One century after its formulation, Einstein's general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

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Testing general relativity with present and future astrophysical observations

Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.

https://link.springer.com/content/pdf/10.12942%2Flrr-2009-2.pdf

Physics, Astrophysics and Cosmology with Gravitational Waves

We explore in a parameterized manner a very large range of physically plausible equations of state (EOSs) for compact stars for matter that is either purely hadronic or that exhibits a phase transition. In particular, we produce two classes of EOSs with and without phase transitions, each containing one million EOSs. We then impose constraints on the maximum mass ($Ml2.16\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$) and on the dimensionless tidal deformability ($\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}l800$) deduced from GW170817, together with recent suggestions of lower limits on $\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}$. Exploiting more than $1{0}^{9}$ equilibrium models for each class of EOSs, we produce distribution functions of all the stellar properties and determine, among other quantities, the radius that is statistically most probable for any value of the stellar mass. In this way, we deduce that the radius of a purely hadronic neutron star with a representative mass of $1.4\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ is constrained to be $12.00l{R}_{1.4}/\mathrm{km}l13.45$ at a $2\ensuremath{\sigma}$ confidence level, with a most likely value of ${\overline{R}}_{1.4}=12.39\text{ }\text{ }\mathrm{km}$; similarly, the smallest dimensionless tidal deformability is ${\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}}_{1.4}g375$, again at a $2\ensuremath{\sigma}$ level. On the other hand, because EOSs with a phase transition allow for very compact stars on the so-called ``twin-star'' branch, small radii are possible with such EOSs although not probable, i.e., $8.53l{R}_{1.4}/\mathrm{km}l13.74$ and ${\overline{R}}_{1.4}=13.06\text{ }\text{ }\mathrm{km}$ at a $2\ensuremath{\sigma}$ level, with ${\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}}_{1.4}g35.5$ at a $3\ensuremath{\sigma}$ level. Finally, since these EOSs exhibit upper limits on $\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}$, the detection of a binary with a total mass of $3.4\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and ${\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}}_{1.7}g461$ can rule out twin-star solutions.

New Constraints on Radii and Tidal Deformabilities of Neutron Stars from GW170817.

The final inspiral of double neutron star and neutron-star-black-hole binaries are likely to be detected by advanced networks of ground-based gravitational wave (GW) interferometers. Maximizing the science returns from such a discovery will require the identification of an electromagnetic counterpart. Here we critically evaluate and compare several possible counterparts, including short-duration gamma-ray bursts (SGRBs), "orphan" optical and radio afterglows, and day-long optical transients powered by the radioactive decay of heavy nuclei synthesized in the merger ejecta ("kilonovae"). We assess the promise of each counterpart in terms of four "Cardinal Virtues": detectability, high fraction, identifiability, and positional accuracy. Taking into account the search strategy for typical error regions of tens of square degrees, we conclude that SGRBs are the most useful to confirm the cosmic origin of a few GW events, and to test the association with neutron star mergers. However, for the more ambitious goal of localizing and obtaining redshifts for a large sample of GW events, kilonovae are instead preferred. Off-axis optical afterglows are detectable for at most tens of percent of events, while radio afterglows are promising only for energetic relativistic ejecta in a high-density medium. Our main recommendations are: (1) an all-sky gamma-ray satellite is essential for temporal coincidence detections, and for GW searches of gamma-ray-triggered events; (2) the Large Synoptic Survey Telescope should adopt a one-day cadence follow-up strategy, ideally with 0.5 hr per pointing to cover GW error regions; and (3) radio searches should focus on the relativistic case, which requires observations for a few months.

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What is the most promising electromagnetic counterpart of a neutron star binary merger

We investigate systematically the dynamical mass ejection, r-process nucleosynthesis, and properties of electromagnetic counterparts of neutron-star (NS) mergers in dependence on the uncertain properties of the nuclear equation of state (EOS) by employing 40 representative, microphysical high-density EOSs in relativistic, hydrodynamical simulations. The crucial parameter determining the ejecta mass is the radius R{sub 1.35} of a 1.35 M{sub Sun} NS. NSs with smaller R{sub 1.35} (''soft'' EOS) eject systematically higher masses. These range from {approx}10{sup -3} M{sub Sun} to {approx}10{sup -2} M{sub Sun} for 1.35-1.35 M{sub Sun} binaries and from {approx}5 Multiplication-Sign 10{sup -3} M{sub Sun} to {approx}2 Multiplication-Sign 10{sup -2} M{sub Sun} for 1.2-1.5 M{sub Sun} systems (with kinetic energies between {approx}5 Multiplication-Sign 10{sup 49} erg and 10{sup 51} erg). Correspondingly, the bolometric peak luminosities of the optical transients of symmetric (asymmetric) mergers vary between 3 Multiplication-Sign 10{sup 41} erg s{sup -1} and 14 Multiplication-Sign 10{sup 41} erg s{sup -1} (9 Multiplication-Sign 10{sup 41} erg s{sup -1} and 14.5 Multiplication-Sign 10{sup 41} erg s{sup -1}) on timescales between {approx}2 hr and {approx}12 hr. If these signals with absolute bolometric magnitudes from -15.0 to -16.7 are measured, the tight correlation of their properties with those of the merging NSs mightmore » provide valuable constraints on the high-density EOS. The r-process nucleosynthesis exhibits a remarkable robustness independent of the EOS, producing a nearly solar abundance pattern above mass number 130. By the r-process content of the Galaxy and the average production per event the Galactic merger rate is limited to 4 Multiplication-Sign 10{sup -5} yr{sup -1} (4 Multiplication-Sign 10{sup -4} yr{sup -1}) for a soft (stiff) NS EOS, if NS mergers are the main source of heavy r-nuclei. The production ratio of radioactive {sup 232}Th to {sup 238}U attains a stable value of 1.64-1.67, which does not exclude NS mergers as potential sources of heavy r-material in the most metal-poor stars.« less

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Systematics of dynamical mass ejection, nucleosynthesis, and radioactively powered electromagnetic signals from neutron-star mergers

A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates are treated as independent functions, and encode the coordinate freedom of solutions. Techniques are discussed to impose particular gauge conditions through a specification of the source functions. A 3D, free evolution, finite difference code implementing this system of equations with a scalar field matter source is described. The second-order-in-space-and-time partial differential equations are discretized directly without the use of first-order auxiliary terms, limiting the number of independent functions to 15—ten metric quantities, four source functions and the scalar field. This also limits the number of constraint equations, which can only be enforced to within truncation error in a numerical free evolution, to four. The coordinate system is compactified to spatial infinity in order to impose physically motivated, constraint-preserving outer boundary conditions. A variant of the cartoon method for efficiently simulating axisymmetric spacetimes with a Cartesian code is described that does not use interpolation, and is easier to incorporate into existing adaptive mesh refinement packages. Preliminary test simulations of vacuum black-hole evolution and black-hole formation via scalar field collapse are described, suggesting that this method may be useful for studying many spacetimes of interest.

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Numerical relativity using a generalized harmonic decomposition

Throughout the Universe many powerful events are driven by strong gravitational effects that require general relativity to fully describe them. These include compact binary mergers, black hole accretion, and stellar collapse, where velocities can approach the speed of light and extreme gravitational fields (ΦNewt/c2≃1) mediate the interactions. Many of these processes trigger emission across a broad range of the electromagnetic spectrum. Compact binaries further source strong gravitational wave emission that could directly be detected in the near future. This feat will open up a gravitational wave window into our Universe and revolutionize our understanding of it. Describing these phenomena requires general relativity, and—where dynamical effects strongly modify gravitational fields—the full Einstein equations coupled to matter sources. Numerical relativity is a field within general relativity concerned with studying such scenarios that cannot be accurately modeled via perturbative or analytical calculati...

Numerical Relativity and Astrophysics

The two-body problem in general relativity is reviewed, focusing on the final stages of the coalescence of the black holes as uncovered by recent successes in numerical solution of the field equations.

Binary Black Hole Coalescence

Using general-relativistic hydrodynamical simulations, we show that merging binary neutron stars can form hypermassive neutrons stars that undergo the one-arm spiral instability. We study the particular case of a dynamical capture merger where the stars have a small spin, as may arise in globular clusters, and focus on an equal-mass scenario where the spins are aligned with the orbital angular momentum. We find that this instability develops when postmerger fluid vortices lead to the generation of a toroidal remnant---a configuration whose maximum density occurs in a ring around the center-of-mass---with high vorticity along its rotation axis. The instability quickly saturates on a time scale of $\ensuremath{\sim}10\text{ }\text{ }\mathrm{ms}$, with the $m=1$ azimuthal density multipole mode dominating over higher modes. The instability also leaves a characteristic imprint on the postmerger gravitational wave signal that could be detectable if the instability persists in long-lived remnants.

One-arm spiral instability in hypermassive neutron stars formed by dynamical-capture binary neutron star mergers

NSF [PHY-1607449]; Simons Foundation; NASA [NNX16AR67G]; JSPS; NSF CAREER Grant [PHY-1250636]; NASA Grant [NNX16AB98G]; NSERC; CIFAR; Perimeter Institute through Industry Canada; Province of Ontario through the Ministry of Research Innovation

Frans Pretorius

Papers

Numerical relativity using a generalized harmonic decomposition

Numerical Relativity and Astrophysics

Binary Black Hole Coalescence

One-arm spiral instability in hypermassive neutron stars formed by dynamical-capture binary neutron star mergers

Gravitational wave spectroscopy of binary neutron star merger remnants with mode stacking