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.

We find the gravity dual of a marginal deformation of = 4 super Yang Mills, and discuss some of its properties. This deformation is intimately connected with an SL(2,) symmetry of the gravity theory. The SL(2,) transformation enables us to find the solutions in a simple way. These field theory deformations, sometimes called β deformations, can be viewed as arising from a star product. Our method works for any theory that has a gravity dual with a U(1) × U(1) global symmetry which is realized geometrically. These include the field theories that live on D3 branes at the conifold or other toric singularities, as well as their cascading versions.

Deforming field theories with U(1) × U(1) global symmetry and their gravity duals

We give a derivation of the gravitational Hamiltonian starting from the Einstein - Hilbert action, keeping track of all surface terms. This derivation can be applied to any spacetime that asymptotically approaches a static background solution. The surface term that arises in the Hamiltonian can be taken as the definition of the `total energy', even for spacetimes that are not asymptotically flat. (In the asymptotically flat case, it agrees with the usual ADM energy.) We also discuss the relation between the Euclidean action and the Hamiltonian when there are horizons of infinite area (e.g. acceleration horizons) as well as the usual finite area black hole horizons. Acceleration horizons seem to be more analogous to extreme than nonextreme black holes, since we find evidence that their horizon area is not related to the total entropy.

http://cds.cern.ch/record/275032/files/9501014.pdf

The Gravitational Hamiltonian, action, entropy and surface terms

The aim of this paper is to provide a general introduction to the problem of time in quantum gravity. This problem originates in the fundamental conflict between the way the concept of ‘time’ is used in quantum theory, and the role it plays in a diffeomorphism-invariant theory like general relativity. Schemes for resolving this problem can be sub-divided into three main categories: (I) approaches in which time is identified before quantising; (II) approaches in which time is identified after quantising; and (III) approaches in which time plays no fundamental role at all. Ten different specific schemes are discussed in this paper which also contain an introduction to the relevant parts of the canonical decomposition of general relativity.

Canonical quantum gravity and the problem of time

We find the gravity dual of a marginal deformation of ${\cal N}=4$ super Yang Mills, and discuss some of its properties. This deformation is intimately connected with an $SL(2,R)$ symmetry of the gravity theory. The $SL(2,R)$ transformation enables us to find the solutions in a simple way. These field theory deformations, sometimes called $\beta$ deformations, can be viewed as arising from a star product. Our method works for any theory that has a gravity dual with a $U(1)\times U(1)$ global symmetry which is realized geometrically. These include the field theories that live on D3 branes at the conifold or other toric singularities, as well as their cascading versions.

Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals

Classical solutions describing charged dilaton black holes accelerating in a background magnetic field have recently been found. They include the Ernst metric of the Einstein-Maxwell theory as a special case. We study the extremal limit of these solutions in detail, both at the classical and quantum levels. It is shown that near the event horizon the extremal solutions reduce precisely to the static extremal black hole solutions. For a particular value of the dilaton coupling, these extremal black holes are five-dimensional Kaluza-Klein monopoles. The Euclidean sections of these solutions can be interpreted as instantons describing the pair creation of extremal black holes and/or Kaluza-Klein monopoles in a magnetic field. The action of these instantons is calculated and found to agree with the Schwinger result in the weak-field limit. For the Euclidean Ernst solution, the action for the extremal solution differs from that of the previously discussed wormhole instanton by the Bekenstein-Hawking entropy. However, in many cases quantum corrections become large in the vicinity of the black hole, and the precise description of the creation process is unknown.

Pair creation of extremal black holes and Kaluza-Klein monopoles.

Global structure of spacetimes.

An example is given of a space-time which satisfies the conditions for an asymptotic region which is not '' as large'' as that of Minkowski space-time.

Asymptotically Simple Does Not Imply Asymptotically Minkowskian.

Semiclassical relativity is a theory in which quantum matter fields interact with a classical gravitational field via the semiclassical Einstein equation G/sub a/b=8..pi.. . We consider, for the case of massless quantum fields, the weak-field limit of this theory. It is shown that the linearized quantum stress energy can be determined in a manner which is essentially independent of the details of any regularization prescription. Using this expression for the quantum stress energy, we solve the linearized semiclassical Einstein equation. The solutions found include (1) perturbations that satisfy the linearized classical Einstein equation G/sub a/b=0, (2) perturbations that grow exponentially in time, and (3) perturbations that (in some sense) travel faster than the speed of light.

Gary T. Horowitz

Papers

Pair creation of extremal black holes and Kaluza-Klein monopoles.

Global structure of spacetimes.

Asymptotically Simple Does Not Imply Asymptotically Minkowskian.

Semiclassical relativity: The weak-field limit

Positive energy in general relativity