Among his many accomplishments was figuring out how giant stars burn helium to form carbon in the 'triple-alpha process' (named after the three helium nuclei - alpha particles - that fuse together in ...the process). While studying Fowler's experimental data, Salpeter realized that the beryllium nucleus ^sup 8^Be - the fusion product of two helium nuclei - is actually metastable, and would exist in low concentrations inside redgiant stars.
We construct equilibrium sequences of rotating neutron stars in general relativity. We compare results for 14 nuclear matter equations of state. We determine a number of important physical parameters ...for such stars, including the maximum mass and maximum spin rate. The stability of the configurations to quasi-radial perturbations is assessed. We employ a numerical scheme particularly well suited to handle rapid rotation and large departures from spherical symmetry. We provide an extensive tabulation of models for future reference. Two classes of evolutionary sequences of fixed baryon rest mass and entropy are explored: normal sequences, which behave very much like Newtonian sequences, and supramassive sequences, which exist for neutron stars solely because of general relativistic effects. Adiabatic dissipation of energy and angular momentum causes a star to evolve in quasi-stationary fashion along an evolutionary sequence. Supramassive sequences have masses exceeding the maximum mass of a nonrotating neutron star. A supramassive star evolves toward eventual catastrophic collapse to a black hole. Prior to collapse, the star actually spins up as it loses angular momentum, an effect that may provide an observable precursor to gravitational collapse to a black hole.
The DG algorithm is a powerful method for solving pdes, especially for evolution equations in conservation form. Since the algorithm involves integration over volume elements, it is not immediately ...obvious that it will generalize easily to arbitrary time-dependent curved spacetimes. We show how to formulate the algorithm in such spacetimes for applications in relativistic astrophysics. We also show how to formulate the algorithm for equations in non-conservative form, such as Einstein's field equations themselves. We find two computationally distinct formulations in both cases, one of which has seldom been used before for flat space in curvilinear coordinates but which may be more efficient. We also give a new derivation of the ALE algorithm (Arbitrary Lagrangian–Eulerian) using 4-vector methods that is much simpler than the usual derivation and explains why the method preserves the conservation form of the equations. The various formulations are explored with some simple numerical experiments that also investigate the effect of the metric identities on the results. The results of this paper may also be of interest to practitioners of DG working with curvilinear elements in flat space.
It has recently been shown that a rapidly rotating Newtonian star can spin up by radiating angular momentum. Extremely fast pulsars losing energy and angular momentum by magnetic dipole radiation or ...gravitational radiation may exhibit this behavior. Here, we show that this phenomenon is more widespread for rapidly rotating stars in general relativity. We construct and tabulate polytropic sequences of fully relativistic rotating stars of constant rest mass and entropy. We find that the range of adiabatic indices allowing spin-up extends somewhat above 4/3 because of the nonlinear effects of relativistic gravity. In addition, there is a new class of 'supramassive' stars which will inevitably spin up by losing angular momentum regardless of their equation of state. A supramassive star, spinning up via angular momentum loss, will ultimately evolve until it becomes unstable to catastrophic collapse to a black hole. Spin-up in a rapidly rotating star may thus be an observational precursor to such collapse.
The behavior of merging black holes (including the emitted gravitational waves and the properties of the remnant) can currently be computed only by numerical simulations. This paper introduces ten ...numerical relativity simulations of binary black holes with equal masses and equal spins aligned or antialigned with the orbital angular momentum. The initial spin magnitudes have chi sub(i) <, ~ 0.95 and are more concentrated in the aligned direction because of the greater astrophysical interest of this case. We combine these data with five previously reported simulations of the same configuration, but with different spin magnitudes, including the highest spin simulated to date, chi sub(i) asymptotically = 0.97. This data set is sufficiently accurate to enable us to offer improved analytic fitting formulas for the final spin and for the energy radiated by gravitational waves as a function of initial spin. The improved fitting formulas can help to improve our understanding of the properties of binary black hole merger remnants and can be used to enhance future approximate waveforms for gravitational wave searches, such as effective-one-body waveforms.
A new numerical code is used to evolve collisionless gas spheroids in full general relativity. In all cases, the spheroids collapse to singularities. When the spheroids are sufficiently compact, the ...singularities are hidden inside black holes. However, when the spheroids are sufficiently large, there are no apparent horizons. These results lend support to the hoop conjecture and appear to demonstrate that naked singularities can form in asymptotically flat spacetimes. (Author)
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