Table of contents

We study the extensions of the Dvali–Gabadadze–Porrati (DGP) model which are described by five-dimensional Einstein gravity coupled covariantly to a 3-brane with an induced gravity term, and consider warped D = 4 de Sitter background field solutions on the brane. The case which includes the D = 5 AdS cosmological term is also considered. Following background field method, we obtain the field equations described by the Lagrangian terms bilinear in the gravitational field. In such a linear field approximation on curved dS background, we explicitly calculate the five-dimensional massive terms as well as the mass-like ones on the brane. We investigate the eigenvalue problem of a Schrödinger-like equation in the fifth dimension for graviton masses and discuss the existence of massless as well as massive graviton modes in the bulk and on the brane without and with induced gravity.

We analyse in detail the highly damped quasinormal modes of d-dimensional Reissner–Nordström black holes with small charge, paying particular attention to the large but finite damping limit in which the Schwarzschild results should be valid. In the infinite damping limit we confirm, using different methods, the results obtained previously in the literature for higher dimensional Reissner–Nordström black holes. Using a combination of analytic and numerical techniques, we also calculate the transition of the real part of the quasinormal mode frequency from the Reissner–Nordström value for very large damping to the Schwarzschild value of ln(3)T_bh for intermediate damping. The real frequency does not interpolate smoothly between the two values. Instead there is a critical value of the damping at which the topology of the Stokes/anti-Stokes lines changes, and the real part of the quasinormal mode frequency dips to zero.

In the present paper, we will investigate the relationship between scalar–tensor theory and f(R) theories of gravity. Such studies have been performed in the past for the metric formalism of f(R) gravity; here we will consider mainly the Palatini formalism, where the metric and the connections are treated as independent quantities. We will try to investigate under which circumstances f(R) theories of gravity are equivalent to scalar–tensor theory and examine the implications of this equivalence, when it exists.

We investigate p-form electromagnetism—with the Maxwell and Kalb–Ramond fields as lowest-order cases—on discrete spacetimes, including not only the regular lattices commonly used in lattice gauge theory, but also more general examples. After constructing a maximally general model of discrete spacetime suitable for our purpose—a chain complex equipped with an inner product on (p + 1)-cochains—we study both the classical and quantum versions of the theory, with either or U(1) as gauge group. We find results—such as a 'p-form Bohm–Aharonov effect'—that depend in interesting ways on the cohomology of spacetime. We quantize the theory via the Euclidean path integral formalism, where the natural kernels in the U(1) theory are not Gaussians but theta functions. As a special case of the general theory, we show that p-form electromagnetism in p + 1 dimensions has an exact solution which reduces when p = 1 to the Abelian case of 2D Yang–Mills theory as studied by Migdal and Witten. Our main result describes p-form electromagnetism as a 'chain field theory'—a theory analogous to a topological quantum field theory, but with chain complexes replacing manifolds. This makes precise a notion of time evolution in the context of discrete spacetimes of arbitrary topology.

Thermal conditions in the LTP, the LISA Technology Package, are required to be very stable, and in such environments precision temperature measurements are also required for various diagnostics objectives. A sensitive temperature gauging system for the LTP is being developed at IEEC, which includes a set of thermistors and associated electronics. In this paper, we discuss the derived requirements applying to the temperature sensing system, and address the problem of how to create in the laboratory a thermally quiet environment, suitable for performing meaningful on-ground tests of the system. The concept is a two-layer spherical body, with a central aluminium core for sensor implantation surrounded by a layer of polyurethane. We construct the insulator transfer function, which relates the temperature at the core to the laboratory ambient temperature, and evaluate the losses caused by heat leakage through connecting wires. The results of the analysis indicate that, in spite of the very demanding stability conditions, a sphere of outer diameter of the order 1 m is sufficient. We provide experimental evidence confirming the model predictions.

We propose a 'master' higher-spin (HS) particle system. The particle model relevant to the unfolded formulation of HS theory, as well as the HS particle model with a bosonic counterpart of supersymmetry, follows from the master model as its two different gauges. Quantization of the master system gives rise to a new form of the massless HS equations in an extended space involving, besides extra spinorial coordinates, a complex scalar one. As solutions to these equations we recover the massless HS multiplet with fields of all integer and half-integer helicities, and obtain new multiplets with a non-zero minimal helicity. The HS multiplets are described by complex wavefunctions which are holomorphic in the scalar coordinate and carry an extra U(1) charge q. The latter fully characterizes the given multiplet by fixing the minimal helicity as q/2. We construct a twistorial formulation of the master system and present the general solution of the associate HS equations through an unconstrained twistor 'prepotential'.

We formulate an interacting theory of a vector-spinor field associated with anti-commuting Majorana spinor charges in arbitrary spacetime dimensions. The field content of the system is , where is a vector spinor in the adjoint representation of an arbitrary gauge group, and is its gauge field, while χ^αIJ is an extra spinor with antisymmetric adjoint indices IJ. Contrary to common wisdom, the consistency of the vector-spinor field equation is maintained, despite its non-trivial interactions and nilpotency of the spinor charges. After establishing the classical system, we perform its quantization with gauge-fixing and Faddeev–Popov ghost terms, confirming the BRST invariance of the total action.

Using an appropriately formulated holographic lightfront projection, we derive an area law for the localization entropy caused by vacuum polarization on the horizon of a wedge region. Its area density has a simple kinematic relation to the volume extensive heat bath entropy of the lightfront algebra. Apart from a change of parametrization, the infinite lightlike length contribution to the lightfront volume factor corresponds to the short-distance divergence of the area density of the localization entropy. This correspondence is a consequence of the conformal invariance of the lightfront holography combined with the well-known fact that conformality relates short to long distances. In the explicit calculation of the strength factor we use the temperature duality relation of rational chiral theories whose derivation will be briefly reviewed. We comment on the potential relevance for the understanding of black hole entropy.

In this paper, we analyse the relativistic quantum motion of a charged spin-0 particle in the presence of a dyon, Aharonov–Bohm magnetic field and scalar potential in the spacetimes produced by an idealized cosmic string and global monopole. In order to develop this analysis, we assume that the dyon and the Aharonov–Bohm magnetic field are superposed to both gravitational defects. Two distinct configurations for the scalar potential, S(r), are considered: (i) the potential proportional to the inverse of the radial distance, i.e. S ∝ 1/r, and (ii) the potential proportional to this distance, i.e. S ∝ r. For both cases the centre of the potentials coincides with the dyon's position. In the case of the cosmic string the Aharonov–Bohm magnetic field is considered along the defect, and for the global monopole this magnetic field pierces the defect. The energy spectra are computed for both cases and their dependence on the electrostatic and scalar coupling constants is explicitly shown. We also analyse scattering states of the Klein–Gordon equations, and show how the phase shifts depend on the geometry of the spacetime and on the coupling constants parameter.

A novel technique for solving some head-on collisions of plane homogeneous light-like signals in Einstein–Maxwell theory is described. The technique is a by-product of a reexamination of the fundamental Bell–Szekeres solution in this field of study. Extensions of the Bell–Szekeres collision problem to include light-like shells and gravitational waves are described and a family of solutions having geometrical and topological properties in common with the Bell–Szekeres solution is derived.

We give an 11- and 10-dimensional supergravity description of M5-branes wrapping 4-cylces in a Calabi–Yau manifold and carrying momentum along a transverse S¹. These wrapped branes descend to a class of N = 2 black holes in 4 dimensions. Our description gives the conditions on the geometry interpolating between the asymptotic and near-horizon regions. We employ the ideas of geometric transitions to show that the near-horizon geometry in 10 dimensions is AdS₂ × S² × CY₃ while in 11 dimensions it is AdS₃ × S² × CY₃. We also show how to obtain the complete N = 2 black hole supergravity solution in 4 dimensions for this class of black holes starting with our 11-dimensional description. Finally, we generalize our results on the 10- and 11-dimensional near-horizon supergravity solution to the case of black holes carrying arbitrary charges (D0–D2–D4–D6 in type IIA description). We argue that the near-horizon geometry corresponding to wrapped D6 and D2 branes in 11 dimensions is AdS₂ × S³ × CY₃.

We use covariant and first-order formalism techniques to study the properties of general relativistic cosmology in three dimensions. The covariant approach provides an irreducible decomposition of the relativistic equations, which allows for a mathematically compact and physically transparent description of the three-dimensional spacetimes. Using this information we review the features of homogeneous and isotropic 3D cosmologies, provide a number of new solutions and study gauge invariant perturbations around them. The first-order formalism is then used to provide a detailed study of the most general 3D spacetimes containing perfect-fluid matter. Assuming the material content to be dust with comoving spatial 2-velocities, we find the general solution of the Einstein equations with a non-zero (and zero) cosmological constant and generalize known solutions of Kriele and the 3D counterparts of the Szekeres solutions. In the case of a non-comoving dust fluid we find the general solution in the case of one non-zero fluid velocity component. We consider the asymptotic behaviour of the families of 3D cosmologies with rotation and shear and analyse their singular structure. We also provide the general solution for cosmologies with one spacelike Killing vector, find solutions for cosmologies containing scalar fields and identify all the PP-wave 2 + 1 spacetimes.

The Kerr–AdS metric in dimension D has cohomogeneity [D/2]; the metric components depend on the radial coordinate r and [D/2] latitude variables μ_i that are subject to the constraint ∑_iμ²_i = 1. We find a coordinate reparametrization in which the μ_i variables are replaced by [D/2] − 1 unconstrained coordinates y_α, and having the remarkable property that the Kerr–AdS metric becomes diagonal in the coordinate differentials dy_α. The coordinates r and y_α now appear in a very symmetrical way in the metric, leading to an immediate generalization in which we can introduce [D/2] − 1 NUT parameters. We find that (D − 5)/2 are non-trivial in odd dimensions whilst (D − 2)/2 are non-trivial in even dimensions. This gives the most general Kerr–NUT–AdS metric in D dimensions. We find that in all dimensions D ⩾ 4, there exist discrete symmetries that involve inverting a rotation parameter through the AdS radius. These symmetries imply that Kerr–NUT–AdS metrics with over-rotating parameters are equivalent to under-rotating metrics. We also consider the BPS limit of the Kerr–NUT–AdS metrics, and thereby obtain, in odd dimensions and after Euclideanization, new families of Einstein–Sasaki metrics.

We discuss the issue of quasi-particle production by 'analogue black holes' with particular attention to the possibility of reproducing Hawking radiation in a laboratory. By constructing simple geometric acoustic models, we obtain a somewhat unexpected result: we show that in order to obtain a stationary and Planckian emission of quasi-particles, it is not necessary to create an ergoregion in the acoustic spacetime (corresponding to a supersonic regime in the flow). It is sufficient to set up a suitable dynamically changing flow. For instance, either a flow that eventually generates an arbitrarily small sonic region v = c, but without any ergoregion, or even a flow that just asymptotically, in laboratory time, approaches a sonic regime with sufficient rapidity.

At densities below the neutron drip threshold, a purely elastic solid model (including, if necessary, a frozen-in magnetic field) can provide an adequate description of a neutron star crust, but at higher densities it will be necessary to allow for the penetration of the solid lattice by an independently moving current of superfluid neutrons. In order to do this, the previously available category of relativistic elasticity models is combined here with a separately developed category of relativistic superfluidity models in a unified treatment based on the use of an appropriate Lagrangian master function. As well as models of the purely variational kind, in which the vortices flow freely with the fluid, such a master function also provides a corresponding category of non-dissipative models in which the vortices are pinned to the solid structure.

A simple formula, invariant under the duality rotation Φ → e^iαΦ, is obtained for the Poynting vector within the framework of the Ernst formalism, and its application to the known exact solutions for a charged massive magnetic dipole is considered.

The rank-three tensor model may be regarded as a theory of dynamical fuzzy spaces, because a fuzzy space is defined by a three-index coefficient of the product between functions on it, f_a*f_b = C_ab^cf_c. In this paper, this proposal is applied to the dynamical generation of commutative non-associative fuzzy spaces. It is numerically shown that fuzzy flat tori and fuzzy spheres of various dimensions are classical solutions of the rank-three tensor model. Since these solutions are obtained for the same coupling constants of the tensor model, the cosmological constant and the dimensions are not fundamental but can be regarded as dynamical quantities. The symmetry of the model under the general linear transformation can be identified with a fuzzy analogue of the general coordinate transformation symmetry in general relativity. This symmetry of the tensor model is broken at the classical solutions. This feature may make the model a concrete finite setting for applying the old idea of obtaining gravity as Nambu–Goldstone fields of the spontaneous breaking of the local translational symmetry.

A numerical simulation of fluid flows in a Laval nozzle is performed to observe the formation of an acoustic black hole and the classical counterpart to Hawking radiation under a realistic setting of the laboratory experiment. We aim to construct a practical procedure for the data analysis to extract the classical counterpart to Hawking radiation from experimental data. Following our procedure, we determine the surface gravity of the acoustic black hole from the obtained numerical data. Some noteworthy points in analysing the experimental data are clarified through our numerical simulation.

Cauchy-characteristic matching (CCM), the combination of a central 3 + 1 Cauchy code with an exterior characteristic code connected across a timelike interface, is a promising technique for the generation and extraction of gravitational waves. While it provides a tool for the exact specification of boundary conditions for the Cauchy evolution, it also allows us to follow gravitational radiation all the way to infinity, where it is unambiguously defined. We present a new fourth-order accurate finite difference CCM scheme for a first-order reduction of the wave equation around a Schwarzschild black hole in axisymmetry. The matching at the interface between the Cauchy and the characteristic regions is done by transferring appropriate characteristic/null variables. Numerical experiments indicate that the algorithm is fourth-order convergent. As an application we reproduce the expected late-time tail decay for the scalar field.

According to general relativity, the gravitomagnetic Lense–Thirring force of Mars would secularly shift the orbital plane of the Mars Global Surveyor (MGS) spacecraft by an amount of 1.5 m, on average, in the cross-track direction over 5 years. The determined cross-track post-fit residuals of MGS, built up by neglecting just the gravitomagnetic force in the dynamical force models and without fitting any empirical cross-track acceleration which could remove the relativistic signal, amount to 1.6 m, on average, over a 5 year time interval spanning from 10 February 2000 to 14 January 2005. The discrepancy with the predictions of general relativity is, thus, about 6%.

In this comment on a recent paper by Dunajski a method of generating solutions of the Einstein-scalar field equations from Einstein metrics is presented. Two spherically symmetric examples are presented.

The full text of this article is available in the PDF provided.

The motion of a charged particle interacting with its own electromagnetic field is an area of research that has a long history; this problem has never ceased to fascinate its investigators. On the one hand the theory ought to be straightforward to formulate: one has Maxwell's equations that tell the field how to behave (given the motion of the particle), and one has the Lorentz-force law that tells the particle how to move (given the field). On the other hand the theory is fundamentally ambiguous because of the field singularities that necessarily come with a point particle. While each separate sub-problem can easily be solved, to couple the field to the particle in a self-consistent treatment turns out to be tricky. I believe it is this dilemma (the theory is straightforward but tricky) that has been the main source of the endless fascination.

For readers of Classical and Quantum Gravity, the fascination does not end there. For them it is also rooted in the fact that the electromagnetic self-force problem is deeply analogous to the gravitational self-force problem, which is of direct relevance to future gravitational wave observations. The motion of point particles in curved spacetime has been the topic of a recent Topical Review [1], and it was the focus of a recent Special Issue [2].

It is surprising to me that radiation reaction is a subject that continues to be poorly covered in the standard textbooks, including Jackson's bible [3]. Exceptions are Rohrlich's excellent text [4], which makes a very useful introduction to radiation reaction, and the Landau and Lifshitz classic [5], which contains what is probably the most perfect summary of the foundational ideas (presented in characteristic terseness).

It is therefore with some trepidation that I received Herbert Spohn's book, which covers both the classical and quantum theories of a charged particle coupled to its own field (the presentation is limited to flat spacetime). Is this the text that graduate students and researchers should turn to in order to get a complete and accessible education in radiation reaction?

My answer is that while the book does indeed contain a lot of useful material, it is not a very accessible source of information, and it is certainly not a student-friendly textbook. Instead, the book presents a technical account of the author's personal take on the theory, and represents a culminating summary of the author's research contributions over more than a decade. The book is written in a fairly mathematical style (the author is Professor of Mathematical Physics at the Technische Universitat in Munich), and it very much emphasises mathematical rigour. This makes the book less accessible than I would wish it to be, but this is perhaps less a criticism than a statement about my taste, expectation, and attitude.

The presentation of the classical theory begins with a point particle, but Spohn immediately smears the charge distribution to eliminate the vexing singularities of the retarded field. He considers both the nonrelativistic Abraham model (in which the extended particle is spherically symmetric in the laboratory frame) and the relativistic Lorentz model (in which the particle is spherical in its rest frame).

In Spohn's work, the smearing of the charge distribution is entirely a mathematical procedure, and I would have wished for a more physical discussion. A physically extended body, held together against electrostatic repulsion by cohesive forces (sometimes called Poincaré stresses) would make a sound starting point for a classical theory of charged particles, and would have nicely (and physically) motivated the smearing operation adopted in the book.

Spohn goes on to derive energy–momentum relations for the extended objects, and to obtain their equations of motion. A compelling aspect of his presentation is that he formally introduces the 'adiabatic limit', the idea that the external fields acting on the charged body should have length and time scales that are long compared with the particle's internal scales (respectively the electrostatic classical radius and its associated time scale).

As a consequence, the equations of motion do not involve a differentiated acceleration vector (as is the case for the Abraham–Lorentz–Dirac equations) but are proper second-order differential equations for the position vector. In effect, the correct equations of motion are obtained from the Abraham–Lorentz–Dirac equations by a reduction-of-order procedure that was first proposed (as far as I know) by Landau and Lifshitz [5]. In Spohn's work this procedure is not {\it ad hoc}, but a natural consequence of the adiabatic approximation.

An aspect of the classical portion of the book that got me particularly excited is Spohn's proposal for an experimental test of the predictions of the Landau–Lifshitz equations. His proposed experiment involves a Penning trap, a device that uses a uniform magnetic field and a quadrupole electric field to trap an electron for very long times. Without radiation reaction, the motion of an electron in the trap is an epicycle that consists of a rapid (and small) cyclotron orbit superposed onto a slow (and large) magnetron orbit. Spohn shows that according to the Landau–Lifshitz equations, the radiation reaction produces a damping of the cyclotron motion. For reasonable laboratory situations this damping occurs over a time scale of the order of 0.1 second. This experiment might well be within technological reach.

The presentation of the quantum theory is based on the nonrelativistic Abraham model, which upon quantization leads to the well-known Pauli-Fierz Hamiltonian of nonrelativistic quantum electrodynamics. This theory, an approximation to the fully relativistic version of QED, has a wide domain of validity that includes many aspects of quantum optics and laser-matter interactions. As I am not an expert in this field, my ability to review this portion of Spohn's book is limited, and I will indeed restrict myself to a few remarks.

I first admit that I found Spohn's presentation to be tough going. Unlike the pair of delightful books by Cohen-Tannoudji, Dupont-Roc, and Grynberg [6, 7], this is not a gentle introduction to the quantum theory of a charged particle coupled to its own electromagnetic field. Instead, Spohn proceeds rather quickly through the formulation of the theory (defining the Hamiltonian and the Hilbert space) and then presents some applications (for example, he constructs the ground states of the theory, he examines radiation processes, and he explores finite-temperature aspects).

There is a lot of material in the eight chapters devoted to the quantum theory, but my insufficient preparation and the advanced nature of Spohn's presentation were significant obstacles; I was not able to draw much appreciation for this material.

One of the most useful resources in Spohn's book are the historical notes and literature reviews that are inserted at the end of each chapter. I discovered a wealth of interesting articles by reading these, and I am grateful that the author made the effort to collect this information for the benefit of his readers.

References [1] Poisson E 2004 Radiation reaction of point particles in curved spacetime Class. Quantum Grav21 R153–R232 [2] Lousto C O 2005 Special issue: Gravitational Radiation from Binary Black Holes: Advances in the Perturbative Approach, Class. Quantum Grav22 S543–S868 [3] Jackson J D 1999 Classical Electrodynamics Third Edition (New York: Wiley) [4] Rohrlich F 1990 Classical Charged Particles (Redwood City, CA: Addison–Wesley) [5] Landau L D and Lifshitz E M 2000 The Classical Theory of FieldsFourth Edition (Oxford: Butterworth–Heinemann) [6] Cohen-Tannoudji C Dupont-Roc J and Grynberg G 1997 Photons and Atoms - Introduction to Quantum Electrodynamics (New York: Wiley-Interscience) [7] Cohen-Tannoudji C, Dupont-Roc J and G Grynberg G 1998 Atom–Photon Interactions: Basic Processes and Applications (New York: Wiley-Interscience)