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

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

Astrophysical magnetic fields and nonlinear dynamo theory

Advanced Mathematical Methods for Scientists and Engineers

When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

On Continued Gravitational Contraction

General N-soliton solution of the AKNS class on arbitrary background

In a recent paper we presented analytic expressions for the axis potential, the disk metric, and the surface mass density of the global solution to Einstein's field equations describing a rigidly rotating disk of dust. Here we add the complete solution in terms of ultraelliptic functions and quadratures.

General relativistic gravitational field of a rigidly rotating disk of dust: solution in terms of ultraelliptic functions.

Preface Notation 1. Rotating fluid bodies in equilibrium: fundamental notions and equations 2. Analytical treatment of limiting cases 3. Numerical treatment of the general case 4. Remarks on stability and astrophysical relevance Appendixes References Index.

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Relativistic Figures of Equilibrium

This paper presents the gravitational field of a uniformly rotating stationary and axisymmetric disk consisting of dust particles as a rigorous global solution to the Einstein equations. The problem is formulated as a boundary value problem of the Ernst equation and solved by means of inverse methods. The solution is given in terms of linear integral equations and depends on two parameters: the angular velocity Ω and the relative redshift z from the center of the disk. The Newtonian limit z<<1 represents the MacLaurin solution of a rotating fluid in the disk limit. For z→∞ the exterior solution is given by the extreme Kerr solution. This proves a conjecture of Bardeen & Wagoner (1969, 1971)

The Einsteinian Gravitational Field of the Rigidly Rotating Disk of Dust

The increasing interest in compact astrophysical objects (neutron stars, binaries, galactic black holes) has stimulated the search for rigorous methods, which allow a systematic general relativistic description of such objects. This article is meant to demonstrate the use of the inverse scattering method, which allows, in particular cases, the treatment of rotating body problems. The idea is to replace the investigation of the matter region of a rotating body by the formulation of boundary values along the surface of the body. In this way we construct solutions describing rotating black holes and disks of dust (“galaxies”). Physical properties of the solutions and consequences of the approach are discussed. Among other things, the balance problem for two black holes can be tackled.

Reinhard Meinel

Papers

General N-soliton solution of the AKNS class on arbitrary background

General relativistic gravitational field of a rigidly rotating disk of dust: solution in terms of ultraelliptic functions.

Relativistic Figures of Equilibrium

The Einsteinian Gravitational Field of the Rigidly Rotating Disk of Dust

Progress in relativistic gravitational theory using the inverse scattering method