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

NSF [PHY-1505124, PHY-1804216, PHY-1752809, PHY-1708081]; Kavli Institute for Cosmological Physics at the University of Chicago through an endowment from the Kavli Foundation; Marion and Stuart Rice Award

Black hole shadows, photon rings, and lensing rings

There is general agreement that the MiSaTaQuWa equations should describe the motion of a 'small body' in general relativity, taking into account the leading order self-force effects. However, previous derivations of these equations have made a number of ad hoc assumptions and/or contain a number of unsatisfactory features. For example, all previous derivations have invoked, without proper justification, the step of 'Lorenz gauge relaxation', wherein the linearized Einstein equation is written in the form appropriate to the Lorenz gauge, but the Lorenz gauge condition is then not imposed—thereby making the resulting equations for the metric perturbation inequivalent to the linearized Einstein equations. (Such a 'relaxation' of the linearized Einstein equations is essential in order to avoid the conclusion that 'point particles' move on geodesics.) In this paper, we analyze the issue of 'particle motion' in general relativity in a systematic and rigorous way by considering a one-parameter family of metrics, gab(λ), corresponding to having a body (or black hole) that is 'scaled down' to zero size and mass in an appropriate manner. We prove that the limiting worldline of such a one-parameter family must be a geodesic of the background metric, gab(λ = 0). Gravitational self-force—as well as the force due to coupling of the spin of the body to curvature—then arises as a first-order perturbative correction in λ to this worldline. No assumptions are made in our analysis apart from the smoothness and limit properties of the one-parameter family of metrics, gab(λ). Our approach should provide a framework for systematically calculating higher order corrections to gravitational self-force, including higher multipole effects, although we do not attempt to go beyond first-order calculations here. The status of the MiSaTaQuWa equations is explained.

https://iopscience.iop.org/article/10.1088/0264-9381/25/20/205009/pdf

A rigorous derivation of gravitational self-force

During the past century, there has been considerable discussion and analysis of the motion of a point charge in an external electromagnetic field in special relativity, taking into account ``self-force'' effects due to the particle's own electromagnetic field. We analyze the issue of ``particle motion'' in classical electromagnetism in a rigorous and systematic way by considering a one-parameter family of solutions to the coupled Maxwell and matter equations corresponding to having a body whose charge-current density ${J}^{a}(\ensuremath{\lambda})$ and stress-energy tensor ${T}_{ab}(\ensuremath{\lambda})$ scale to zero size in an asymptotically self-similar manner about a worldline $\ensuremath{\gamma}$ as $\ensuremath{\lambda}\ensuremath{\rightarrow}0$. In this limit, the charge, $q$, and total mass, $m$, of the body go to zero, and $q/m$ goes to a well-defined limit. The Maxwell field ${F}_{ab}(\ensuremath{\lambda})$ is assumed to be the retarded solution associated with ${J}^{a}(\ensuremath{\lambda})$ plus a homogeneous solution (the ``external field'') that varies smoothly with $\ensuremath{\lambda}$. We prove that the worldline $\ensuremath{\gamma}$ must be a solution to the Lorentz force equations of motion in the external field ${F}_{ab}(\ensuremath{\lambda}=0)$. We then obtain self-force, dipole forces, and spin force as first-order perturbative corrections to the center-of-mass motion of the body. We believe that this is the first rigorous derivation of the complete first-order correction to Lorentz force motion. We also address the issue of obtaining a self-consistent perturbative equation of motion associated with our perturbative result, and argue that the self-force equations of motion that have previously been written down in conjunction with the ``reduction of order'' procedure should provide accurate equations of motion for a sufficiently small charged body with negligible dipole moments and spin. (There is no corresponding justification for the non-reduced-order equations.) We restrict consideration in this paper to classical electrodynamics in flat spacetime, but there should be no difficulty in extending our results to the motion of a charged body in an arbitrary globally hyperbolic curved spacetime.

Rigorous derivation of electromagnetic self-force

Force-Free Electrodynamics (FFE) describes magnetically dominated relativistic plasma via non-linear equations for the electromagnetic field alone Such plasma is thought to play a key role in the physics of pulsars and active black holes Despite its simple covariant formulation, FFE has primarily been studied in 3+1 frameworks, where spacetime is split into space and time In this article we systematically develop the theory of force-free magnetospheres taking a spacetime perspective Using a suite of spacetime tools and techniques (notably exterior calculus) we cover 1) the basics of the theory, 2) exact solutions that demonstrate the extraction and transport of the rotational energy of a compact object (in the case of a black hole, the Blandford-Znajek mechanism), 3) the behavior of current sheets, 4) the general theory of stationary, axisymmetric magnetospheres and 5) general properties of pulsar and black hole magnetospheres We thereby synthesize, clarify and generalize known aspects of the physics of force-free magnetospheres, while also introducing several new results

Spacetime approach to force-free magnetospheres

Interpreting horizon-scale observations of astrophysical black holes demands a general understanding of null geodesics in the Kerr spacetime. These may be divided into two classes: ``direct'' rays that primarily determine the observational appearance of a given source, and highly bent rays that produce a nested sequence of exponentially demagnified images of the main emission: the so-called ``photon ring.'' We develop heuristics that characterize the direct rays and study the highly bent geodesics analytically. We define three critical parameters $\ensuremath{\gamma}$, $\ensuremath{\delta}$, and $\ensuremath{\tau}$ that respectively control the demagnification, rotation, and time delay of successive images of the source, thereby providing an analytic theory of the photon ring. These observable parameters encode universal effects of general relativity, independent of the details of the emitting matter.

Samuel E. Gralla

Papers

Black hole shadows, photon rings, and lensing rings

A rigorous derivation of gravitational self-force

Rigorous derivation of electromagnetic self-force

Spacetime approach to force-free magnetospheres

Lensing by Kerr Black Holes