There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

On 17 August 2017, the LIGO and Virgo observatories made the first direct detection of gravitational waves from the coalescence of a neutron star binary system. The detection of this gravitational-wave signal, GW170817, offers a novel opportunity to directly probe the properties of matter at the extreme conditions found in the interior of these stars. The initial, minimal-assumption analysis of the LIGO and Virgo data placed constraints on the tidal effects of the coalescing bodies, which were then translated to constraints on neutron star radii. Here, we expand upon previous analyses by working under the hypothesis that both bodies were neutron stars that are described by the same equation of state and have spins within the range observed in Galactic binary neutron stars. Our analysis employs two methods: the use of equation-of-state-insensitive relations between various macroscopic properties of the neutron stars and the use of an efficient parametrization of the defining function pðρÞ of the equation of state itself. From the LIGO and Virgo data alone and the first method, we measure the two neutron star radii as R1 ¼ 10.8 þ2.0 −1.7 km for the heavier star and R2 ¼ 10.7 þ2.1 −1.5 km for the lighter star at the 90% credible level. If we additionally require that the equation of state supports neutron stars with masses larger than 1.97 M⊙ as required from electromagnetic observations and employ the equation-of-state parametrization, we further constrain R1 ¼ 11.9 þ1.4 −1.4 km and R2 ¼ 11.9 þ1.4 −1.4 km at the 90% credible level. Finally, we obtain constraints on pðρÞ at supranuclear densities, with pressure at twice nuclear saturation density measured at 3.5 þ2.7 −1.7 × 1034 dyn cm−2 at the 90% level.

GW170817: Measurements of Neutron Star Radii and Equation of State.

The field of laser-matter interaction traditionally deals with the response of atoms, molecules, and plasmas to an external light wave. However, the recent sustained technological progress is opening up the possibility of employing intense laser radiation to trigger or substantially influence physical processes beyond atomic-physics energy scales. Available optical laser intensities exceeding ${10}^{22}\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$ can push the fundamental light-electron interaction to the extreme limit where radiation-reaction effects dominate the electron dynamics, can shed light on the structure of the quantum vacuum, and can trigger the creation of particles such as electrons, muons, and pions and their corresponding antiparticles. Also, novel sources of intense coherent high-energy photons and laser-based particle colliders can pave the way to nuclear quantum optics and may even allow for the potential discovery of new particles beyond the standard model. These are the main topics of this article, which is devoted to a review of recent investigations on high-energy processes within the realm of relativistic quantum dynamics, quantum electrodynamics, and nuclear and particle physics, occurring in extremely intense laser fields.

Extremely high-intensity laser interactions with fundamental quantum systems

University of Wisconsin–Milwaukee(Dated: February 28, 2005)We numerically calculate the dissipative part of the self-force on a scalar charge moving on acircular, geodesic, equatorial orbit in Kerr spacetime. The solution to the scalar ﬁeld equation iscomputed 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 thehalf-retarded-minus-half-advanced ﬁeld, and an indirect method which uses the energy and angularmomentum ﬂux at the horizon and at inﬁnity to infer the force. We are able to show numericallyand analytically that the force-per-mode is the same for both methods. To enforce the boundaryconditions (ingoing radiation at the horizon and outgoing radiation at inﬁnity for the retardedsolution) numerical solutions to the radial equation are matched to asymptotic expansions for theﬁelds at the boundaries. Recursion relations for the coeﬃcients in the asymptotic expansions aregiven in an appendix.I. INTRODUCTION: MOTIVATION AND SUMMARY

Numerical radiation reaction for a scalar charge in Kerr circular orbit

Magnetars are surrounded by diffuse plasma in magnetic field strengths well above the quantum electrodynamic critical value. We derive equations of "quantum force-free electrodynamics" for this plasma using effective field theory arguments. We argue that quantum effects do not modify the large scale structure of the magnetosphere, and in particular that the spin-down rate does not deviate significantly from the classical result. We provide definite evolution equations that can be used to explore potentially important small-scale corrections, such as shock formation, which has been proposed as a mechanism for both burst and quiescent emission from magnetars.

QED Plasma and Magnetars

A stationary magnetic dipole immersed in an electric field carries "hidden" mechanical momentum. However, the fate of this momentum if the fields are turned off is unclear. We consider a charge-and-dipole hidden momentum configuration, and turn off the fields by collapsing a null shell onto the system, forming a black hole. In numerical calculations we find that the black hole receives a kick corresponding to 0.1% of the initial stored momentum. When extrapolated to apply to purely gravitational phenomena, this efficiency suggests a role for the hidden momentum kick mechanism in generating the binary black hole "superkicks" observed in numerical simulations of Einstein's equation.

Hidden Momentum and Black Hole Kicks

A shared property of several of the known exact solutions to the equations of force-free electrodynamics is that their charge-current four-vector is \textit{null}. We examine the general properties of null-current solutions and then focus on the principal congruences of the Kerr black hole spacetime. We obtain a large class of exact solutions, which are in general time-dependent and non-axisymmetric. These solutions include waves that, surprisingly, propagate without scattering on the curvature of the black hole's background. They may be understood as generalizations to Robinson's solutions to vacuum electrodynamics associated with a shear-free congruence of null geodesics. When stationary and axisymmetric, our solutions reduce to those of Menon and Dermer, the only previously known solutions in Kerr. In Kerr, all of our solutions have null electromagnetic fields ($\vec{E} \cdot \vec{B} = 0$ and $E^2=B^2$). However, in Schwarzschild or flat spacetime there is freedom to add a magnetic monopole field, making the solutions magnetically dominated ($B^2>E^2$). This freedom may be used to reproduce the various flat-spacetime and Schwarzschild-spacetime (split) monopole solutions available in the literature (due to Michel and later authors), and to obtain a large class of time-dependent, non-axisymmetric generalizations. These generalizations may be used to model the magnetosphere of a conducting star that rotates with arbitrary prescribed time-dependent rotation axis and speed. We thus significantly enlarge the class of known exact solutions, while organizing and unifying previously discovered solutions in terms of their null structure.

Exact Solutions to Force-Free Electrodynamics in Black Hole Backgrounds


 The 2017 Event Horizon Telescope (EHT) observations of M87* detected a ring-shaped feature ∼40μas in diameter, consistent with the event horizon scale of a black hole of the expected mass. The thickness of this ring, however, proved difficult to measure, despite being an important parameter for constraining the observational appearance. In the first paper of this series we asked whether the width of the ring was sensitive to the choice of likelihood function used to compare observed closure phases and closure amplitudes to model predictions. In this paper we investigate whether the ring width is robust to changes in the model itself. We construct a more realistic geometric model with two new features: an adjustable radial falloff in brightness, and a secondary ‘photon ring’ component in addition to the primary annulus. This thin, secondary ring is predicted by gravitational lensing for any black hole with an optically thin accretion flow. Analyzing the data using the new model, we find that the primary annulus remains narrow (fractional width ≤0.25) even with the added model freedom. This provides further evidence in favour of a narrow ring for the true sky appearance of M87*, a surprising feature that, if confirmed, would demand theoretical explanation. Comparing the Bayesian evidence for models with and without a secondary ring, we find no evidence for the presence of a lensed photon ring in the 2017 observations. However, the techniques we introduce may prove useful for future observations with a larger and more sensitive array.

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Samuel E. Gralla

Papers

Numerical radiation reaction for a scalar charge in Kerr circular orbit

QED Plasma and Magnetars

Hidden Momentum and Black Hole Kicks

Exact Solutions to Force-Free Electrodynamics in Black Hole Backgrounds

How narrow is the M87* ring? II. A new geometric model