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.

We study static neutron stars with poloidal magnetic Ðelds and a simple class of electric current distributions consistent with the requirement of stationarity. For this class of electric current distributions, we Ðnd that magnetic Ðelds are too large for static conÐgurations to exist when the magnetic force pushes a sufficient amount of mass o †-center that the gravitational force points outward near the origin in the equatorial plane. (In our coordinates an outward gravitational force corresponds to L ln g tt /Lr [ 0, where t and r are respectively time and radial coordinates and is coefficient of dt2 in the line element.) g tt For the equations of state (EOSs) employed in previous work, we obtain conÐgurations of higher mass than had been reported ; we also present results with more recent EOSs. For all EOSs studied, we Ðnd that the maximum mass among these static conÐgurations with magnetic Ðelds is noticeably larger than the maximum mass attainable by uniform rotation, and that for Ðxed values of baryon number the maximum mass conÐgurations are all characterized by an o †-center density maximum.

We discuss neutrino oscillations in curved spacetime. Our heuristic approach can accommodate matter effects and gravitational contributions to neutrino spin precession in the presence of a magnetic field. By way of illustration, we perform explicit calculations in the Schwarzschild geometry. In this case, gravitational effects on neutrino oscillations are intimately related to the redshift. We discuss how spacetime curvature could affect the resonance position and adiabaticity of matter-enhanced neutrino flavor conversion.

We discuss general relativistic effects in the steady-state neutrino-driven "wind" which may arise from nascent neutron stars. In particular, we generalize previous analytic estimates of the entropy per baryon S, the mass outflow ratė M , and the dynamical expansion time scale τ dyn . We show that S increases and τ dyn decreases with increasing values of the mass-to-radius ratio describing the supernova core. Both of these trends indicate that a more compact core will lead to a higher number of neutrons per iron peak seed nucleus. Such an enhancement in the neutron-to-seed ratio may be required for successful r-process nucleosynthesis in neutrino-heated supernova ejecta.

We extend our investigation of magnetic field evolution in three-dimensional flows driven by the stationary accretion shock instability (SASI) with a suite of higher-resolution idealized models of the post-bounce corecollapse supernova environment. Our magnetohydrodynamic simulations vary in initial magnetic field strength, rotation rate, and grid resolution. Vigorous SASI-driven turbulence inside the shock amplifies magnetic fields exponentially; but while the amplified fields reduce the kinetic energy of small-scale flows, they do not seem to affect the global shock dynamics. The growth rate and final magnitude of the magnetic energy are very sensitive to grid resolution, and both are underestimated by the simulations. Nevertheless our simulations suggest that neutron star magnetic fields exceeding 10 14 G can result from dynamics driven by the SASI, even for non-rotating progenitors.

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.

In the simplistic quantum mechanical picture of flavor mixing, conditions on the maximum size and minimum coherence time of the source and detector regions for the observation of interferenceas well as the very viability of the approach-can only be argued in an ad hoc way from principles external to the formalism itself. To examine these conditions in a more fundamental way, the quantum field theoretical S-matrix approach is employed in this paper, without the unrealistic assumption of microscopic stationarity. The fully normalized, time-dependent neutrino flavor mixing event rates presented here automatically reveal the coherence conditions in a natural, self-contained, and physically unambiguous way, while quantitatively describing the transition to their failure.14.60. Pq, 26.65.+t, 13.15.+g

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.