Numerical simulations of generic singularities

Numerical simulations of the approach to the singularity in vacuum spacetimes are presented here. The spacetimes examined have no symmetries and can be regarded as representing the general behavior of singularities. It is found that the singularity is spacelike and that, as it is approached, the spacetime dynamics becomes local and oscillatory.

Gravitational Lensing from a Spacetime Perspective

The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime. It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images. The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others.

Physical limits to communication

The limits posed by physics to the quantity of information that can be transmitted with a certain amount of power are investigated. The same ultimate limits are found for transmission of information encoded using matter and massless fields.

Entropy, holography, and the second law

The geometric entropy in quantum field theory is not a Lorentz scalar and has no invariant meaning, while the black hole entropy is invariant. Renormalization of entropy and energy for reduced density matrices may lead to the negative free energy even if no boundary conditions are imposed. The presence of particles outside the horizon of a uniformly accelerated observer prevents the description in terms of a single Unruh temperature.

Pulsars in Binary Systems: Probing Binary Stellar Evolution and General Relativity

Radio pulsars in binary orbits often have short millisecond spin periods as a result of mass transfer from their companion stars. They therefore act as very precise, stable, moving clocks that allow us to investigate a large set of otherwise inaccessible astrophysical problems. The orbital parameters derived from high-precision binary pulsar timing provide constraints on binary evolution, characteristics of the binary pulsar population, and the masses of neutron stars with different mass-transfer histories. These binary systems also test gravitational theories, setting strong limits on deviations from general relativity. Surveys for new pulsars yield new binary systems that increase our understanding of all these fields and may open up whole new areas of physics, as most spectacularly evidenced by the recent discovery of an extremely relativistic double-pulsar system.

Resonant excitations of the 't Hooft-Polyakov monopole

The spherically symmetric magnetic monopole in an SU(2) gauge theory coupled to a massless Higgs field is shown to possess an infinite number of resonances or quasinormal modes. These modes are eigenfunctions of the isospin 1 perturbation equations with complex eigenvalues, E(n)=omega(n)-igamma(n), satisfying the outgoing radiation condition. For n--> infinity, their frequencies omega(n) approach the mass of the vector boson, M(W), while their lifetimes 1/gamma(n) tend to infinity. The response of the monopole to an arbitrary initial perturbation is largely determined by these resonant modes, whose collective effect leads to the formation of a long living breatherlike excitation with an amplitude decaying at late times as t(-5/6).

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operatorvalued) stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole (enclosed in a box). We derive a fluctuation-dissipation relation between the fluctuations in the radiation and the dissipative dynamics of metric fluctuations.

Palatini form of 1/R gravity

It has been suggested that the Universe's recent acceleration is due to a contribution to the gravitational action proportional to the reciprocal of the Ricci scalar. Although the original version of this theory disagrees with solar system observations, a modified Palatini version, in which the metric and connection are treated as independent variables, has been suggested as a viable model of the cosmic acceleration. We show that this theory is equivalent to a scalar-tensor theory in which the scalar field kinetic energy term is absent from the action. Integrating out the scalar field gives rise to additional interactions among the matter fields of the standard model of particle physics at an energy scale of order 10(-3) eV (the geometric mean of the Hubble and the Planck scales), and so the theory is excluded by, for example, electron-electron scattering experiments.

Quantum suppression of the generic chaotic behavior close to cosmological singularities

In classical general relativity, the generic approach to the initial singularity is very complicated as exemplified by the chaos of the Bianchi IX model which displays the generic local evolution close to a singularity. Quantum gravity effects can potentially change the behavior and lead to a simpler initial state. This is verified here in the context of loop quantum gravity, using methods of loop quantum cosmology: The chaotic behavior stops once quantum effects become important. This is consistent with the discrete structure of space predicted by loop quantum gravity.

Conformal Infinity

The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, "conformal infinity" is related to almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved from physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation, and how it lends itself very naturally to the solution of radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection.

Analytic Black Hole Perturbation Approach to Gravitational Radiation

We review the analytic methods used to perform the post-Newtonian expansion of gravitational waves induced by a particle orbiting a massive, compact body, based on black hole perturbation theory. There exist two different methods of performing the post-Newtonian expansion. Both are based on the Teukolsky equation. In one method, the Teukolsky equation is transformed into a Regge-Wheeler type equation that reduces to the standard Klein Gordon equation in the flat-space limit, while in the other method (which was introduced by Mano, Suzuki, and Takasugi relatively recently, the Teukolsky equation is used directly in its original form. The former's advantage is that it is intuitively easy to understand how various curved space effects come into play. However, it becomes increasingly complicated when one goes to higher and higher post-Newtonian orders. In contrast, the latter's advantage is that a systematic calculation to higher post-Newtonian orders can be implemented relatively easily, but otherwise, it is so mathematical that it is hard to understand the interplay of higher order terms. In this paper, we review both methods so that their pros and cons may be seen clearly. We also review some results of calculations of gravitational radiation emitted by a particle orbiting a black hole.

Millisecond pulsars with r-modes as steady gravitational radiators

Millisecond pulsars (MSPs) probably achieve their fast rotation by mass transfer from their companion stars in low-mass x-ray binaries (LMXBs). The lack of MSPs and LMXBs rotating near breakup has been attributed to the accretion torque being balanced, at fast rotation, by gravitational radiation, perhaps caused by an unstable oscillation mode. It has been argued that internal dissipation involving hyperons may cause LMXBs to evolve into a quasisteady state, with nearly constant rotation rate, temperature, and mode amplitude. We show that MSPs descending from these LMXBs spend a long time in a similar state, as extremely steady sources of gravitational waves and thermal x rays, while they spin down due to gravitational radiation and the standard magnetic torque. Observed MSP braking torques already place meaningful constraints on this scenario.

Model for gravitational interaction between dark matter and baryons

We propose a phenomenological model where the gravitational interaction between dark matter and baryons is suppressed on small, subgalactic scales. We describe the gravitational force by adding a Yukawa contribution to the standard Newtonian potential and show that this interaction scheme is effectively suggested by the available observations of the inner rotation curves of small mass galaxies. Besides helping in interpreting the cuspy profile of dark matter halos observed in N-body simulations, this potential regulates the quantity of baryons within halos of different masses.

Towards quantum superpositions of a mirror

We propose an experiment for creating quantum superposition states involving of the order of 10(14) atoms via the interaction of a single photon with a tiny mirror. This mirror, mounted on a high-quality mechanical oscillator, is part of a high-finesse optical cavity which forms one arm of a Michelson interferometer. By observing the interference of the photon only, one can study the creation and decoherence of superpositions involving the mirror. A detailed analysis of the requirements shows that the experiment is within reach using a combination of state-of-the-art technologies.

Testing General Relativity with Pulsar Timing

Pulsars of very different types, including isolated objects and binaries (with short- and long-period orbits, and white-dwarf and neutron-star companions) provide the means to test both the predictions of general relativity and the viability of alternate theories of gravity. This article presents an overview of pulsars, then discusses the current status of and future prospects for tests of equivalence-principle violations and strong-field gravitational experiments.

A test of general relativity using radio links with the Cassini spacecraft

According to general relativity, photons are deflected and delayed by the curvature of space-time produced by any mass. The bending and delay are proportional to gamma + 1, where the parameter gamma is unity in general relativity but zero in the newtonian model of gravity. The quantity gamma - 1 measures the degree to which gravity is not a purely geometric effect and is affected by other fields; such fields may have strongly influenced the early Universe, but would have now weakened so as to produce tiny--but still detectable--effects. Several experiments have confirmed to an accuracy of approximately 0.1% the predictions for the deflection and delay of photons produced by the Sun. Here we report a measurement of the frequency shift of radio photons to and from the Cassini spacecraft as they passed near the Sun. Our result, gamma = 1 + (2.1 +/- 2.3) x 10(-5), agrees with the predictions of standard general relativity with a sensitivity that approaches the level at which, theoretically, deviations are expected in some cosmological models.

Numerical Hydrodynamics in General Relativity

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.

ELECTRONIC SUPPLEMENTARY MATERIAL

Supplementary material is available for this article at 10.12942/lrr-2003-4.

Rotating Stars in Relativity

Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information they might yield about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on the equilibrium properties and on the nonaxisymmetric instabilities in f-modes and r-modes have been updated and several new sections have been added on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity.

ELECTRONIC SUPPLEMENTARY MATERIAL

Supplementary material is available for this article at 10.12942/lrr-2003-3.

Light sheets and Bekenstein's entropy bound

From the covariant bound on the entropy of partial light sheets, we derive a version of Bekenstein's bound: S/M<or=pix/ variant Planck's over 2pi, where S, M, and x are the entropy, total mass, and width of any isolated, weakly gravitating system. Because x can be measured along any spatial direction, the bound becomes unexpectedly tight in thin systems. Our result completes the identification of older entropy bounds as special cases of the covariant bound. Thus, light sheets exhibit a connection between information and geometry far more general, but in no respect weaker, than that initially revealed by black hole thermodynamics.

Quasinormal modes, the area spectrum, and black hole entropy

The results of loop quantum gravity concerning geometric operators and black hole entropy are beset by an ambiguity labeled by the Immirzi parameter. We use a result from classical gravity concerning the quasinormal mode spectrum of a black hole to fix this parameter in a new way. As a result we arrive at the Bekenstein-Hawking expression of A/4l(2)(P) for the entropy of a black hole and in addition see an indication that the appropriate gauge group of quantum gravity is SO(3) and not its covering group SU(2).

Inflation from quantum geometry

Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present day cosmological acceleration is so tiny.

Runaway dilaton and equivalence principle violations

In a recently proposed scenario, where the dilaton decouples while cosmologically attracted towards infinite bare string coupling, its residual interactions can be related to the amplitude of density fluctuations generated during inflation, and are large enough to be detectable through a modest improvement on present tests of free-fall universality. Provided it has significant couplings to either dark matter or dark energy, a runaway dilaton can also induce time variations of the natural "constants" within the reach of near-future experiments.