Some pairs of neutron star models can intuitively be thought of as being `closer' together than others, in the sense that more precise observations might be required to distinguish between them than would be necessary for other pairs. In this paper, borrowing ideas from the study of geometrodynamics, we introduce a mathematical formalism to define a geometric distance between stellar models, to provide a quantitative meaning to this notion of closeness. In particular, it is known that the set of all metrics on a Riemannian manifold itself admits the structure of a Riemannian manifold (`configuration manifold'), which comes equipped with a canonical metric. By thinking of a stationary star as being a particular $3+1$ metric, the structure of which is determined through the Tolman-Oppenheimer-Volkoff relations and their generalisations, points on a suitably restricted configuration manifold can be thought of as representing different stars, and distances between these points can be computed. We develop the necessary mathematical machinery to build the configuration manifold of neutron star models, and provide some worked examples to illustrate how this space might be used in future studies of stellar structure.
We review the current status of attempts to numerically model the merger of neutron star-neutron star (NSNS) and black hole-neutron star (BHNS) binary systems, and we describe the understanding of such events that is emerging from these calculations. To accurately model the physics of NSNS and BHNS mergers is a difficult task. It requires solving Einstein's equations for dynamic spacetimes containing black holes. It also requires evolving the hot, supernuclear-density neutron star matter together with the magnetic and radiation fields that can influence the post-merger dynamics. Older studies …
Recently it was shown that slowly rotating neutron stars exhibit an interesting correlation between their moment of inertia $I$, their quadrupole moment $Q$, and their tidal deformation Love number $λ$ (the I-Love-Q relations), independently of the equation of state of the compact object. In the present work a similar, more general, universality is shown to hold true for all rotating neutron stars within General Relativity; the first four multipole moments of the neutron star are related in a way independent of the nuclear matter equation of state we assume. By exploiting this relation, we can…
Neutron stars are known to host extremely powerful magnetic fields. Among other effects, one of the consequences of harbouring such fields is the deformation of the neutron star structure, leading, together with rotation, to the emission of continuous gravitational waves. On the one hand, the details of their internal magnetic fields are mostly unknown. Likewise, their internal structure, encoded by the equation of state, is highly uncertain. Here we present a study of axisymmetric models of isolated magnetised neutron stars, for various realistic equations of state considered viable by observ…
We study gravitational waves emitted in the late inspiral stage of binary neutron stars by analyzing the waveform obtained in numerical-relativity simulations. For deriving the physical gravitational waveforms from the numerical results, the resolution extrapolation plays an essential role for our simulations. The extrapolated gravitational-wave phases are compared with those calculated in the post-Newtonian (PN) and effective-one-body (EOB) formalisms including corrections of tidal effects. We show that the extrapolated gravitational-wave phases in numerical relativity agree well with those b…
We construct closed-form gravitational waveforms (GWs) with tidal effects for the coalescence and merger of binary neutron stars. The method relies on a new set of eccentricity-reduced and high-resolution numerical relativity (NR) simulations and is composed of three steps. First, tidal contributions to the GW phase are extracted from the time-domain NR data. Second, those contributions are employed to fix high-order coefficients in an effective and resummed post-Newtonian expression. Third, frequency-domain tidal approximants are built using the stationary phase approximation. Our tidal appro…
The theoretical modeling of gravitational waveforms from binary neutron star mergers requires precise numerical relativity simulations. Assessing convergence of the numerical data and building the error budget is currently challenging due to the low accuracy of general-relativistic hydrodynamics schemes and to the grid resolutions that can be employed in $(3+1)$-dimensional simulations. In this work, we explore the use of high-order weighted-essentially-nonoscillatory (WENO) schemes in neutron star merger simulations and investigate the accuracy of the waveforms obtained with such methods. We …
Creating a modified Belinfante/Rosenfeld procedure, Mathisson-Papapetrou-like equations are derived by which a comparison of General-Covariant Continuum Physics with General Relativity Theory becomes possible.
Mergers of binary neutron stars and black hole-neutron star binaries are one of the most promising sources for the ground-based gravitational-wave (GW) detectors and also a high-energy astrophysical phenomenon as illustrated by the observations of gravitational waves and electromagnetic (EM) waves in the event of GW170817. Mergers of these neutron-star binaries are also the most promising site for r-process nucleosynthesis. Numerical simulation in full general relativity (numerical relativity) is a unique approach to the theoretical prediction of the merger process, GWs emitted, mass ejection …
Targets for ground-based gravitational wave interferometers include continuous, quasiperiodic sources of gravitational radiation, such as isolated, spinning neutron stars. In this work we perform evolution simulations of uniformly rotating, triaxially deformed stars, the compressible analogues in general relativity of incompressible, Newtonian Jacobi ellipsoids. We investigate their stability and gravitational wave emission. We employ five models, both normal and supramassive, and track their evolution with different grid setups and resolutions, as well as with two different evolution codes. W…
I present two results that show that, despite its unusual non-linear form, the phenomenology of entangled relativity remains close to the one of general relativity -- without having any free parameter that can be fine tuned in order to facilitate this. In particular, I present the analytical solutions for spherically charged black-holes, and both the analytical and numerical solutions for neutron stars.
We report simulations of the inspiral and merger of binary neutron stars performed with \texttt{WhiskyTHC}, the first of a new generation of numerical relativity codes employing higher than second-order methods for both the spacetime and the hydrodynamic evolution. We find that the use of higher-order schemes improves substantially the quality of the gravitational waveforms extracted from the simulations when compared to those computed using traditional second-order schemes. The reduced de-phasing and the faster convergence rate allow us to estimate the phase evolution of the gravitational wav…
We implement advanced Riemann solvers HLLC and HLLD \cite{Mignone:2005ft,MUB:2009} together with an advanced constrained transport scheme \cite{Gardiner:2007nc} in a numerical-relativity neutrino-radiation magnetohydrodynamics code. We validate our implementation by performing a series of one- and multi-dimensional test problems for relativistic hydrodynamics and magnetohydrodynamics in both Minkowski spacetime and a static black hole spacetime. We find that the numerical solutions with the advanced Riemann solvers are more accurate than those with the HLLE solver \cite{DelZanna:2002rv}, which…
We present the first set of numerical relativity simulations of binary neutron mergers that include spin precession effects and are evolved with multiple resolutions. Our simulations employ consistent initial data in general relativity with different spin configurations and dimensionless spin magnitudes $\sim 0.1$. They start at a gravitational-wave frequency of $\sim392$~Hz and cover more than $1$ precession period and about 15 orbits up to merger. We discuss the spin precession dynamics by analyzing coordinate trajectories, quasi-local spin measurements, and energetics, by comparing spin ali…
We present ${\tt NRPMw}$, an analytical model of gravitational-waves from neutron star merger remnants informed using 618 numerical relativity (NR) simulations. ${\tt NRPMw}$ is designed in the frequency domain using a combination of complex Gaussian wavelets. The wavelet's parameters are calibrated to equations of state (EOS) insensitive relations from NR data. The NR simulations are computed with 21 EOS (7 of which are finite-temperature microphysical models, and 3 of which contain quark phase transitions or hyperonic degrees of freedom) and span total binary masses $M\in[2.4,3.4]~{\rm M}_\o…
We present the first stationary, axisymmetric neutron star models with meridional circulation in general relativity. For that purpose, we developed GRNS, a new code based on a fixed point iteration. We find a two-dimensional set of meridional circulation modes, which differ by the number of vortices in the stream lines of the neutron star fluid. For expected maximal meridional circulation velocities of about 1000 km/s, the vortices cause surface deformations of about a percent. The deformations depend on the shape of the vortices close to the surface and increase with the meridional circulatio…
We perform new longterm (15-16 orbits) simulations of coalescing binary neutron stars in numerical relativity using an updated Einstein's equation solver, employing low-eccentricity initial data, and modeling the neutron stars by a piecewise polytropic equation of state. A convergence study shows that our new results converge more rapidly than the third order and using the determined convergence order, we construct an extrapolated waveform for which the estimated total phase error should be less than 1 radian. We then compare the extrapolated waveforms with those calculated by the latest effec…
We present results about the effect of the use of a stiffer equation of state, namely the ideal-fluid $Γ=2.75$ ones, on the dynamical bar-mode instability in rapidly rotating polytropic models of neutron stars in full General Relativity. We determine the change on the critical value of the instability parameter $β$ for the emergence of the instability when the adiabatic index $Γ$ is changed from 2 to 2.75 in order to mimic the behavior of a realistic equation of state. In particular, we show that the threshold for the onset of the bar-mode instability is reduced by this change in the stiffness…
The masses and radii of neutron stars are discussed in general relativity and scalar-tensor theory of gravity and the differences are compared with the current uncertainties stemming from the nuclear equation of state in the relativistic mean-field framework. It is shown that astrophysical and gravitational waves observations of radii of neutron stars with masses $M \lesssim 1.4 M_{\odot}$ constrain only the nuclear equation of state, and in particular the density dependence of the nuclear symmetry energy. Future observations of massive neutron stars may constrain the coupling parameters of th…
Neutron stars harbour extremely powerful magnetic fields, leading to their shape being deformed. Their magnetic deformation depends both on the geometry - and strength - of their internal magnetic field and on their composition, encoded by the equation of state. However, both the details of the internal magnetic structure and the equation of state of the innermost part of neutron stars are mostly unkown. We performed a study of numerical models of magnetised, static, axisymmetric neutron stars in general relativity and in one of its most promising extensions, scalar-tensor theories. We did so …
We study the black hole thermodynamics and obtain the correction terms for temperature, entropy, and heat capacity of the Schwarzschild black hole, resulting from the commutation relations in the framework of {\it Modified Generalized Uncertainty Principle} suggested by {\it Doubly Special Relativity}.
The recent detection of gravitational waves and electromagnetic counterparts emitted during and after the collision of two neutron stars marks a breakthrough in the field of multi-messenger astronomy. Numerical relativity simulations are the only tool to describe the binary's merger dynamics in the regime when speeds are largest and gravity is strongest. In this work we report state-of-the-art binary neutron star simulations for irrotational (non-spinning) and spinning configurations. The main use of these simulations is to model the gravitational-wave signal. Key numerical requirements are th…
The maximum mass limits of neutron stars in scalar-tensor gravity is discussed and compared with the limits set by general relativity. The limit is parametrized with respect to the combination of the nuclear saturation parameters and the maximum sound velocity in the core. It is shown that, for smaller values of the sound velocity in the core, the maximum mass limit of the scalarized neutron stars is larger than that of in general relativity. However, for stiff equations of state with sound velocity higher than $79\%$ of the velocity of light, the maximum mass limit in general relativity is la…
We present a detailed comparison between tidal effective-one-body (EOB) models and new state-of-the-art numerical relativity simulations for non-spinning binary neutron star systems. This comparison is the most extensive one to date, covering a wide range in the parameter space and encompassing the energetics of the binary, the periastron advance, the time and frequency evolution of the gravitational wave phase for the dominant mode, and several subdominant modes. We consider different EOB models with tidal effects that have been proposed, including the model with dynamical tides of [Phys.Rev.…
We present a Bayesian data analysis pipeline for testing GR using gravitational wave signals from coalescing compact binaries, and in particular binary neutron stars. In this study, we investigate its performance when sources with spins are taken into account.
We present fitting formulae for the dynamical ejecta properties and remnant disk masses from the largest to date sample of numerical relativity simulations. The considered data include some of the latest simulations with microphysical nuclear equations of state (EOS) and neutrino transport as well as other results with polytropic EOS available in the literature. Our analysis indicates that the broad features of the dynamical ejecta and disk properties can be captured by fitting expressions that depend on mass ratio and reduced tidal parameter. The comparative analysis of literature data shows …
To study binary neutron star systems and to interpret observational data such as gravitational-wave and kilonova signals, one needs an accurate description of the processes that take place during the final stages of the coalescence, e.g., through numerical-relativity simulations. In this work, we present an updated version of the numerical-relativity code BAM in order to incorporate nuclear-theory based Equations of State and a simple description of neutrino interactions through a Neutrino Leakage Scheme. Different test simulations, for stars undergoing a neutrino-induced gravitational collaps…
We continue our investigation of massive gravity in the massless limit of vanishing graviton mass. From gauge invariance we derive the most general coupling between scalar matter and gravity. We get further couplings beside the standard coupling to the energy-momentum tensor. On the classical level this leads to a further modification of general relativity.
Tidal effects have an important impact on the late inspiral of compact binary systems containing neutron stars. Most current models of tidal deformations of neutron stars assume that the tidal bulge is directly related to the tidal field generated by the companion, with a constant response coefficient. However, if the orbital motion approaches a resonance with one of the internal modes of the neutron star, this adiabatic description of tidal effects starts to break down, and the tides become dynamical. In this paper, we consider dynamical tides in general relativity due to the quadrupolar fund…
The third observing run of the LIGO-Virgo collaboration has resulted in about hundred gravitational-wave triggers including the binary neutron star merger GW190425. However, none of these events have been accompanied with an electromagnetic transient found during extensive follow-up searches. In this article, we perform new numerical-relativity simulations of binary neutron star and black hole - neutron star systems that have a chirp mass consistent with GW190425. Assuming that the GW190425's sky location was covered with sufficient accuracy during the electromagnetic follow-up searches, we in…
General relativity probably is not the definitive theory of gravity, due a number or issues, both from the theoretical and from the observational point of view. Alternative theories of gravity were conceived to extend general relativity and account for such issues. Among the most promising ones are scalar-tensor theories, which predict an enrichment of the phenomenology of compact objects, like neutron stars. We updated the well-tested XNS code to numerically solve the Einstein-Maxwell equations for a stationary, magnetised neutron star in a class of scalar-tensor theories containing the spont…
Characteristic classes in space-time manifolds are discussed for both even- and odd-dimensional spacetimes. In particular, it is shown that the Einstein--Hilbert action is equivalent to a second Chern-class on a modified Poincare bundle in four dimensions. Consequently, the cosmological constant and the trace of an energy-momentum tensor become divisible modulo R/Z.
We present results on the effect of the stiffness of the equation of state on the dynamical bar-mode instability in rapidly rotating polytropic models of neutron stars in full General Relativity. We determine the change in the threshold for the emergence of the instability for a range of the adiabatic $Γ$ index from 2.0 to 3.0, including two values chosen to mimic more realistic equations of state at high densities.
We study the solution space of general relativistic, axisymmetric, equilibria of differentially rotating neutron stars with realistic, nuclear equations of state. We find that different types of stars, which were identified by earlier works for polytropic equations of state, arise for realistic equations of state, too. Scanning the solution space for the sample of realistic equations of state we treat, we find lower limits on the maximum rest masses supported by cold, differentially rotating stars for each type of stars. We often discover equilibrium configurations that can support more than 2…
Extending our previous studies, we perform high-resolution simulations of inspiraling binary neutron stars in numerical relativity. We thoroughly carry through a convergence study in our currently available computational resources with the smallest grid spacing of $\approx 63$--86~meter for the neutron-star radius 10.9--13.7\,km. The estimated total error in the gravitational-wave phase is of order 0.1~rad for the total phase of $\gtrsim 210$\,rad in the last $\sim 15$--16 inspiral orbits. We then compare the waveforms (without resolution extrapolation) with those calculated by the latest effe…
Gravitational waves have been detected from the inspiral of a binary neutron-star, GW170817, which allowed constraints to be placed on the neutron star equation of state. The equation of state can be further constrained if gravitational waves from a post-merger remnant are detected. Post-merger waveforms are currently generated by numerical-relativity simulations, which are computationally expensive. Here we introduce a hierarchical model trained on numerical-relativity simulations, which can generate reliable post-merger spectra in a fraction of a second. Our spectra have mean fitting factors…
We reanalyze gravitational waves from binary-neutron-star mergers GW170817 and GW190425 using a numerical-relativity (NR) calibrated waveform model, the TF2+_Kyoto model, which includes nonlinear tidal terms. For GW170817, by imposing a uniform prior on the binary tidal deformability $\tildeΛ$, the symmetric $90\%$ credible interval of $\tildeΛ$ is estimated to be $481^{+436}_{-359}$ and $402^{+465}_{-279}$ for the case of $f_\mathrm{max}=1000$ and $2048~\mathrm{Hz}$, respectively, where $f_\mathrm{max}$ is the maximum frequency in the analysis. We also reanalyze the event with other waveform …
We construct the conserved charges (mass and angular momentum) of the Chern-Simons modified General Relativity in asymptotically flat and Anti-de Sitter (AdS) spacetimes. Our definition is based on background Killing symmetries and reduces to the known expressions in the proper limits.
Various formalisms proposed recently for irrotational binary systems in general relativity are compared and explicit relations between them are exhibited. It is notably shown that the formalisms of (i) Teukolsky, (ii) Shibata and (iii) Bonazzola et al. (as corrected by Asada) are equivalent, i.e. yield exactly the same solution, although the former two are simpler than the latter one.
A new class of solutions describing analytical solutions for compact stellar structures has been developed within the tenets of General Relativity. Considering the inherent anisotropy in compact stars, a stable and causal model for realistic anisotropic neutron stars was obtained using the general theory of relativity. Assuming a physically acceptable non-singular form of one metric potential and radial pressure containing the curvature parameter $R$, the constant $k$, and the radius $r$, analytical solutions to Einstein's field equations for anisotropic matter distribution were obtained. Taki…
We perform high-resolution magnetohydrodynamics simulations of binary neutron star mergers in numerical relativity on the Japanese supercomputer K. The neutron stars and merger remnants are covered by a grid spacing of 70\,m, which yields the highest-resolution results among those derived so far. By an in-depth resolution study, we clarify several amplification mechanisms of magnetic fields during the binary neutron star merger for the first time. First, the Kelvin-Helmholtz instability developed in the shear layer at the onset of the merger significantly amplifies the magnetic fields. A hyper…
Some models (such as the Skyrme model, a low-energy effective field theory for QCD) suggest that the high-density matter prevailing in neutron star interiors may be significantly anisotropic. Anisotropy is known to affect the bulk properties of nonrotating neutron stars in General Relativity. In this paper we study the effects of anisotropy on slowly rotating stars in General Relativity. We also consider one of the most popular extensions of Einstein's theory, namely scalar-tensor theories allowing for spontaneous scalarization (a phase transition similar to spontaneous magnetization in ferrom…
Adopting our new method for matching general relativistic, ideal magnetohydrodynamics to its force-free limit, we perform the first systematic simulations of force-free pulsar magnetospheres in general relativity. We endow the neutron star with a general relativistic dipole magnetic field, model the interior with ideal magnetohydrodynamics, and adopt force-free electrodynamics in the exterior. Comparing the spin-down luminosity to its corresponding Minkowski value, we find that general relativistic effects give rise to a modest enhancement: the maximum enhancement for $n=1$ polytropes is $\sim…
The Neutron Star Interior Composition Explorer (NICER) recently measured the mass and equatorial radius of the isolated neutron star PSR J0030+0451. We use these measurements to infer the moment of inertia, the quadrupole moment, and the surface eccentricity of an isolated neutron star for the first time, using relations between these quantities that are insensitive to the unknown equation of state of supranuclear matter. We also use these results to forecast the moment of inertia of neutron star A in the double pulsar binary J0737-3039, a quantity anticipated to be directly measured in the co…
Chern-Simons modified gravity is an effective extension of general relativity that captures leading-order, gravitational parity violation. Such an effective theory is motivated by anomaly cancelation in particle physics and string theory. In this review, we begin by providing a pedagogical derivation of the three distinct ways such an extension arises: (1) in particle physics, (2) from string theory and (3) geometrically. We then review many exact and approximate, vacuum solutions of the modified theory, and discuss possible matter couplings. Following this, we review the myriad astrophysical,…
We present a code to construct initial data for binary neutron star systems in which the stars are rotating. Our code, based on a formalism developed by Tichy, allows for arbitrary rotation axes of the neutron stars and is able to achieve rotation rates near rotational breakup. We compute the neutron star angular momentum through quasi-local angular momentum integrals. When constructing irrotational binary neutron stars, we find a very small residual dimensionless spin of $\sim 2\times 10^{-4}$. Evolutions of rotating neutron star binaries show that the magnitude of the stars' angular momentum…
We consider spatially covariant modified gravity in which the would-be scalar degree of freedom is made non-dynamical and hence there are just two tensorial degrees of freedom, i.e., the same number of dynamical degrees of freedom as in general relativity. Focusing on a class of such modified gravity theories characterized by three functions of time, we discuss how modified gravity with two tensorial degrees of freedom can be distinguished observationally or phenomenologically from general relativity. It is checked that the theory gives the same predictions as general relativity for weak gravi…
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.
