astro-ph/0106539 , primaryClass =

    work page doi:10.1086/339872

  55. [56]

    , keywords =

    A Numerical Method for Solving the Neutrino Boltzmann Equation Coupled to Spherically Symmetric Stellar Core Collapse. , keywords =. doi:10.1086/172395 , adsurl =

    work page doi:10.1086/172395

  56. [57]

    Journal of Computational and Applied Mathematics , keywords =

    Neutrino transport in core collapse supernovae. Journal of Computational and Applied Mathematics , keywords =. doi:10.1016/S0377-0427(99)00162-4 , adsurl =

    work page doi:10.1016/s0377-0427(99)00162-4