Table of contents

One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by the recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of Brownian motion whose correlation length is given by the Planck length up to a scaling factor. With input from recent matter wave experiments, we show the minimum value of this factor to be well within the expected range for quantum gravity theories. This suggests that the sensitivities of advanced matter wave interferometers may be approaching the fundamental level due to quantum spacetime fluctuations, and that investigating Planck scale physics using matter wave interferometry may become a reality in the near future.

In a series of papers (see de Felice et al 2004 Astrophys. J.607 580–95, and references therein) a relativistic astrometric model, termed RAMOD, was developed, with the purpose of deducing from the observations made by the satellite GAIA the position and motion of the stars of our galaxy. In this model, the solar system is assumed to be the only source of gravity; moreover, since GAIA is expected to provide data with an accuracy of a microarcsecond in the measurements of angles, the model has been conceived to include terms of the order —with c being the vacuum light velocity—in order to reach the same accuracy. Since RAMOD is operated by a numerical code, it can produce numerical solutions only; some analytical form of the solutions is yet needed, in order to write down and solve the error equations. Using variational methods, in this paper we provide an analytical solution which agrees with the numerically determined one to the same order of accuracy and in the same operational conditions of the satellite. Thanks to this approach, we are also able both to identify the position of a star with only one integration from observations made at two different satellite positions and to derive the coordinate components of the stellar motion—if detectable—simply by iterating the above procedure of position measurements after a suitable interval of the orbital time. Finally, we also determine the uncertainties of the solutions—the error budget—arising from the statistical errors of the boundary conditions. The relations linking the errors in the solutions with the uncertainties of the observables are known as 'condition equations'.

Gravitational waves from coalescing compact binaries are searched for using the matched filtering technique. As the model waveform depends on a number of parameters, it is necessary to filter the data through a template bank covering the astrophysically interesting region of the parameter space. The choice of templates is defined by the maximum allowed drop in signal-to-noise ratio due to the discreteness of the template bank. In this paper we describe the template-bank algorithm that was used in the analysis of data from the Laser Interferometer Gravitational Wave Observatory (LIGO) and GEO 600 detectors to search for signals from binaries consisting of non-spinning compact objects. Using Monte Carlo simulations, we study the efficiency of the bank and show that its performance is satisfactory for the design sensitivity curves of ground-based interferometric gravitational wave detectors GEO 600, initial LIGO, advanced LIGO and Virgo. The bank is efficient in searching for various compact binaries such as binary primordial black holes, binary neutron stars, binary black holes, as well as a mixed binary consisting of a non-spinning black hole and a neutron star.

We develop a flux-conservative formalism for a Newtonian multi-fluid system, including dissipation and entrainment (i.e. allowing the momentum of one fluid to be a linear combination of the velocities of all fluids). Maximum use is made of mass, energy and linear and angular momentum conservation to specify the equations of motion. Also used extensively are insights gleaned from a convective variational action principle, the key being the distinction between each velocity and its canonically conjugate momentum (which is modified because of entrainment). Dissipation is incorporated to second order in the 'thermodynamic forces' via the approach pioneered by Onsager, which makes it transparent how to guarantee the law of increase of entropy. An immediate goal of the investigation is to understand better the number, and form, of independent dissipation terms required for a consistent set of equations of motion in the multi-fluid context. A significant, but seemingly innocuous detail is that one must be careful to isolate 'forces' that can be written as total gradients, otherwise errors can be made in relating the net internal force to the net externally applied force. Our long-range aim is to provide a formalism that can be used to model dynamical multi-fluid systems both perturbatively and via fully nonlinear 3D numerical evolutions. To elucidate the formalism we consider the standard model for a heat-conducting, superfluid neutron star, which is believed to be dominated by superfluid neutrons, superconducting protons and a highly degenerate, ultra-relativistic gas of normal fluid electrons. We determine that in this case there are, in principle, 19 dissipation coefficients in the final set of equations. A final reduction of the system is made by neglecting heat conduction. This leads to an extension of the standard two-fluid model for neutron star cores, which has been used in a number of previous applications, and illustrates how mutual friction is represented in our formalism.

We consider the Casimir effect for the massless conformal scalar field in an n-dimensional, closed, static universe. We calculate the renormalized vacuum energy density using the covariant point-splitting method, the mode-sum regularization and the renormalized vacuum energy with the zeta-function regularization. We observe that all odd spacetime dimensions give us the zero renormalized vacuum energy density. For even spacetime dimensions the renormalized vacuum energy density oscillates in sign. The result agrees with three regularization techniques. The Casimir energy density for spherical universes in n-dimensional spacetime is regarded as interesting both to understand the correspondence between the sign of the effect and the dimension of manifold in topology and as a key to confirming the Casimir energy for half spherical universes (manifold with boundary) in n-dimensional spacetime.

We are concerned with the issue of the quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in loop quantum gravity. It relies on the specific choice of scalar field variables referred to as the polymer variables. The quantization, in our formulation, amounts to introducing the 'quantum' polymer ∗-star algebra and looking for positive linear functionals, called states. As assumed in our paper, homeomorphism invariance allows us to derive the complete class of the states. They are determined by the homeomorphism invariant states defined on the CW-complex ∗-algebra. The corresponding GNS representations of the polymer ∗-algebra and their self-adjoint extensions are derived, the equivalence classes are found, and invariant subspaces characterized. In part I we outlined those results. Here, we present the technical details.

We study the quantum properties of the Kantowski–Sachs spacetime, using ideas from loop quantum gravity. This spacetime coincides with the Schwarzschild black hole solution inside the horizon. Recently it was shown that the classical black hole singularity is controlled by the quantum theory, using ADM variables. In this paper we have used Ashtekar-like variables, obtaining information both on quantum effects on the singularity and on the dynamics across the r = 0 singular point. Finally, we have found a regular spacetime inside the horizon and that the dynamics can be extended beyond the classical singularity.

An attempt is made to follow up earlier investigations regarding the non-asymptotic flatness of the Wahlquist solution to second order, and to use this property to suggest a physical interpretation for the shape of the fluid. We demonstrate that by perturbing the boundary of the Wahlquist solution, it is possible to generate boundary data so that once the exterior metric has been obtained to first and second orders in the rotation speed using the Ernst potential method, it is possible in principle to perform up to second-order Cauchy matching of the interior and exterior fields. Finally, it is shown that while the first-order solution is asymptotically flat, the second-order solution is not so, and we briefly describe a reason for this.

The time-independent spherically symmetric solutions of general relativity coupled to a dynamical unit timelike vector are studied. We find that there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness restricts to two parameters and requiring that the aether be aligned with the timelike Killing field further restricts to one parameter, the total mass. These 'static aether' solutions are given analytically up to solution of a transcendental equation. The positive mass solutions have spatial geometry with a minimal area 2-sphere, inside which the area diverges at a curvature singularity occurring at an extremal Killing horizon that lies at a finite affine parameter along a radial null geodesic. Regular perfect fluid star solutions are shown to exist with static aether exteriors, and the range of stability for constant density stars is identified.

We study black hole solutions in general relativity coupled to a unit timelike vector field dubbed the 'aether'. To be causally isolated, a black hole interior must trap matter fields as well as all aether and metric modes. The theory possesses spin-0, spin-1 and spin-2 modes whose speeds depend on four coupling coefficients. We find that the full three-parameter family of local spherically symmetric static solutions is always regular at a metric horizon, but only a two-parameter subset is regular at a spin-0 horizon. Asymptotic flatness imposes another condition, leaving a one-parameter family of regular black holes. These solutions are compared to the Schwarzschild solution using numerical integration for a special class of coupling coefficients. They are very close to Schwarzschild outside the horizon for a wide range of couplings, and have a spacelike singularity inside, but differ inside quantitatively. Some quantities constructed from the metric and aether oscillate in the interior as the singularity is approached. The aether is at rest at spatial infinity and flows into the black hole, but differs significantly from the 4-velocity of freely falling geodesics.

We present a discussion of the problems associated with generation of multiple control sidebands for length sensing and control of dual-recycled, cavity-enhanced Michelson interferometers and the motivation behind more complicated sideband generation methods. We focus on the Mach–Zehnder interferometer as a topological solution to the problem and present results from tests carried out at the Caltech 40 m prototype gravitational wave detector. The consequences for sensing and control for advanced interferometry are discussed, as are the implications for future interferometers such as Advanced LIGO.

The volume operator plays a pivotal role for the quantum dynamics of loop quantum gravity (LQG). It is essential to construct triad operators that enter the Hamiltonian constraint and which become densely defined operators on the full Hilbert space, even though in the classical theory the triad becomes singular when classical GR breaks down. The expression for the volume and triad operators derives from the quantization of the fundamental electric flux operator of LQG by a complicated regularization procedure. In fact, there are two inequivalent volume operators available in the literature and, moreover, both operators are unique only up to a finite, multiplicative constant which should be viewed as a regularization ambiguity. Now on the one hand, classical volumes and triads can be expressed directly in terms of fluxes and this fact was used to construct the corresponding volume and triad operators. On the other hand, fluxes can be expressed in terms of triads and triads can be replaced by Poisson brackets between the holonomy and the volume operators. Therefore one can also view the holonomy operators and the volume operator as fundamental and consider the flux operator as a derived operator. In this paper we mathematically implement this second point of view and thus can examine whether the volume, triad and flux quantizations are consistent with each other. The results of this consistency analysis are rather surprising. Among other findings we show the following. (1) The regularization constant can be uniquely fixed. (2) One of the volume operators can be ruled out as inconsistent. (3) Factor ordering ambiguities in the definition of triad operators are immaterial for the classical limit of the derived flux operator. The results of this paper show that within full LQG triad operators are consistently quantized. In this paper we merely present ideas and the results of the consistency check. In a companion paper we supply detailed proofs.

In this paper, we provide the techniques and proofs for the results presented in our companion paper concerning the consistency check on volume and triad operator quantization in loop quantum gravity.

In this pedagogical note, we discuss obstacles to the usual Palatini formulations of gauge and gravity theories in the presence of odd-derivative order, Chern–Simons terms.