The merger of two neutron stars leaves behind a rapidly spinning hypermassive object whose survival is believed to depend on the maximum mass supported by the nuclear equation of state (EOS), angular momentum redistribution by (magneto-)rotational instabilities, and spindown by gravitational waves. The high temperatures (∼5-40 MeV) prevailing in the merger remnant may provide thermal pressure support that could increase its maximum mass and, thus, its life on a neutrino-cooling timescale. We investigate the role of thermal pressure support in hypermassive merger remnants by computing sequences of spherically symmetric and axisymmetric uniformly and differentially rotating equilibrium solutions to the general-relativistic stellar structure equations. Using a set of finite-temperature nuclear EOS, we find that hot maximum-mass critically spinning configurations generally do not support larger baryonic masses than their cold counterparts. However, subcritically spinning configurations with mean density of less than a few times nuclear saturation density yield a significantly thermally enhanced mass. Even without decreasing the maximum mass, cooling and other forms of energy loss can drive the remnant to an unstable state. We infer secular instability by identifying approximate energy turning points in equilibrium sequences of constant baryonic mass parameterized by maximum density. Energy loss carries the remnant along the direction of decreasing gravitational mass and higher density until instability triggers collapse. Since configurations with more thermal pressure support are less compact and thus begin their evolution at a lower maximum density, they remain stable for longer periods after merger.

When one splits spacetime into space plus time, the Weyl curvature tensor (vacuum Riemann tensor) gets split into two spatial, symmetric, and trace-free (STF) tensors: (i) the Weyl tensor's so-called "electric" part or tidal field E jk , which raises tides on the Earth's oceans and drives geodesic deviation (the relative acceleration of two freely falling test particles separated by a spatial vector ξ k is ∆aj = −E jk ξ k ); and (ii) the Weyl tensor's so-called "magnetic" part or (as we call it) frame-drag field B jk , which drives differential frame dragging (the precessional angular velocity of a gyroscope at the tip of ξ k , as measured using a local inertial frame at the tail of ξ k , is ∆Ωj = B jk ξ k ). Being STF, E jk and B jk each have three orthogonal eigenvector fields which can be depicted by their integral curves. We call the integral curves of E jk 's eigenvectors tidal tendex lines or simply tendex lines, we call each tendex line's eigenvalue its tendicity, and we give the name tendex to a collection of tendex lines with large tendicity. The analogous quantities for B jk are frame-drag vortex lines or simply vortex lines, their vorticities, and vortexes.These concepts are powerful tools for visualizing spacetime curvature. We build up physical intuition into them by applying them to a variety of weak-gravity phenomena: a spinning, gravitating point particle, two such particles side-by-side, a plane gravitational wave, a point particle with a dynamical current-quadrupole moment or dynamical mass-quadrupole moment, and a slow-motion binary system made of nonspinning point particles. We show that a rotating current quadrupole has four rotating vortexes that sweep outward and backward like water streams from a rotating sprinkler. As they sweep, the vortexes acquire accompanying tendexes and thereby become outgoing current-quadrupole gravitational waves. We show similarly that a rotating mass quadrupole has four rotating, outward-and-backward sweeping tendexes that acquire accompanying vortexes as they sweep, and become outgoing mass-quadrupole gravitational waves. We show, further, that an oscillating current quadrupole ejects sequences of vortex loops that acquire accompanying tendex loops as they travel, and become current-quadrupole gravitational waves; and similarly for an oscillating mass quadrupole. And we show how a binary's tendex lines transition, as one moves radially, from those of two static point particles in the deep near zone, to those of a single spherical body in the outer part of the near zone and inner part of the wave zone (where the binary's mass monopole moment dominates), to those of a rotating quadrupole in the far wave zone (where the quadrupolar gravitational waves dominate).In paper II we will use these vortex and tendex concepts to gain insight into the quasinormal modes of black holes, and in subsequent papers, by combining these concepts with numerical simulations, we will explore the nonlinear dynamics of curved spacetime around colliding black holes. We have published a ...

These findings suggest that velocity-encoded NMR imaging can be used to estimate regurgitant volume and regurgitant fraction in patients with mitral regurgitation and can discriminate patients with moderate or severe mitral regurgitation from normal subjects and patients with mild regurgitation. It may be useful for monitoring the effect of therapy intended to reduce the severity of mitral regurgitation.

We investigate the formation of the double pulsar PSR J0737-3039 and examine its most likely progenitors, taking into account the most recent and all currently available observational constraints. We show that the most likely kick velocity and progenitor parameters depend strongly on the consideration of the full five-dimensional probability distribution function for the magnitude and direction of the kick velocity imparted to pulsar B at birth, the mass of pulsar B's presupernova helium star progenitor, and the presupernova orbital separation rather than marginalized one-or two-dimensional distributions for the kick velocity and progenitor mass. The priors that enter the analysis are the age of the system, the minimum helium star mass required to form a neutron star, the transverse systemic velocity, and the treatment of the unknown radial velocity. Since the latter cannot be measured observationally, we adopt a statistical approach and use theoretical radial-velocity distributions obtained from population synthesis calculations for coalescing double neutron stars. We find that when the minimum presupernova helium star mass required for neutron star formation is assumed to be 2:1 M , the most likely kick velocity ranges from 70 km s ÿ1 to 180 km s ÿ1 . When, on the other hand, masses lower than 2:1 M are allowed as neutron star progenitors, the most likely kick velocity can reach very low values (as low as a few km s ÿ1 ), although the majority of the models still yield most likely kick velocities of 50 km s ÿ1 to 170 km s ÿ1 . Hence, we agree with Piran and Shaviv [T. Piran and N. J. Shaviv, Phys. Rev. Lett. 94, 051102 (2005).] that the observed system properties, including the low transverse systemic velocity, can indeed be compatible with low progenitor masses and low kick velocities. Equally important though, we show that this is not the only likely formation path of pulsar B, due to the role of different prior assumptions that are necessary in the analysis. Moreover, in contrast to earlier claims in the literature, we show that the proximity of the double pulsar to the Galactic plane and the small proper motion do not pose stringent constraints on the kick velocity and progenitor mass of pulsar B at all. Instead, the constraints imposed by the current orbital semimajor axis and eccentricity and the orbital dynamics of asymmetric supernova explosions turn out to be much more restrictive. We conclude that without further knowledge of the priors, the currently available observational constraints cannot be used to unambiguously favor a specific corecollapse and neutron star-formation mechanism. Both electron capture and neutrino-driven supernovae therefore remain viable formation mechanisms for pulsar B.

We present results on the inspiral, merger, and post-merger evolution of a neutron star -neutron star (NSNS) system. Our results are obtained using the hybrid pseudospectral-finite volume Spectral Einstein Code (SpEC). To test our numerical methods, we evolve an equal-mass system for ≈ 22 orbits before merger. This waveform is the longest waveform obtained from fully general-relativistic simulations for NSNSs to date. Such long (and accurate) numerical waveforms are required to further improve semi-analytical models used in gravitational wave data analysis, for example the effective one body models. We discuss in detail the improvements to SpEC's ability to simulate NSNS mergers, in particular mesh refined grids to better resolve the merger and post-merger phases. We provide a set of consistency checks and compare our results to NSNS merger simulations with the independent BAM code. We find agreement between them, which increases confidence in results obtained with either code. This work paves the way for future studies using long waveforms and more complex microphysical descriptions of neutron star matter in SpEC.