Thomas W. Baumgarte

Numerical relativity and compact binaries

Abstract Numerical relativity is the most promising tool for theoretically modeling the inspiral and coalescence of neutron star and black hole binaries, which, in turn, are among the most promising sources of gravitational radiation for future detection by gravitational wave observatories. In this article we review numerical relativity approaches to modeling compact binaries. Starting with a brief introduction to the 3+1 decomposition of Einsteins equations, we discuss important components of numerical relativity, including the initial data problem, reformulations of Einsteins equations, coordinate conditions, and strategies for locating and handling black holes on numerical grids. We focus on those approaches which currently seem most relevant for the compact binary problem. We then outline how these methods are used to model binary neutron stars and black holes, and review the current status of inspiral and coalescence simulations.

Evolution of Rotating Supermassive Stars to the Onset of Collapse

We launch a fully relativistic study of the formation of supermassive black holes via the collapse of supermassive stars. Here we initiate our investigation by analyzing the secular evolution of supermassive stars up to the onset of dynamical instability and collapse. We focus on the effects of rotation, assumed uniform, and general relativity. We identify the critical configuration at which radial instability sets in and determine its structure in detail. We show that the key nondimensional ratios R/M, T/|W|, and J/M2 (T is the rotational kinetic energy, and W is the gravitational potential energy) for this critical configuration are universal numbers, independent of the mass, spin, radius, or history of the star. We compare results from an approximate, analytic treatment with a fully relativistic, numerical calculation and find good agreement. We solve analytically for the time evolution of these parameters up to the onset of instability. Cooling by photon radiation drives the evolution, which is accompanied by mass, angular momentum, and entropy loss. The critical configuration serves as initial data for a future relativistic, hydrodynamical, three-dimensional simulation of the collapse of an unstable supermassive star. Since this implosion starts from a universal critical configuration, the collapse is also uniquely determined and should produce a universal gravitational waveform. In this paper we briefly speculate on the possible outcome of this collapse and assess to what extent it offers a promising route to forming a supermassive black hole.

Effect of Differential Rotation on the Maximum Mass of Neutron Stars: Realistic Nuclear Equations of State

The merger of binary neutron stars is likely to lead to differentially rotating remnants. In this paper, we survey several cold nuclear equations of state (EOSs) and numerically construct models of differentially rotating neutron stars in general relativity. For each EOS we tabulate maximum allowed masses as a function of the degree of differential rotation. We also determine effective polytropic indices and compare the maximum allowed masses with those for the corresponding polytropes. We consistently find larger mass increases for the polytropes, but even for the nuclear EOSs we typically find maximum masses 50% higher than the corresponding values for nonrotating (Tolman-Oppenheimer-Volkoff) stars. We evaluate our findings for the six observed binary neutron star (pulsar) systems, including the recently discovered binary pulsar J0737-3039. For each EOS we determine whether their merger could automatically lead to prompt collapse to a black hole, or whether the remnant can be supported against collapse by uniform rotation (possibly as a supramassive star) or differential rotation (possibly as a hypermassive star). For hypermassive stars, delayed collapse to a black hole is likely. For the most recent EOSs we survey the merger remnants can all be supported by rotation against prompt collapse, but their actual fate will depend on the nonequilibrium dynamics of the coalescence event. Gravitational wave observations of coalescing binary neutron stars may be able to distinguish these outcomes—no, delayed, or prompt collapse—and thereby constrain possible EOSs.

Stability and collapse of rapidly rotating, supramassive neutron stars: 3D simulations in general relativity

We perform 3D numerical simulations in full general relativity to study the stability of rapidly rotating, supramassive neutron stars at the mass-shedding limit to dynamical collapse. We adopt an adiabatic equation of state with G52 and focus on uniformly rotating stars. We find that the onset of dynamical instability along mass-shedding sequences nearly coincides with the onset of secular instability. Unstable stars collapse to rotating black holes within about one rotation period. We also study the collapse of stable stars which have been destabilized by pressure depletion ~e.g., via a phase transition! or mass accretion. In no case do we find evidence for the formation of massive disks or any ejecta around the newly formed Kerr black holes, even though the progenitors are rapidly rotating.

Binary neutron stars in general relativity: Quasiequilibrium models

We perform fully relativistic calculations of binary neutron stars in quasiequilibrium circular orbits. We integrate Einsteins equations together with the relativistic equation of hydrostatic equilibrium to solve the initial-value problem for equal-mass binaries of arbitrary separation. We construct sequences of constant rest mass and identify the innermost stable circular orbit and its angular velocity. We find that the quasiequilibrium maximum allowed mass of a neutron star in a close binary is slightly larger than in isolation.

Prompt merger collapse and the maximum mass of neutron stars

We perform hydrodynamical simulations of neutron-star mergers for a large sample of temperature-dependent nuclear equations of state and determine the threshold mass above which the merger remnant promptly collapses to form a black hole. We find that, depending on the equation of state, the threshold mass is larger than the maximum mass of a nonrotating star in isolation by between 30 and 70 percent. Our simulations also show that the ratio between the threshold mass and maximum mass is tightly correlated with the compactness of the nonrotating maximum-mass configuration. We speculate on how this relation can be used to derive constraints on neutron-star properties from future observations.

Boosted three-dimensional black-hole evolutions with singularity excision

Binary black-hole interactions provide potentially the strongest source of gravitational radiation for detectors currently under development. We present some results from the Binary Black Hole Grand Challenge Alliance three-dimensional Cauchy evolution module. These constitute essential steps towards modeling such interactions and predicting gravitational radiation waveforms. We report on single black-hole evolutions and the first successful demonstration of a black hole moving freely through a three-dimensional computational grid via a Cauchy evolution: a hole moving near 6M at 0.1c during a total evolution of duration near 60M. [S0031-9007(98)05652-X]

General Relativistic Models of Binary Neutron Stars in Quasiequilibrium

We perform fully relativistic calculations of binary neutron stars in corotating, circular orbit. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to lose energy and slowly spiral inwards. However, since inspiral occurs on a time scale much longer than the orbital period, we can treat the binary to be in quasiequilibrium. In this approximation, we integrate a subset of the Einstein equations coupled to the relativistic equation of hydrostatic equilibrium to solve the initial value problem for binaries of arbitrary separation. We adopt a polytropic equation of state to determine the structure and maximum mass of neutron stars in close binaries for polytropic indices n = 1, 1.5 and 2. We construct sequences of constant rest-mass and locate turning points along energy equilibrium curves to identify the onset of orbital instability. In particular, we locate the innermost stable circular orbit and its angular velocity. We construct the first contact binary systems in full general relativity. These arise whenever the equation of state is sufficiently soft (n ≳ 1.5). A radial stability analysis reveals no tendency for neutron stars in close binaries to collapse to black holes prior to merger.

General relativistic binary merger simulations and short gamma-ray bursts

The recent localization of some short-hard gamma-ray bursts (GRBs) in galaxies with low star formation rates has lent support to the suggestion that these events result from compact object binary mergers. We discuss how new simulations in general relativity are helping to identify the central engine of short-hard GRBs. Motivated by our latest relativistic black hole-neutron star merger calculations, we discuss a scenario in which these events may trigger short-hard GRBs and compare this model to competing relativistic models involving binary neutron star mergers and the delayed collapse of hypermassive neutron stars. Distinguishing features of these models may help guide future GRB and gravitational wave observations to identify the nature of the sources.

Regularity of spherically symmetric static solutions of the Einstein equations

It is shown that all spherically symmetric state solutions of the Einstein equations are regular without assuming the equation of state to be monotonic nor the pressure to be isotropic. This is not only a generalization of earlier results, but may also replace much more complicated arguments in earlier treatments.