arXiv subjects

T. W. Baumgarte

Publications and source records attributed to T. W. Baumgarte.

14 recordsLinked to original sources

arXiv2013

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 non-rotating star in isolation by between 30 and 70 per cent. Our simulations also show that the ratio between the threshold mass and maximum mass is tightly correlated with the compactness of the non-rotating maximum-mass configuration. We speculate on how this relation can be used to derive constraints on neutron-star properties from future observations.

astro-ph.SR↗

arXiv2009

Equilibrium initial data for moving puncture simulations: The stationary 1+log slicing

We propose and explore a "stationary 1+log" slicing condition for the construction of solutions to Einstein's constraint equations. For stationary spacetimes, these initial data will give a stationary foliation when evolved with "moving puncture" gauge conditions that are often used in black hole evolutions. The resulting slicing is time-independent and agrees with the slicing generated by being dragged along a time-like Killing vector of the spacetime. When these initial data are evolved with moving puncture gauge conditions, numerical errors arising from coordinate evolution are minimized. In the construction of initial data for binary black holes it is often assumed that there exists an approximate helical Killing vector that generates the binary's orbit. We show that, unfortunately, 1+log slices that are stationary with respect to such a helical Killing vector cannot be asymptotically flat, unless the spacetime possesses an additional axial Killing vector.

gr-qc↗

arXiv2004

The Moment of Inertia of the Binary Pulsar J0737-3039A: Constraining the Nuclear Equation of State

We construct numerical models of the newly discovered binary pulsar J0737-3039A, both with a fully relativistic, uniformly rotating, equilibrium code that handles arbitrary spins and in the relativistic, slow-rotation approximation. We compare results for a representative sample of viable nuclear equations of state (EOS) that span three, qualitatively different, classes of models for the description of nuclear matter. A future dynamical measurement of the neutron star's moment of inertia from pulsar timing data will impose significant constraints on the nuclear EOS. Even a moderately accurate measurement (<~ 10 %) may be able to rule out some of these competing classes. Using the measured mass, spin and moment of inertia to identify the optimal model computed from different EOSs, one can determine the pulsar's radius.

astro-ph↗

arXiv2002

Illustrating Stability Properties of Numerical Relativity in Electrodynamics

We show that a reformulation of the ADM equations in general relativity, which has dramatically improved the stability properties of numerical implementations, has a direct analogue in classical electrodynamics. We numerically integrate both the original and the revised versions of Maxwell's equations, and show that their distinct numerical behavior reflects the properties found in linearized general relativity. Our results shed further light on the stability properties of general relativity, illustrate them in a very transparent context, and may provide a useful framework for further improvement of numerical schemes.

gr-qc↗

arXiv2001

A numerical testbed for singularity excision in moving black hole spacetimes

We evolve a scalar field in a fixed Kerr-Schild background geometry to test simple $(3+1)$-dimensional algorithms for singularity excision. We compare both centered and upwind schemes for handling the shift (advection) terms, as well as different approaches for implementing the excision boundary conditions, for both static and boosted black holes. By first determining the scalar field evolution in a static frame with a $(1+1)$-dimensional code, we obtain the solution to very high precision. This solution then provides a useful testbed for simulations in full $(3+1)$ dimensions. We show that some algorithms which are stable for non-boosted black holes become unstable when the boost velocity becomes high.

gr-qc↗

arXiv1999

Implementing fully relativistic hydrodynamics in three dimensions

We report on our numerical implementation of fully relativistic hydrodynamics coupled to Einstein's field equations in three spatial dimensions. We briefly review several steps in our code development, including our recasting of Einstein's equations and several tests which demonstrate its advantages for numerical integrations. We outline our implementation of relativistic hydrodynamics, and present numerical results for the evolution of both stable and unstable Oppenheimer-Volkov equilibrium stars, which represent a very promising first test of our code.

gr-qc↗

arXiv1999

Constructing a Mass-Current Radiation-Reaction Force For Numerical Simulations

We present a new set of 3.5 Post-Newtonian equations in which Newtonian hydrodynamics is coupled to the nonconservative effects of gravitational radiation emission. Our formalism differs in two significant ways from a similar 3.5 Post-Newtonian approach proposed by Blanchet (1993, 1997). Firstly we concentrate only on the radiation-reaction effects produced by a time-varying mass-current quadrupole $S_{ij}$. Secondly, we adopt a gauge in which the radiation-reaction force densities depend on the fourth time derivative of $S_{ij}$, rather than on the fifth, as in Blanchet's approach. This difference makes our formalism particularly well-suited to numerical implementation and could prove useful in performing fully numerical simulations of the recently discovered $r$-mode instability for rotating neutron stars subject to axial perturbations.

gr-qc↗

arXiv1998

Stability of coalescing binary stars against gravitational collapse: hydrodynamical simulations

We perform simulations of relativistic binary stars in post-Newtonian gravity to investigate their dynamical stability prior to merger against gravitational collapse in a tidal field. In general, our equations are only strictly accurate to first post-Newtonian order, but they recover full general relativity for spherical, static stars. We study both corotational and irrotational binary configurations of identical stars in circular orbits. We adopt a soft, adiabatic equation of state with $Γ= 1.4$, for which the onset of instability occurs at a sufficiently small value of the compaction $M/R$ that a post-Newtonian approximation is quite accurate. For such a soft equation of state there is no innermost stable circular orbit, so that we can study arbitrarily close binaries. This choice still allows us to study all the qualitative features exhibited by any adiabatic equation of state regarding stability against gravitational collapse. We demonstrate that, independent of the internal stellar velocity profile, the tidal field from a binary companion stabilizes a star against gravitational collapse.

gr-qc↗

arXiv1997

Waveform propagation in black hole spacetimes: evaluating the quality of numerical solutions

We compute the propagation and scattering of linear gravitational waves off a Schwarzschild black hole using a numerical code which solves a generalization of the Zerilli equation to a three dimensional cartesian coordinate system. Since the solution to this problem is well understood it represents a very good testbed for evaluating our ability to perform three dimensional computations of gravitational waves in spacetimes in which a black hole event horizon is present.

gr-qc↗

arXiv1997

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 ~6M at 0.1c during a total evolution of duration ~60M.

gr-qc↗

arXiv1997

Gravitational wave extraction and outer boundary conditions by perturbative matching

We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code.

gr-qc↗

arXiv1997

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 (ISCO) 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 >= 1.5. A radial stability analysis reveals no tendency for neutron stars in close binaries to collapse to black holes prior to merger.

gr-qc↗

arXiv1997

The Stability of Relativistic Neutron Stars in Binary Orbit

We analyze the stability of relativistic, quasi-equilibrium binary neutron stars in synchronous circular orbit. We explore stability against radial collapse to black holes prior to merger, and against orbital plunge. We apply theorems based on turning points along uniformly rotating sequences of constant angular momentum and rest mass to locate the onset of secular instabilities. We find that inspiraling binary neutron stars are stable against radial collapse to black holes all the way down to the innermost stable circular orbit.

gr-qc↗

arXiv1997

Binary Neutron Stars in General Relativity: Quasi-Equilibrium Models

We perform fully relativistic calculations of binary neutron stars in quasi-equilibrium circular orbits. We integrate Einstein's 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 quasi-equilibrium maximum allowed mass of a neutron star in a close binary is slightly larger than in isolation.

gr-qc↗