arXiv subjects

John L. Friedman

Publications and source records attributed to John L. Friedman.

At least 37 records · Page 2Linked to original sources

arXiv2008

Constraints on a phenomenologically parameterized neutron-star equation of state

We introduce a parameterized high-density equation of state (EOS) in order to systematize the study of constraints placed by astrophysical observations on the nature of neutron-star matter. To obtain useful constraints, the number of parameters should be smaller than the number of neutron-star properties that have been measured or will have been measured in the next several years. And the set must be large enough to accurately approximate the large set of candidate EOSs. We find that a parameterized EOS based on piecewise polytropes with 3 free parameters matches to about 4% rms error an extensive set of candidate EOSs at densities below the central density of 1.4 solar mass stars. Adding observations of more massive stars constrains the higher density part of the EOS and requires an additional parameter. We obtain constraints on the allowed parameter space set by causality and by present and near-future astronomical observations. In particular, we emphasize potentially stringent constraints on the EOS parameter space associated with two measured properties of a single star; and we find that a measurement of the moment of inertia of PSR J0737-3039A can strongly constrain the maximum neutron-star mass. We also present in an appendix a more efficient algorithm than has previously been used for finding points of marginal stability and the maximum angular velocity of stable stars.

astro-ph↗

arXiv2008

Topological censorship and chronology protection

Over the past two decades, substantial efforts have been made to understand the way in which physics enforces the ordinary topology and causal structure that we observe, from subnuclear to cosmological scales. We review the status of topological censorship and the topology of event horizons; chronology protection in classical and semiclassical gravity; and related progress in establishing quantum energy inequalities.

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arXiv2007

On finding fields and self-force in a gauge appropriate to separable wave equations

Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. This paper presents progress on finding the electromagnetic and gravitational field of a point particle in a black-hole spacetime and on computing the self-force in a ``radiation gauge.'' The gauge is chosen to allow one to compute the perturbed metric from a gauge-invariant component $ψ_0$ (or $ψ_4$) of the Weyl tensor and follows earlier work by Chrzanowski and Cohen and Kegeles (we correct a minor, but propagating, error in the Cohen-Kegeles formalism). The electromagnetic field tensor and vector potential of a static point charge and the perturbed gravitational field of a static point mass in a Schwarzschild geometry are found, surprisingly, to have closed-form expressions. The gravitational field of a static point charge in the Schwarzschild background must have a strut, but $ψ_0$ and $ψ_4$ are smooth except at the particle, and one can find local radiation gauges for which the corresponding spin $\pm 2$ parts of the perturbed metric are smooth. Finally a method for finding the renormalized self-force from the Teukolsky equation is presented. The method is related to the Mino, Sasaki, Tanaka and Quinn and Wald (MiSaTaQuWa) renormalization and to the Detweiler-Whiting construction of the singular field. It relies on the fact that the renormalized $ψ_0$ (or $ψ_4$) is a {\em sourcefree} solution to the Teukolsky equation; and one can therefore reconstruct a nonsingular renormalized metric in a radiation gauge.

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arXiv2006

Binary neutron stars: Equilibrium models beyond spatial conformal flatness

Equilibria of binary neutron stars in close circular orbits are computed numerically in a waveless formulation: The full Einstein-relativistic-Euler system is solved on an initial hypersurface to obtain an asymptotically flat form of the 4-metric and an extrinsic curvature whose time derivative vanishes in a comoving frame. Two independent numerical codes are developed, and solution sequences that model inspiraling binary neutron stars during the final several orbits are successfully computed. The binding energy of the system near its final orbit deviates from earlier results of third post-Newtonian and of spatially conformally flat calculations. The new solutions may serve as initial data for merger simulations and as members of quasiequilibrium sequences to generate gravitational wave templates, and may improve estimates of the gravitational-wave cutoff frequency set by the last inspiral orbit.

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arXiv2006

Models of helically symmetric binary systems

Results from helically symmetric scalar field models and first results from a convergent helically symmetric binary neutron star code are reported here; these are models stationary in the rotating frame of a source with constant angular velocity omega. In the scalar field models and the neutron star code, helical symmetry leads to a system of mixed elliptic-hyperbolic character. The scalar field models involve nonlinear terms that mimic nonlinear terms of the Einstein equation. Convergence is strikingly different for different signs of each nonlinear term; it is typically insensitive to the iterative method used; and it improves with an outer boundary in the near zone. In the neutron star code, one has no control on the sign of the source, and convergence has been achieved only for an outer boundary less than approximately 1 wavelength from the source or for a code that imposes helical symmetry only inside a near zone of that size. The inaccuracy of helically symmetric solutions with appropriate boundary conditions should be comparable to the inaccuracy of a waveless formalism that neglects gravitational waves; and the (near zone) solutions we obtain for waveless and helically symmetric BNS codes with the same boundary conditions nearly coincide.

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arXiv2006

Post-Minkowski action for point particles and a helically symmetric binary solution

Two Fokker actions and corresponding equations of motion are obtained for two point particles in a post-Minkowski framework, in which the field of each particle is given by the half-retarded + half-advanced solution to the linearized Einstein equations. The first action is parametrization invariant, the second a generalization of the affinely parametrized quadratic action for a relativistic particle. Expressions for a conserved 4-momentum and angular momentum tensor are obtained in terms of the particles' trajectories in this post-Minkowski approximation. A formal solution to the equations of motion is found for a binary system with circular orbits. For a bound system of this kind, the post-Minkowski solution is a toy model that omits nonlinear terms of relevant post-Newtonian order; and we also obtain a Fokker action that is accurate to first post-Newtonian order, by adding to the post-Minkowski action a term cubic in the particle masses. Curiously, the conserved energy and angular momentum associated with the Fokker action are each finite and well-defined for this bound 2-particle system despite the fact that the total energy and angular momentum of the radiation field diverge. Corresponding solutions and conserved quantities are found for two scalar charges (for electromagnetic charges we exhibit the solution found by Schild). For a broad class of parametrization-invariant Fokker actions and for the affinely parametrized action, binary systems with circular orbits satisfy the relation $dE = ΩdL$ (a form of the first law of thermodynamics), relating the energy, angular velocity and angular momentum of nearby equilibrium configurations.

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arXiv2005

Numerical Radiation Reaction for a Scalar Charge in Kerr Circular Orbit

We numerically calculate the dissipative part of the self-force on a scalar charge moving on a circular, geodesic, equatorial orbit in Kerr spacetime. The solution to the scalar field equation is computed by separating variables and is expressed as a mode sum over radial and angular modes. The force is then computed in two ways: a direct, instantaneous force calculation which uses the half-retarded-minus-half-advanced field, and an indirect method which uses the energy and angular momentum flux at the horizon and at infinity to infer the force. We are able to show numerically and analytically that the force-per-mode is the same for both methods. To enforce the boundary conditions (ingoing radiation at the horizon and outgoing radiation at infinity for the retarded solution) numerical solutions to the radial equation are matched to asymptotic expansions for the fields at the boundaries. Recursion relations for the coefficients in the asymptotic expansions are given in an appendix.

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arXiv2004

Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits

Two relations, the virial relation $M_{\rm ADM}=M_{\rm K}$ and the first law in the form $δM_{\rm ADM}=ΩδJ$, should be satisfied by a solution and a sequence of solutions describing binary compact objects in quasiequilibrium circular orbits. Here, $M_{\rm ADM}$, $M_{\rm K}$, $J$, and $Ω$ are the ADM mass, Komar mass, angular momentum, and orbital angular velocity, respectively. $δ$ denotes an Eulerian variation. These two conditions restrict the allowed formulations that we may adopt. First, we derive relations between $M_{\rm ADM}$ and $M_{\rm K}$ and between $δM_{\rm ADM}$ and $ΩδJ$ for general asymptotically flat spacetimes. Then, to obtain solutions that satisfy the virial relation and sequences of solutions that satisfy the first law at least approximately, we propose a formulation for computation of quasiequilibrium binary neutron stars in general relativity. In contrast to previous approaches in which a part of the Einstein equation is solved, in the new formulation, the full Einstein equation is solved with maximal slicing and in a transverse gauge for the conformal three-metric. Helical symmetry is imposed in the near zone, while in the distant zone, a waveless condition is assumed. We expect the solutions obtained in this formulation to be excellent quasiequilibria as well as initial data for numerical simulations of binary neutron star mergers.

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arXiv2004

The Cauchy problem on spacetimes that are not globally hyperbolic

The initial value problem is well-defined on a class of spacetimes broader than the globally hyperbolic geometries for which existence and uniqueness theorems are traditionally proved. Simple examples are the time-nonorientable spacetimes whose orientable double cover is globally hyperbolic. These spacetimes have generalized Cauchy surfaces on which smooth initial data sets yield unique solutions. A more difficult problem is to characterize the class of spacetimes with closed timelike curves that admit a well-posed initial value problem. Examples of spacetimes with closed timelike curves are given for which smooth initial data at past null infinity has been recently shown to yield solutions. These solutions appear to be unique, and uniquesness has been proved in particular cases. Other examples, however, show that confining closed timelike curves to compact regions is not sufficient to guarantee uniqueness. An approach to the characterization problem is suggested by the behavior of congruences of null rays. Interacting fields have not yet been studied, but particle models suggest that uniqueness (and possibly existence) is likely to be lost as the strength of the interaction increases.

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arXiv2003

Nonlinear r-Modes in Neutron Stars: Instability of an unstable mode

We study the dynamical evolution of a large amplitude r-mode by numerical simulations. R-modes in neutron stars are unstable growing modes, driven by gravitational radiation reaction. In these simulations, r-modes of amplitude unity or above are destroyed by a catastrophic decay: A large amplitude r-mode gradually leaks energy into other fluid modes, which in turn act nonlinearly with the r-mode, leading to the onset of the rapid decay. As a result the r-mode suddenly breaks down into a differentially rotating configuration. The catastrophic decay does not appear to be related to shock waves at the star's surface. The limit it imposes on the r-mode amplitude is significantly smaller than that suggested by previous fully nonlinear numerical simulations.

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arXiv2001

Thermodynamics of binary black holes and neutron stars

We consider compact binary systems, modeled in general relativity as vacuum or perfect-fluid spacetimes with a helical Killing vector k^α, heuristically, the generator of time-translations in a corotating frame. Systems that are stationary in this sense are not asymptotically flat, but have asymptotic behavior corresponding to equal amounts of ingoing and outgoing radiation. For black-hole binaries, a rigidity theorem implies that the Killing vector lies along the horizon's generators, and from this one can deduce the zeroth law (constant surface gravity of the horizon). Remarkably, although the mass and angular momentum of such a system are not defined, there is an exact first law, relating the change in the asymptotic Noether charge to the changes in the vorticity, baryon mass, and entropy of the fluid, and in the area of black holes. Binary systems with MΩsmall have an approximate asymptopia in which one can write the first law in terms of the asymptotic mass and angular momentum. Asymptotic flatness is precise in two classes of solutions used to model binary systems: spacetimes satisfying the post-Newtonian equations, and solutions to a modified set of field equations that have a spatially conformally flat metric. (The spatial conformal flatness formalism with helical symmetry, however, is consistent with maximal slicing only if replaces the extrinsic curvature in the field equations by an artificially tracefree expression in terms of the shift vector.) For these spacetimes, nearby equilibria whose stars have the same vorticity obey the relation δM = ΩδJ, from which one can obtain a turning point criterion that governs the stability of orbits.

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arXiv2001

Hydrostatic Expansion and Spin Changes During Type I X-Ray Bursts

We present calculations of the spin-down of a neutron star atmosphere due to hydrostatic expansion during a Type I X-ray burst. We show that (i) Cumming and Bildsten overestimated the spin-down of rigidly-rotating atmospheres by a factor of two, and (ii) general relativity has a small (5-10%) effect on the angular momentum conservation law. We rescale our results to different neutron star masses, rotation rates and equations of state, and present some detailed rotational profiles. Comparing with recent observations of large frequency shifts in MXB 1658-298 and 4U 1916-053, we find that the spin-down expected if the atmosphere rotates rigidly is a factor of two to three less than the observed values. If differential rotation is allowed to persist, we find that the upper layers of the atmosphere spin down by an amount comparable to the observed values; however, there is no compelling reason to expect the observed spin frequency to be that of only the outermost layers. We conclude that hydrostatic expansion and angular momentum conservation alone cannot account for the largest frequency shifts observed during Type I bursts.

astro-ph↗

arXiv2001

Implications of the r-mode instability of rotating relativistic stars

Several recent surprises appear dramatically to have improved the likelihood that the spin of rapidly rotating, newly formed neutron stars (and, possibly, of old stars spun up by accretion) is limited by a nonaxisymmetric instability driven by gravitational waves. Except for the earliest part of the spin-down, the axial l=m=2 mode (an r-mode) dominates the instability, and the emitted waves may be observable by detectors with the sensitivity of LIGO II. A review of these hopeful results is followed by a discussion of constraints on the instability set by dissipative mechanisms, including viscosity, nonlinear saturation, and energy loss to a magnetic field driven by differential rotation.

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arXiv2000

The rotational modes of relativistic stars: Analytic results

We study the r-modes and rotational ``hybrid'' modes of relativistic stars. As in Newtonian gravity, the spectrum of low-frequency rotational modes is highly sensitive to the stellar equation of state. If the star and its perturbations obey the same one-parameter equation of state (as with isentropic stars), there exist {\it no pure r-modes at all} - no modes whose limit, for a star with zero angular velocity, is an axial-parity perturbation. Rotating stars of this kind similarly have no pure g-modes, no modes whose spherical limit is a perturbation with polar parity and vanishing perturbed pressure and density. We compute the post-Newtonian corrections to the $l=m$ r-modes of isentropic and non-isentropic uniform density stars.

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arXiv1999

Gravitational-wave driven instability of rotating relativistic stars

A brief review of the stability of rotating relativistic stars is followed by a more detailed discussion of recent work on an instability of r-modes, modes of rotating stars that have axial parity in the slow-rotation limit. These modes may dominate the spin-down of neutron stars that are rapidly rotating at birth, and the gravitational waves they emit may be detectable.

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arXiv1999

Where are the r-modes of isentropic stars?

Almost none of the r-modes ordinarily found in rotating stars exist, if the star and its perturbations obey the same one-parameter equation of state; and rotating relativistic stars with one-parameter equations of state have no pure r-modes at all, no modes whose limit, for a star with zero angular velocity, is a perturbation with axial parity. Similarly (as we show here) rotating stars of this kind have no pure g-modes, no modes whose spherical limit is a perturbation with polar parity and vanishing perturbed pressure and density. Where have these modes gone? In spherical stars of this kind, r-modes and g-modes form a degenerate zero-frequency subspace. We find that rotation splits the degeneracy to zeroth order in the star's angular velocity $Ω$, and the resulting modes are generically hybrids, whose limit as $Ω\to 0$ is a stationary current with axial and polar parts. Because each mode has definite parity, its axial and polar parts have alternating values of $l$. We show that each mode belongs to one of two classes, axial-led or polar-led, depending on whether the spherical harmonic with lowest value of $l$ that contributes to its velocity field is axial or polar. We numerically compute these modes for slowly rotating polytropes and for Maclaurin spheroids, using a straightforward method that appears to be novel and robust. Timescales for the gravitational-wave driven instability and for viscous damping are computed using assumptions appropriate to neutron stars.

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arXiv1998

Axial instability of rotating relativistic stars

Perturbations of rotating relativistic stars can be classified by their behavior under parity. For axial perturbations (r-modes), initial data with negative canonical energy is found with angular dependence $e^{imϕ}$ for all values of $m\geq 2$ and for arbitrarily slow rotation. This implies instability (or marginal stability) of such perturbations for rotating perfect fluids. This low $m$-instability is strikingly different from the instability to polar perturbations, which sets in first for large values of $m$. The timescale for the axial instability appears, for small angular velocity $Ω$, to be proportional to a high power of $Ω$. As in the case of polar modes, viscosity will again presumably enforce stability except for hot, rapidly rotating neutron stars. This work complements Andersson's numerical investigation of axial modes in slowly rotating stars.

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arXiv1998

Hamiltonian spacetime dynamics with a spherical null-dust shell

We consider the Hamiltonian dynamics of spherically symmetric Einstein gravity with a thin null-dust shell, under boundary conditions that fix the evolution of the spatial hypersurfaces at the two asymptotically flat infinities of a Kruskal-like manifold. The constraints are eliminated via a Kuchar-type canonical transformation and Hamiltonian reduction. The reduced phase space $\tildeΓ$ consists of two disconnected copies of $R^4$, each associated with one direction of the shell motion. The right-moving and left-moving test shell limits can be attached to the respective components of $\tildeΓ$ as smooth boundaries with topology $R^3$. Choosing the right-hand-side and left-hand-side masses as configuration variables provides a global canonical chart on each component of $\tildeΓ$, and renders the Hamiltonian simple, but encodes the shell dynamics in the momenta in a convoluted way. Choosing the shell curvature radius and the "interior" mass as configuration variables renders the shell dynamics transparent in an arbitrarily specifiable stationary gauge "exterior" to the shell, but the resulting local canonical charts do not cover the three-dimensional subset of $\tildeΓ$ that corresponds to a horizon-straddling shell. When the evolution at the infinities is freed by introducing parametrization clocks, we find on the unreduced phase space a global canonical chart that completely decouples the physical degrees of freedom from the pure gauge degrees of freedom. Replacing one infinity by a flat interior leads to analogous results, but with the reduced phase space $R^2 \cup R^2$. The utility of the results for quantization is discussed.

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