A. Spallicci

Mass and motion in general relativity

We discuss some effects induced by quantum field fluctuations on mass, inertia and gravitation. Recalling the problem raised by vacuum field fluctuations with respect to inertia and gravitation, we show that vacuum energy differences, such as Casimir energy, do contribute to inertia. Mass behaves as a quantum observable and in particular possesses quantum fluctuations. We show that the compatibility of the quantum nature of mass with gravitation can be ensured by conformal symmetries, which allow one to formulate a quantum version of the equivalence principle. Finally, we consider some corrections to the coupling between metric fields and energy-momentum tensors induced by radiative corrections. Newton gravitation constant is replaced by two different running coupling constants in the sectors of traceless and traced tensors. There result metric extensions of general relativity, which can be characterized by modified Ricci curvatures or by two gravitation potentials. The corresponding phenomenological framework extends the usual Parametrized Post-Newtonian one, with the ability to remain compatible with classical tests of gravity while accounting for new features, such as Pioneer like anomalies or anomalous light deflection.

Expected coalescence rates of NS-NS binaries for laser beam interferometers

The coalescence rate of two neutron stars (NS) is revisited. To estimate the number of bound NS-NS and the probability of their coalescence in a time scale τ, the galactic star formation history, directly derived from observations, and the evolution of massive stars are considered. The newly established galactic merging rate is (1.7±1.0) × 10-5yr-1, while the local merging rate, including the contribution of elliptical galaxies, is about a factor of two higher, 3.4 × 10-5yr-1. Using the present data basis on galaxy distribution in the local universe and the expected sensitivity of the first generation of laser beam interferometers, we estimate that one event should occur every 125 years for LIGO and one event each 148 years for VIRGO. The situation is considerably improved for advanced-LIGO, since we predict that 6 events per year should be detected whereas for a recently proposed VIRGO new configuration, the event rate might increase up to 3 events every two years.

Associated radius, energy and pressure of McVittie's metric, in its astrophysical application

SummaryThe McVittie metric is found to suffer inherent limitations. It is shown that the radius of the metric associated to the sphere has a correct asymptotic behaviour, àla Schwarzschild at the origin and àla Robertson- Walker when the the radial coordinater approaches infinity; but for intermediate values ofr and acceptable mass values of the Schwarzschild singularity, minimum and maximum are present, both disappearing solely for mass values larger than the universe radius. Furthermore, the pressure is infinite at the Schwarzschild radius, while the energy is negative for particular values of negative universe curvature. An alternative interpretation, reverse to the purposes of the McVittie solution, hints at a metric comparable to an internal solution.

Photon mass limits from fast radio bursts

The frequency-dependent time delays in fast radio bursts (FRBs) can be used to constrain the photon mass, if the FRB redshifts are known, but the similarity between the frequency dependences of dispersion due to plasma effects and a photon mass complicates the derivation of a limit on mγ. The dispersion measure (DM) of FRB 150418 is known to ∼0.1%, and there is a claim to have measured its redshift with an accuracy of ∼2%, but the strength of the constraint on mγ is limited by uncertainties in the modelling of the host galaxy and the Milky Way, as well as possible inhomogeneities in the intergalactic medium (IGM). Allowing for these uncertainties, the recent data on FRB 150418 indicate that mγ≲1.8×10−14 eVc−2 (3.2×10−50 kg), if FRB 150418 indeed has a redshift z=0.492 as initially reported. In the future, the different redshift dependences of the plasma and photon mass contributions to DM can be used to improve the sensitivity to mγ if more FRB redshifts are measured. For a fixed fractional uncertainty in the extra-galactic contribution to the DM of an FRB, one with a lower redshift would provide greater sensitivity to mγ.

Experiments on fundamental physics on the space station

Original proposals and experiments on gravitation and fundamental metrology on the space station are described. These experiments were formulated in the Metrology and Gravitation Science Team, in two ESA industrial study contracts, on microsatellites and on time and frequency science, within the space station scenario. Although limited by the design constraints of the space station, the experiments range from clock-based tests on special and general relativity to, with additional infrastructure, the equivalence principle and the detection of gravitational waves. Supporting technology, such as damping systems and microgravity cooled atom clocks, is also described. Finally, the major scientific goals, the experiments, hardware and the status are summarized. This work represents the first coordinated attempt, at least within the European space programmes, to consider experiments on relativity and fundamental physics without resorting to experiment dedicated space missions. For details on specific issues a large bibliography is referred to.

Dispersion by pulsars, magnetars, fast radio bursts and massive electromagnetism at very low frequencies

Our understanding of the universe relies mostly on electromagnetism. As photons are the messengers, fundamental physics is concerned in testing their properties. Photon mass upper limits have been earlier set through pulsar observations, but new investigations are offered by the excess of dispersion measure (DM), sometimes observed with pulsar and magnetar data at low frequencies, or with the fast radio bursts (FRBs), of yet unknown origin. Arguments for the excess of DM do not reach a consensus, but are not mutually exclusive. Thus, we remind that for massive electromagnetism, dispersion goes as the inverse of the frequency squared. Thereby, new avenues are offered also by the recently operating ground observatories in 10–80 MHz domain and by the proposed Orbiting Low Frequency Antennas for Radio astronomy (OLFAR). The latter acts as a large aperture dish by employing a swarm of nano-satellites observing the sky for the first time in the 0.1–15 MHz spectrum. The swarm must be deployed sufficiently away from the ionosphere to avoid distorsions from terrestrial interference, especially during solar maxima, and offer stable conditions for calibration during observations.

Effective photon mass by Super and Lorentz symmetry breaking

In the context of Standard Model Extensions (SMEs), we analyse four general classes of Super Symmetry (SuSy) and Lorentz Symmetry (LoSy) breaking, leading to observable imprints at our energy scales. The photon dispersion relations show a non-Maxwellian behaviour for the CPT (Charge-Parity-Time reversal symmetry) odd and even sectors. The group velocities exhibit also a directional dependence with respect to the breaking background vector (odd CPT) or tensor (even CPT). In the former sector, the group velocity may decay following an inverse squared frequency behaviour. Thus, we extract a massive Carroll–Field–Jackiw photon term in the Lagrangian and show that the effective mass is proportional to the breaking vector and moderately dependent on the direction of observation. The breaking vector absolute value is estimated by ground measurements and leads to a photon mass upper limit of 10−19eVor 2 ×10−55kg, and thereby to a potentially measurable delay at low radio frequencies.

Expected coalescence rate of double neutron stars for ground-based interferometers

In this paper we present new estimates of the coalescence rate of neutron star binaries in the local universe, and we discuss its consequences for the first generations of ground-based interferometers. Our approach based on both evolutionary and statistical methods gives a galactic merging rate of 1.7 × 10−5 yr−1, in the range of previous estimates 10−6 to 10−4 yr−1. The local rate which includes the contribution of elliptical galaxies is two times higher, in the order of 3.4 × 10−5 yr−1. We predict one detection every 148 and 125 years with initial VIRGO and LIGO, and up to six events per year with their advanced configuration. Our recent detection rate estimates from investigations on VIRGO future improvements are quoted.

A fully relativistic radial fall

Radial fall has historically played a momentous role. It is one of the most classical problems, the solutions of which represent the level of understanding of gravitation in a given epoch. A {\it gedankenexperiment} in a modern frame is given by a small body, like a compact star or a solar mass black hole, captured by a supermassive black hole. The mass of the small body itself and the emission of gravitational radiation cause the departure from the geodesic path due to the back-action, that is the self-force. For radial fall, as any other non-adiabatic motion, the instantaneous identity of the radiated energy and the loss of orbital energy cannot be imposed and provide the perturbed trajectory. In the first part of this letter, we present the effects due to the self-force computed on the geodesic trajectory in the background field. Compared to the latter trajectory, in the Regge-Wheeler, harmonic and all others smoothly related gauges, a far observer concludes that the self-force pushes inward (not outward) the falling body, with a strength proportional to the mass of the small body for a given large mass; further, the same observer notes an higher value of the maximal coordinate velocity, this value being reached earlier on during infall. In the second part of this letter, we implement a self-consistent approach for which the trajectory is iteratively corrected by the self-force, this time computed on osculating geodesics. Finally, we compare the motion driven by the self-force without and with self-consistent orbital evolution. Subtle differences are noticeable, even if self-force effects have hardly the time to accumulate in such a short orbit.

VIRGO detector optimization for gravitational waves by inspiralling binaries

For future configurations, we study the relation between the abatement of the noise sources and the signal-to-noise ratio (SNR) for coalescing binaries. Our aim is not the proposition of a new design, but an indication of where in the bandwidth or for which noise source a noise reduction would be most efficient. We take VIRGO as the reference for our considerations, solely applicable to the inspiralling phase of a coalescing binary. Thus, only neutron stars and small black holes of a few solar masses are encompassed by our analysis. The contributions to the SNR given by final merge and quasi-normal ringing are neglected. It is identified that (i) the reduction in the mirror thermal noise band provides the highest gain for the SNR, when the VIRGO bandwidth is divided according to the dominant noises; (ii) there exists a specific frequency at which lies the largest potential increment in the SNR, and the enlargement of the bandwidth, where the noise is reduced, produces a shift of such an optimal frequency to higher values; (iii) the abatement of the pendulum thermal noise provides the largest, but modest, gain, when noise sources are considered separately. Our recent astrophysical analysis of event rates for neutron stars leads to a detection rate of one every 148 or 125 years for VIRGO and LIGO, respectively, while a recently proposed and improved, but still conservative, VIRGO configuration would provide an increase to 1.5 events per year. Instead, a bi-monthly event rate, similar to advanced LIGO, requires a 16 times gain. We analyse the 3D (pendulum, mirror, shot noises) parameter space showing how such a gain could be achieved.