Table of contents

We argue for the existence of plasma balls—metastable, nearly homogeneous lumps of gluon plasma at just above the deconfinement energy density—in a class of large-N confining gauge theories that undergo first-order deconfinement transitions. Plasma balls decay over a time scale of order N² by thermally radiating hadrons at the deconfinement temperature. In gauge theories that have a dual description that is well approximated by a theory of gravity in a warped geometry, we propose that plasma balls map to a family of classically stable finite-energy black holes localized in the IR. We present a conjecture for the qualitative nature of large-mass black holes in such backgrounds and numerically construct these black holes in a particular class of warped geometries. These black holes have novel properties; in particular, their temperature approaches a nonzero constant value at large mass. Black holes dual to plasma balls shrink as they decay by Hawking radiation; towards the end of this process, they resemble ten-dimensional Schwarzschild black holes, which we propose are dual to small plasma balls. Our work may find practical applications in the study of the physics of localized black holes from a dual viewpoint.

The Hamiltonian constraint remains the major unsolved problem in loop quantum gravity (LQG). Some time ago, a mathematically consistent candidate Hamiltonian constraint was proposed but there are still several unsettled questions which concern the algebra of commutators among smeared Hamiltonian constraints which must be faced in order to make progress. In this paper, we propose a solution to this set of problems based on the so-called master constraint which combines the smeared Hamiltonian constraints for all smearing functions into a single constraint. Due to a harmonic interplay of several mathematical facts, the problems with the commutator algebra disappear and chances are good that one can control the solution space and the (quantum) Dirac observables of LQG. Even a decision on whether the theory has the correct classical limit and a connection with the path integral (or spin foam) formulation could be in reach.

Recently the master constraint programme (MCP) for loop quantum gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single master constraint. The MCP is designed to overcome the complications associated with the non-Lie-algebra structure of the Dirac algebra of Hamiltonian constraints and was successfully tested in various field theory models. For the case of 3+1 gravity itself, so far only a positive quadratic form for the master constraint operator was derived. In this paper, we close this gap and prove that the quadratic form is closable and thus stems from a unique self-adjoint master constraint operator. The proof rests on a simple feature of the general pattern according to which Hamiltonian constraints in LQG are constructed and thus extends to arbitrary matter coupling and holds for any metric signature. With this result the existence of a physical Hilbert space for LQG is established by standard spectral analysis.

The most general action, quadratic in the B fields as well as in the curvature F, having SO(3, 1) or SO(4) as the internal gauge group for a four-dimensional BF theory is presented and its symplectic geometry is displayed. It is shown that the space of solutions to the equations of motion for the BF theory can be endowed with symplectic structures alternative to the usual one. The analysis also includes topological terms and cosmological constant. The implications of this fact for gravity are briefly discussed.

We show that for hypersurface orthogonal Killing vectors the corresponding Chevreton superenergy currents will be conserved and proportional to the Killing vectors. This holds for four-dimensional Einstein–Maxwell spacetimes with an electromagnetic field that is source-free and inherits the symmetry of the spacetime. A similar result also holds for the trace of the Chevreton tensor. The corresponding Bel currents have previously been proven to be conserved and our result can be seen as giving further support to the concept of conserved mixed superenergy currents. The analogous case for a scalar field has also previously been proven to give conserved currents and we show, for completeness, that these currents also are proportional to the Killing vectors.

The boundary conditions for canonical vacuum general relativity are investigated at the quasi-local level. It is shown that fixing the area element on the 2-surface (rather than the induced 2-metric) is enough to have a well-defined constraint algebra, and a well-defined Poisson algebra of basic Hamiltonians parametrized by shifts that are tangent to and divergence free on. The evolution equations preserve these boundary conditions, and the value of the basic Hamiltonians gives 2+2-covariant, gauge-invariant 2-surface observables. The meaning of these observables is also discussed.

We study the gravitational vacuum star (gravastar) configuration as proposed by Cattoen et al (2005 Class. Quantum Grav.22 4189) in a model where the interior de Sitter spacetime segment is continuously extended to the exterior Schwarzschild spacetime. The multilayered structure of Mazur and Mottola (2001 Preprint gr-qc/0109035, 2003 Proc. 6th Workshop on Quantum Field Theory Under the Influence of External Conditions (Oklahoma) (Princeton, NJ: Rinton), Preprint gr-qc/0405111 (2004 Proc. Natl Acad. Sci.111 9545) is replaced by a continuous stress–energy tensor at the price of introducing anisotropy in the (fluid) model of the gravastar. Either with an ansatz for the equation of state connecting the radial p_r and tangential p_t pressure or with a calculated equation of state with non-homogeneous energy/fluid density, solutions are obtained which in all aspects satisfy the conditions expected for an anisotropic gravastar (Cattoen et al 2005 Class. Quantum Grav.22 4189). Certain energy conditions have been shown to be obeyed and a polytropic equation of state has been derived. Stability of the solution with respect to possible axial perturbation is shown to hold.

The current understanding of the quantum origin of cosmic structure is discussed critically. We point out that in the existing treatments a transition from a symmetric quantum state to an (essentially classical) non-symmetric state is implicitly assumed, but not specified or analysed in any detail. In facing this issue, we are led to conclude that new physics is required to explain the apparent predictive power of the usual schemes. Furthermore, we show that the novel way of looking at the relevant issues opens new windows from where relevant information might be extracted regarding cosmological issues and perhaps even clues about aspects of quantum gravity.

Cosmology in extended theories of gravity is considered assuming the Palatini variational principle, for which the metric and connection are independent variables. The field equations are derived to linear order in perturbations about the homogeneous and isotropic but possibly spatially curved background. The results are presented in a unified form applicable to a broad class of gravity theories allowing arbitrary scalar–tensor couplings and nonlinear dependence on the Ricci scalar in the gravitational action. The gauge-ready formalism exploited here makes it possible to obtain the equations immediately in any of the commonly used gauges. Of the three type of perturbations, the main attention is on the scalar modes responsible for the cosmic large-scale structure. Evolution equations are derived for perturbations in a late universe filled with cold dark matter and accelerated by curvature corrections. Such corrections are found to induce effective pressure gradients which are problematical in the formation of large-scale structure. This is demonstrated by analytic solutions in a particular case. A physical equivalence between scalar–tensor theories in metric and in Palatini formalisms is pointed out.

Transonic accretion onto astrophysical objects is a unique example of an analogue black hole realized in nature. In the framework of acoustic geometry, we study axially symmetric accretion and wind of a rotating astrophysical black hole or of a neutron star assuming isentropic flow of a fluid described by a polytropic equation of state. In particular, we analyse the causal structure of multitransonic configurations with two sonic points and a shock. Retarded and advanced null curves clearly demonstrate the presence of the acoustic black hole at regular sonic points and of the white hole at the shock. We calculate the analogue surface gravity and the Hawking temperature for the inner and outer acoustic horizons.

We present a general study about the relation between the vorticity tensor and the Poynting vector of the electromagnetic field for axially symmetric stationary electrovacuum metrics. The obtained expressions allow us to understand the role of the Poynting vector in the dragging of inertial frames. The particular case of the rotating massive charged magnetic dipole is analysed in detail. In addition, the electric and magnetic parts of the Weyl tensor are calculated and the link between the latter and the vorticity is established. Then we show that, in the vacuum case, the necessary and sufficient condition for the vanishing of the magnetic part is that the spacetime be static.

The paper considers the spectrum of axial perturbations ('pure r-modes') of slowly uniformly rotating, general relativistic stars. In a first step towards a full analysis, we analyse the evolution equations without the constraint. It is found that the system is unstable due to a continuum of oscillation frequencies with real parts smaller than zero. In addition, the resolvent of the corresponding generator of time evolution is found to have a special structure which was considered in a previous investigation on the oscillations of spherical Newtonian stars. From this structure follows the occurrence of a continuous part in the oscillation spectrum if the system is artificially restricted to a finite space, as is the case in most numerical investigations. Up to first order in the angular velocity Ω of the star that continuous part coincides with a corresponding part found in the low-frequency approximation.

We investigate the formation of acoustic horizons for an inviscid fluid moving in a pipe in the case of stationary, axi-symmetric, one-dimensional (rotations around the symmetry axis are absent) flow. We show that, differently from what is generally believed, the acoustic horizon forms in correspondence to either a local minimum or maximum of the flux tube cross-section. Similarly, the external potential is required to have either a maximum or a minimum at the horizon, so that the external force has to vanish there. Choosing a power-law equation of state for the fluid, P ∝ ρⁿ, we solve the equations of the fluid dynamics and show that the two possibilities are realized, respectively, for n > −1 and n < −1. The Chaplygin gas, characterized by n = −1, corresponds to the crossover between the normal and unusual behaviour. These results are also extended to the case of spherically symmetric flow.

The detection of the cosmic microwave background radiation (CMB) was one of the most important cosmological discoveries of the last century. With the development of interferometric gravitational wave detectors, we may be in a position to detect the gravitational equivalent of the CMB in this century. The cosmic gravitational background (CGB) is likely to be isotropic and stochastic, making it difficult to distinguish from instrument noise. The contribution from the CGB can be isolated by cross-correlating the signals from two or more independent detectors. Here we extend previous studies that considered the cross-correlation of two Michelson channels by calculating the optimal signal-to-noise ratio that can be achieved by combining the full set of interferometry variables that are available with a six link triangular interferometer. In contrast to the two channel case, we find that the relative orientation of a pair of coplanar detectors does not affect the signal-to-noise ratio. We apply our results to the detector design described in the Big Bang Observer (BBO) mission concept study and find that the BBO could detect a background with Ω_gw > 2.2 × 10⁻¹⁷.

The well-known Regge–Wheeler equation describes the axial perturbations of the Schwarzschild metric in the linear approximation. From a mathematical point of view it presents a particular case of the confluent Heun equation and can be solved exactly, due to recent mathematical developments. We present the basic properties of its general solution. A novel analytical approach and numerical techniques to study the boundary problems which correspond to quasi-normal modes of black holes and other simple models of compact objects are developed.

This paper concerns the absolute versus relative motion debate. The Barbour and Bertotti (1982) work may be viewed as an indirectly set up relational formulation of a portion of Newtonian mechanics. I consider further direct formulations of this and argue that the portion in question—universes with zero total angular momentum that are conservative and with kinetic terms that are (homogeneous) quadratic in their velocities—is capable of accommodating a wide range of classical physics phenomena. Furthermore, as I develop in paper II, this relational particle model is a useful toy model for canonical general relativity. I consider what happens if one quantizes relational rather than absolute mechanics, indeed whether the latter is misleading. By exploiting Jacobi coordinates, I show how to access many examples of quantized relational particle models and then interpret these from a relational perspective. By these means, previous suggestions of bad semiclassicality for such models can be eluded. I show how small (particle number) universe relational particle model examples display eigenspectrum truncation, gaps, energy interlocking and counterbalanced total angular momentum. These features mean that these small universe models make interesting toy models for some aspects of closed-universe quantum cosmology. Meanwhile, these features do not compromise the recovery of reality as regards the practicalities of experimentation in a large universe such as our own.

Relational particle models are employed as toy models for the study of the problem of time in quantum geometrodynamics. These models' analogue of the thin sandwich is resolved. It is argued that the relative configuration space and shape space of these models are close analogues from various perspectives of superspace and conformal superspace, respectively. The geometry of these spaces and quantization thereupon is presented. A quantity that is frozen in the scale-invariant relational particle model is demonstrated to be an internal time in a certain portion of the relational particle reformulation of Newtonian mechanics. The semiclassical approach for these models is studied as an emergent time resolution for these models, as are consistent records approaches.

We show, under certain conditions, that regular Israel–Wilson–Perjés black holes necessarily belong to the Majumdar–Papapetrou family.

The effect of the length of inflation on the power spectra of scalar and tensor perturbations is estimated using the power-law inflation model with a scale factor of a(η) = (−η)^p = t^q. Considering various pre-inflation models with radiation-dominated or scalar matter-dominated periods before inflation in combination with two matching conditions, the temperature angular power spectrum (TT) and temperature–polarization cross-power spectrum (TE) are calculated and a likelihood analysis is performed. It is shown that the discrepancies between the Wilkinson microwave anisotropy probe (WMAP) data and the ΛCDM model, such as suppression of the spectrum at l = 2, 3 and oscillatory behaviour, may be explained by the finite length of inflation model if the length of inflation is near 60 e-folds and q ⩾ 300. The proposed models retain similar values of χ² to that achieved by the ΛCDM model with respect to fit to the WMAP data, but display different characteristics of the angular TE power spectra at l ⩽ 20.

We study spherically symmetric dynamical horizons (SSDH) in spherically symmetric Einstein/matter spacetimes. We first determine sufficient and necessary conditions for an initial data set for the gravitational and matter fields to satisfy the dynamical horizon condition in the spacetime development. The constraint equations reduce to a single second-order linear 'master' equation, which leads to a systematic construction of all SSDH initial data sets with certain boundedness conditions. Turning from construction to existence, we find necessary and sufficient conditions for a given spherically symmetric spacetime to contain a SSDH.

The 'braneworld' (described by the usual worldvolume action) is a D-dimensional timelike surface embedded in an N-dimensional (N > D) warped, nonfactorizable spacetime. We first address the conditions on the warp factor required to have an extremal flat brane in a five-dimensional background. Subsequently, we deal with normal deformations of such extremal branes. The ensuing Jacobi equations are analysed to obtain the stability condition. It turns out that to have a stable brane, the warp factor should have a minimum at the location of the brane in the given background spacetime. To illustrate our results, we explicitly check the extremality and stability criteria for a few known co-dimension one braneworld models. Generalizations of the above formalism for the cases of (i) curved branes, (ii) asymmetrical warping and (iii) higher co-dimension braneworlds are then presented along with some typical examples for each. Finally, we summarize our results and provide perspectives for future work along these lines.

In several approaches to the quantum-gravity problem evidence has emerged of the validity of a 'GUP' (a generalized position–momentum uncertainty principle) and/or a 'MDR' (a modification of the energy–momentum dispersion relation), but very little is known about the implications of GUPs and MDRs for black-hole thermodynamics, another key topic for quantum-gravity research. We investigate an apparent link, already suggested in an earlier exploratory study involving two of us, between the possibility of a GUP and/or an MDR and the possibility of a log term in the area–entropy black-hole formula. We then obtain, from that same perspective, a modified relation between the mass of a black hole and its temperature, and we examine the validity of the 'generalized second law of black-hole thermodynamics' in theories with a GUP and/or an MDR. After an analysis of GUP- and MDR-modifications of the black-body radiation spectrum, we conclude the study with a description of the black-hole evaporation process.

We discuss three complementary aspects of scalar curvature singularities: asymptotic causal properties, asymptotic Ricci and Weyl curvature, and asymptotic spatial properties. We divide scalar curvature singularities into two classes: so-called asymptotically silent singularities and singularities that break asymptotic silence. The emphasis in this paper is on the latter class which has not been previously discussed. We illustrate the above aspects and concepts by describing the singularities of a number of representative explicit perfect fluid solutions.

Numerical results from a study of boson stars under nonspherical perturbations using a fully general relativistic 3D code are presented together with the analysis of emitted gravitational radiation. We have constructed a simulation code suitable for the study of scalar fields in space-times of general symmetry by bringing together components for addressing the initial value problem, the full evolution system and the detection and analysis of gravitational waves. Within a series of numerical simulations, we explicitly extract the Zerilli and Newman–Penrose scalar Ψ₄ gravitational waveforms when the stars are subjected to different types of perturbations. Boson star systems have rapidly decaying nonradial quasinormal modes and thus the complete gravitational waveform could be extracted for all configurations studied. The gravitational waves emitted from stable, critical and unstable boson star configurations are analysed and the numerically observed quasinormal mode frequencies are compared with known linear perturbation results. The superposition of the high frequency nonspherical modes on the lower frequency spherical modes was observed in the metric oscillations when perturbations with radial and nonradial components were applied. The collapse of unstable boson stars to black holes was simulated. The apparent horizons were observed to be slightly nonspherical when initially detected and became spherical as the system evolved. The application of nonradial perturbations proportional to spherical harmonics is observed not to affect the collapse time. An unstable star subjected to a large perturbation was observed to migrate to a stable configuration.

It is shown explicitly that when the characteristic vector field that defines a Gödel-type metric is also a Killing vector, there always exist closed timelike or null curves in spacetimes described by such a metric. For these geometries, the geodesic curves are also shown to be characterized by a lower-dimensional Lorentz force equation for a charged point particle in the relevant Riemannian background. Moreover, two explicit examples are given for which timelike and null geodesics can never be closed.

One of the possible noise sources for the space-based gravitational wave detector LISA (the Laser Interferometer Space Antenna), associated with its test masses, is that due to spatial variations in surface potential (or patch effect) across the surfaces of the test mass and its housing. Such variations will lead to force gradients which may result in a significant acceleration noise term. Another noise source is that due to temporal variations in the surface potential, which in conjunction with any ambient dc voltage or net free charge on the test mass may also produce a significant acceleration noise term. The ST-7 demonstrator mission is designed to test technologies for LISA, including the gravitational reference sensor, which contains a gold-coated gold/platinum (Au/Pt) alloy test mass, surrounded by a housing that carries the electrodes for sensing and control. We have used a Kelvin probe at the Goddard Space Flight Center to make spatial and temporal measurements of contact potential differences for a selection of materials (Au/Pt, beryllia, alumina, titanium) and coatings (gold, diamond-like carbon, indium tin oxide, titanium carbide). Our investigations indicate that subject to certain assumptions all of these coatings appear to satisfy the ST-7 requirement that patch effect spatial variations should be less than 100 mV. The data also revealed evidence of behavioural trends with pressure and possible contamination effects. Regarding temporal variations, the current accuracy of the instrument is limiting the measurements at a level above the likely LISA requirements. We discuss our results and draw some conclusions of relevance to LISA.

Full relativistic simulations in three dimensions invariably develop runaway modes that grow exponentially and are accompanied by violations of the Hamiltonian and momentum constraints. Recently, we introduced a numerical method (Hamiltonian relaxation) that greatly reduces the Hamiltonian constraint violation and helps improve the quality of the numerical model. We present here a method that controls the violation of the momentum constraint. The method is based on the addition of a longitudinal component to the traceless extrinsic curvature , generated by a vector potential w_i, as outlined by York. The components of w_i are relaxed to solve approximately the momentum constraint equations, slowly pushing the evolution towards the space of solutions of the constraint equations. We test this method with simulations of binary neutron stars in circular orbits and show that it effectively controls the growth of the aforementioned violations. We also show that a full numerical enforcement of the constraints, as opposed to the gentle correction of the momentum relaxation scheme, results in the development of instabilities that stop the runs shortly.

We study the Einstein–Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein–Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.

The Lagrangian formulation of the D = 4 bosonic string and superstring in terms of the (super)twistors is considered. The (super)twistor form of the equations of motion is derived and the κ-symmetry transformation for the supertwistors is given. It is shown that the covariant κ-symmetry gauge fixation results in the action quadratic in the (super)twistor variables.

In a paper by Maartens, Lesame and Ellis (1998) it was shown that irrotational dust solutions with vanishing electric part of the Weyl tensor are subject to severe integrability conditions and it was conjectured that the only such solutions are FLRW spacetimes. In their analysis the possibility of a cosmological constant Λ was omitted. The conjecture is proved, irrespective of whether Λ is zero or not, and qualitative differences with the case of vanishing magnetic Weyl curvature are pointed out.

In the last 20 years, loop quantum gravity, a background-independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to gravity in this framework. A Hamiltonian operator for the scalar field can be well defined in the coupled diffeomorphism-invariant Hilbert space, which is both self-adjoint and positive. On the other hand, the Hamiltonian constraint operator for the scalar field coupled to gravity can be well defined in the coupled kinematical Hilbert space. There are one-parameter ambiguities due to scalar field in the construction of both operators. The results heighten our confidence that there is no divergence within this background-independent and diffeomorphism-invariant quantization approach of matter coupled to gravity. Moreover, to avoid possible quantum anomaly, the master constraint programme can be carried out in this coupled system by employing a self-adjoint master constraint operator on the diffeomorphism-invariant Hilbert space.