Kinematical conditions in the construction of spacetime

Smarr, Larry; York, James W.

doi:10.1103/physrevd.17.2529

Cited by 326 publications

(306 citation statements)

References 51 publications

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“…This derivative is equated to the changes in the distribution function due to collisions, which are described by the right-hand side of the equation. Once a 1 þ 1 decomposition of spacetime (Arnowitt, Deser, & Misner 1962;Smarr & York 1978) and a basis in the momentum phase space for the particle four-momentum have been chosen, the directional derivative along the phase flow can be expressed in terms of partial derivatives of the distribution function with respect to the spacetime coordinates and momenta (Lindquist 1966;Mezzacappa & Matzner 1989). We measure the particle four-momentum in a comoving orthonormal frame, with components…”

Section: Radiation Hydrodynamics In Spherical Symmetrymentioning

confidence: 99%

A Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Spacetime

Liebendörfer

Messer

Mezzacappa

et al. 2004

ASTROPHYS J SUPPL S

316

388

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We present an implicit finite difference representation for general relativistic radiation hydrodynamics in spherical symmetry. Our code, AGILE-BOLTZTRAN, solves the Boltzmann transport equation for the angular and spectral neutrino distribution functions in self-consistent simulations of stellar core collapse and postbounce evolution. It implements a dynamically adaptive grid in comoving coordinates. A comoving frame in the momentum phase space facilitates the evaluation and tabulation of neutrino-matter interaction cross sections but produces a multitude of observer corrections in the transport equation. Most macroscopically interesting physical quantities are defined by expectation values of the distribution function. We optimize the finite differencing of the microscopic transport equation for a consistent evolution of important expectation values. We test our code in simulations launched from progenitor stars with 13 solar masses and 40 solar masses. Half a second after core collapse and bounce, the protoneutron star in the latter case reaches its maximum mass and collapses further to form a black hole. When the hydrostatic gravitational contraction sets in, we find a transient increase in electron flavor neutrino luminosities due to a change in the accretion rate. The -and -neutrino luminosities and rms energies, however, continue to rise because previously shock-heated material with a nondegenerate electron gas starts to replace the cool degenerate material at their production site. We demonstrate this by supplementing the concept of neutrinospheres with a more detailed statistical description of the origin of escaping neutrinos. Adhering to our tradition, we compare the evolution of the 13 M progenitor star to corresponding simulations with the multigroup flux-limited diffusion approximation, based on a recently developed flux limiter. We find similar results in the postbounce phase and validate this MGFLD approach for the spherically symmetric case with standard input physics.

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Section: Radiation Hydrodynamics In Spherical Symmetrymentioning

confidence: 99%

A Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Spacetime

Liebendörfer

Messer

Mezzacappa

et al. 2004

ASTROPHYS J SUPPL S

316

388

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“…(3)(4)(5)(6)(7)(8) can be written in conservative form. Optimal for a numerical implementation is a formulation that contains quantities that are either conserved or local.…”

Section: Conservative Einstein Equationsmentioning

confidence: 99%

“…However, comoving coordinates are only one possible choice out of a variety of 3+1 decompositions enabled by the covariance of general relativity in four-dimensional space-time (Arnowitt, Deser, and Misner [6]; Smarr and York [7]). The Boltzmann transport equation is usually split into a left-hand side and a right-hand side.…”

Section: Introductionmentioning

confidence: 99%

Conservative general relativistic radiation hydrodynamics in spherical symmetry and comoving coordinates

2001

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The description of general relativistic radiation hydrodynamics in spherical symmetry is presented in natural coordinate choices. For hydrodynamics, comoving coordinates are chosen and the momentum phase space for the radiation particles is described in comoving frame four momenta. We also investigate a description of the momentum phase space in terms of particle impact parameter and energy at infinity and derive a simple approximation to the general relativistic Boltzmann equation. Further developed are, however, the exact equations in comoving coordinates since the description of the interaction between matter and radiation particles is best described in the closely related orthonormal basis comoving with the fluid elements. We achieve a conservative and concise formulation of radiation hydrodynamics that is well suited for numerical implementation by a variety of methods. The contribution of radiation to the general relativistic jump conditions at shock fronts is discussed and artificial viscosity is consistently included in the derivations in order to support approaches relying on this option.

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“…strong energy condition), one can use the maximum-minimum principle to determine the qualitative behavior for the lapse (cf. [49,62]). The lapse function has a minimum at r = 0 and a maximum at r → ∞ and during the evolution the minimum tends to zero as t → ∞ (the collapse of the lapse) halting the propertime separation between neighbouring slices as the singularity forms.…”

Section: Gauge and Slicing Conditionmentioning

confidence: 99%

“…[49,62,63] for a more general discussion on the slicing choices). Moreover, it is in the framework of asymptotically flat spacetimes (condition usually demanded in astrophysical applications) that they become specially useful; it is in this context that such gauges and time slicings will be discussed in the following.…”

Section: Gauge and Slicing Conditionmentioning

confidence: 99%

Dynamics of spherically symmetric spacetimes: Hydrodynamics and radiation

Salgado

2002

Phys. Rev. D

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Using the 3+1 formalism of general relativity we obtain the equations governing the dynamics of spherically symmetric spacetimes with arbitrary sources. We then specialize for the case of perfect fluids accompanied by a flow of interacting massless or massive particles (e.g. neutrinos)which are described in terms of relativistic transport theory. We focus in three types of coordinates: 1) isotropic gauge and maximal slicing, 2) radial gauge and polar slicing, and 3) isotropic gauge and polar slicing.

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Kinematical conditions in the construction of spacetime

Cited by 326 publications

References 51 publications

A Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Spacetime

A Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Spacetime

Conservative general relativistic radiation hydrodynamics in spherical symmetry and comoving coordinates

Dynamics of spherically symmetric spacetimes: Hydrodynamics and radiation

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