A new approach to general relativity by means of a tetrad or spinor formalism is presented. The essential feature of this approach is the consistent use of certain complex linear combinations of Ricci rotation coefficients which give, in effect, the spinor affine connection. It is applied to two problems in radiationtheory; a concise proof of a theorem of Goldberg and Sachs and a description of the asymptotic behavior of the Riemann tensor and metric tensor, for outgoing gravitational radiation.

An Approach to Gravitational Radiation by a Method of Spin Coefficients

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the postNewtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail eects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

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Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.

With an aim towards understanding the time-dependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal of hep-th/0603001. Apart from providing several examples of possible covariant generalizations, we study a particular construction based on light-sheets, motivated in similar spirit to the covariant entropy bound underlying the holographic principle. In particular, we argue that the entanglement entropy associated with a specified region on the boundary in the context of the AdS/CFT correspondence is given by the area of a co-dimension two bulk surface with vanishing expansions of null geodesics. We demonstrate our construction with several examples to illustrate its reduction to the holographic entanglement entropy proposal in static spacetimes. We further show how this proposal may be used to understand the time evolution of entanglement entropy in a time varying QFT state dual to a collapsing black hole background. Finally, we use our proposal to argue that the Euclidean wormhole geometries with multiple boundaries should be regarded as states in a non-interacting but entangled set of QFTs, one associated to each boundary.

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A covariant holographic entanglement entropy proposal

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

Part I. Astronomical Background: 1. High energy astrophysics - an introduction 2. The stars and stellar evolution 3. The galaxies 4. Clusters of galaxies Part II. Physical Processes: 5. Ionisation losses 6. Radiation of accelerated charged particles and bremsstrahlung of electrons 7. The dynamics of charged particles in magnetic fields 8. Synchrotron radiation 9. Interactions of high energy photons 10. Nuclear interactions 11. Aspects of plasma physics and magnetohydrodynamics Part III. High Energy Astrophysics in our Galaxy: 12. Interstellar gas and magnetic fields 13. Dead stars 14. Accretion power in astrophysics 15. Cosmic rays 16. The origin of cosmic rays in our galaxy 17. The acceleration of high energy particles Part IV. Extragalactic High Energy Astrophysics: 18. Active galaxies 19. Black holes in the nuclei of galaxies 20. The vicinity of the black hole 21. Extragalactic radio sources 22. Compact extragalactic sources and superluminal motions 23. Cosmological aspects of high energy astrophysics Appendix References Index.

High Energy Astrophysics

: The final report covering the research performed under the Air Force Office of Scientific Research by the Dallas relativity group, summarizes information on personnel involved, on the scientific work done, and on the results obtained in the four years of the grant's duration. Topics investigated were in areas of General relativity, cosmology, and electrodynamics.

Exact Solutions of Einstein's Field Equations.

Spherical Gravitational Waves

It is shown that a field of null rays is geodetic and shear‐free if and only if the associated family of null bivectors includes a solution to Maxwell's equations for charge‐free space.

Null Electromagnetic Fields

: Contents include: Gravitational collapse; Properties of massive objects; Relativistic astrophysics; Massive stars, relativistic polytropes, and gravitational radiation; Massive stars in quasi-static equilibrium; Collapse of massive stars; Instability of a toridal magnetic geon against gravitational collapse; Stability of multistar systems; Gravitational collapse and rotation; Galaxies identified with radio sources; Structure of the extra-galactic radio sources; Brightness distribution in discrete radio sources; Quasi-stellar radio sources 3C 48 and 3C 273; Galactic interstellar absorption lines in the spectrum of 3C 273; Proper motion of 3C 273; Light variations of 3C 273; Optical identification of 3C 48, 3C 196, and 3C 286 with stellar objects; Optical identification of three new radio objects of the 3C 48 class; Intensity variations of 3C 48, 3C 196, and 3C 273 in optical wavelengths; Redshifts of the quasi-stellar radio sources 3C 47 and 3C 147; Brightness of 3C 273; Mechanism of radiation of the galaxy 3C 273B; Magnetic fields of collapsing masses and the nature of superstars; Origin of radio sources; Distribution of ionized hydrogen in some radio galaxies; An explosion in the center of the galaxy M82; Occurrence of violent events in the nuclei of galaxies; Radio structure of 3C 273 and spectra of radio sources; Radio spectra of a variety of non-thermal radio sources; Gradients of galaxies; Dipole magnetic fields of galactic dimensions; Superdense equilibrium stars; Formation of neutron stars and their surface properties; Neutron stars.

Quasi-stellar sources and gravitational collapse,

Plane‐fronted waves in spaces with nonzero cosmological constant are studied. In particular their complete classification, which depends essentially on the sign of the cosmological constant and that of some second‐order invariant determined by the congruence of null rays, is provided.

Ivor Robinson

Papers

Exact Solutions of Einstein's Field Equations.

Spherical Gravitational Waves

Null Electromagnetic Fields

Quasi-stellar sources and gravitational collapse,

Plane‐fronted gravitational and electromagnetic waves in spaces with cosmological constant