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.

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

Rotating, charged, and uniformly accelerating mass in general relativity

Chern-Simons Modified General Relativity

Three dimensional Einstein gravity with negative cosmological constant ?1/?2 deformed by a gravitational Chern-Simons action with coefficient 1/? is studied in an asymptotically AdS3 spacetime. It is argued to violate unitary or positivity for generic ? due to negative-energy massive gravitons. However at the critical value ?? = 1, the massive gravitons disappear and BTZ black holes all have mass and angular momentum related by ?M = J. The corresponding chiral quantum theory of gravity is conjectured to exist and be dual to a purely right-moving boundary CFT with central charges (cL,?cR) = (0,?3?/G).

https://iopscience.iop.org/article/10.1088/1126-6708/2008/04/082/pdf

Chiral gravity in three dimensions

An algorithm is developed for computing the nth gravitational multipole moment of an asymptotically flat, empty, stationary axisymmetric space‐time. The moments are expressed in terms of the expansion coefficients of the Ernst potential on the axis of symmetry. The values of the first ten multipole moments are given.

Multipole moments of axisymmetric systems in relativity

A wide class of exact solutions of the stationary Einstein-Maxwell equations characterized by a flat "background" three-space is obtained. The solutions can be interpreted as the external gravitational and electromagnetic fields of one or more spinning sources with unit specific charge in stationary configuration.

Solutions of the Coupled Einstein-Maxwell Equations Representing the Fields of Spinning Sources

A real version of the Newman-Penrose formalism is developed for (2+1)-dimensional space-times. The complete algebraic classification of the (Ricci) curvature is given. The field equations of Deser, Jackiw, and Templeton, expressing balance between the Einstein and Bach tensors, are reformulated in triad terms. Two exact solutions are obtained, one characterized by a null geodesic eigencongruence of the Ricci tensor, and a second for which all the polynomial curvature invariants are constant.

Three-dimensional space-times

A generalized SU(2) spinor calculus is established on the ``background space'' V3 of the stationary space‐time. The method of spin coefficients is developed in three dimensions. The stationary field equations can be put to a form which in V3 is analogous to the Newman‐Penrose equations. A V3 filling family of curves is determined by the gravitational field and is called the eigenray congruence. Stationary space‐times may be characterized by the geometric properties of eigenrays. The relation of this classification to the algebraic ones is discussed. The method of solving the equations obtainable for various classes is illustrated on the case of nonshearing geodetic eigenrays. Assuming asymptotic flatness, we obtain the Kerr metric.

Spinor Treatment of Stationary Space‐Times

It is proven that the Wahlquist perfect fluid spacetime cannot be smoothly joined to an exterior asymptotically flat vacuum region. The proof uses a power-series expansion in the angular velocity, to a precision of the second order. In this approximation, the Wahlquist metric is a special case of the rotating Whittaker spacetime. The exterior vacuum domain is treated in a like manner. We compute the conditions of matching at the possible boundary surface in both the interior and the vacuum domain. The conditions for matching the induced metrics and the extrinsic curvatures are mutually contradictory.

http://iopscience.iop.org/article/10.1088/0264-9381/17/2/306/pdf

Zoltán Perjés

Papers

Multipole moments of axisymmetric systems in relativity

Solutions of the Coupled Einstein-Maxwell Equations Representing the Fields of Spinning Sources

Three-dimensional space-times

Spinor Treatment of Stationary Space‐Times

The Wahlquist metric cannot describe an isolated rotating body