Satellite measurement of the Hannay angle

The concept of a measurement of the yet unevaluated Hannay angle, by means of an Earth-bound satellite, adiabatically driven by the Moon, is shown herein. Numerical estimates are given for the angles, the orbital displacements, the shortening of the orbital periods, for different altitudes. It is concluded that the Hannay effect is measurable in high Earth orbits, by means of atomic clocks, accurate Time & Frequency transfer system and precise positioning.Comment: Lette

Solar wind test of the de Broglie-Proca's massive photon with Cluster multi-spacecraft data

Our understanding of the universe at large and small scales relies largely on electromagnetic observations. As photons are the messengers, fundamental physics has a concern in testing their properties, including the absence of mass. We use Cluster four spacecraft data in the solar wind at 1 AU to estimate the mass upper limit for the photon. We look for deviations from Amp\`ere's law, through the curlometer technique for the computation of the magnetic field, and through the measurements of ion and electron velocities for the computation of the current. We show that the upper bound for $m_\gamma$ lies between $1.4 \times 10^{-49}$ and $3.4 \times 10^{-51}$ kg, and thereby discuss the currently accepted lower limits in the solar wind.Comment: The paper points out that actual photon mass upper limits (in the solar wind) are too optimistic and model based. We instead perform a much more experiment oriented measurement. This version matches that accepted by Astroparticle Physic

A source-free integration method for black hole perturbations and self-force computation: Radial fall

Perturbations of Schwarzschild-Droste black holes in the Regge-Wheeler gauge benefit from the availability of a wave equation and from the gauge invariance of the wave function, but lack smoothness. Nevertheless, the even perturbations belong to the C\textsuperscript{0} continuity class, if the wave function and its derivatives satisfy specific conditions on the discontinuities, known as jump conditions, at the particle position. These conditions suggest a new way for dealing with finite element integration in time domain. The forward time value in the upper node of the $(t, r^*$) grid cell is obtained by the linear combination of the three preceding node values and of analytic expressions based on the jump conditions. The numerical integration does not deal directly with the source term, the associated singularities and the potential. This amounts to an indirect integration of the wave equation. The known wave forms at infinity are recovered and the wave function at the particle position is shown. In this series of papers, the radial trajectory is dealt with first, being this method of integration applicable to generic orbits of EMRI (Extreme Mass Ratio Inspiral).Comment: This arXiv version differs from the one to be published by Phys. Rev. D for the use of British English and other minor editorial difference

Newtonian free fall with an Einsteinian view

Free fall is revisited through the legendary Pisa tower experiment. We suppose the absence of air friction and neglect the Earth non-spherical shape, its inhomogeneities and rotation. Asking whether 1kg stone falls like one of 2kg, young pupils may reply negatively, possibly supposing a difference of a factor two. Instead, teachers may say "exactly yes". The right reply is multi-faceted. It is "exactly yes" only in the Earth fixed frame, that by construction is unaffected by any falling mass, whereas in all other frames the answer is "approximately yes". We start considering each mass being released separately and keep the Earth-stone initial distance as fixed throughout the work. If the observer is at a fixed distance from the Earth centre, e.g., on the Earth surface, he will measure the sum of the acceleration of the stone towards the Earth and of the Earth towards the stone: the larger the stone, the larger the sum perceived by the observer. If the observer is at a fixed distance from the system (Earth and stone) centre of mass (or else imagine that the stone is that heavy to shift the system centre of mass outside the Earth), he will observe the Earth and the stone falling toward him and reaching the system centre of mass at the same instant. Keeping the initial distance Earth-stone constant, by increasing the mass of the stone, the system centre of mass will shift towards the stone and this latter will undergo a smaller acceleration having to cover a smaller distance: the larger the stone, the smaller the acceleration.    In these two last frames, the difference in fall is minuscule, being of the order of the stone/Earth mass ratio, thus not yet measurable by state-of-the-art technology. For the Commander Scott of Apollo 15, the difference in fall between the plume and the hammer was in the order of 6x10-24 s. Nevertheless, this ratio may take large values and be of considerable impact in astronomy. But most stimulating, the heavier stone falls faster or slower than the lighter one depending on the observer. The physics dependency on the observer rises to feature of paramount significance in Einstein's general relativity and thus Newtonian radial fall may be used to introduce gauge dependence. Dealing with two masses released simultaneously, the answer to the three body-problem is numerical, knowing that the system centre of mass will not be equidistant to the two small, but different, masses. The preceding doesn’t violate in any manner the equivalence principle of inertial and gravitational mass. We briefly deal with radial fall in general relativity where the motion of the falling mass is influenced by the mass ratio as in Newtonian gravity but also by the radiation emitted. In the context of the Pisa tower, the energy-time Heisenberg indetermination impedes measuring the gravitational radiation. Instead, the capture of small black holes falling into supermassive ones is the source targeted by LISA to explore general relativity in the strong field. Finally, the analysis of falling observers in black holes during emission of Hawking radiation is of interest for combining quantum mechanics and general relativity. FURTHER READING Barausse E. et al. (2020). Prospects for fundamental physics with LISA. General Relativity and Gravitation, 52, 81. https://doi.org/10.1007/s10714-020-02691-1 Ritter P., Aoudia S., Spallicci A.D.A.M., Cordier S. (2016). Indirect (source-free) integration method. II. Self-force consistent radial fall, Int. J. Geom. Meth. Mod. Phys., 13, 1650019. https://doi.org/10.1142/S0219887816500195 Spallicci A., (2011). Self-force and free fall: an historical perspective, Springer Series on Fundamental Theory of Physics Vol. 162, L. Blanchet, A. Spallicci, B. Whiting, Eds., p. 561. https://link.springer.com/book/10.1007%2F978-90-481-3015-3 Spallicci A.D.A.M., van Putten M.H.P.M., (2016). Gauge dependence and self-force in Galilean and Einsteinian free falls, Pisa tower and evaporating black holes at general relativity centennial. International Journal of Geometric Methods in Modern Physics, 13(8), 1630014. https://doi.org/10.1142/S021988781630014

Towards a self-consistent orbital evolution for EMRIs

We intend to develop part of the theoretical tools needed for the detection of gravitational waves coming from the capture of a compact object, 1-100 solar masses, by a Supermassive Black Hole, up to a 10 billion solar masses, located at the centre of most galaxies. The analysis of the accretion activity unveils the star population around the galactic nuclei, and tests the physics of black holes and general relativity. The captured small mass is considered a probe of the gravitational field of the massive body, allowing a precise measurement of the particle motion up to the final absorption. The knowledge of the gravitational signal, strongly affected by the self-force - the orbital displacement due to the captured mass and the emitted radiation - is imperative for a successful detection. The results include a strategy for wave equations with a singular source term for all type of orbits. We are now tackling the evolution problem, first for radial fall in Regge- Wheeler gauge, and later for generic orbits in the harmonic or de Donder gauge for Schwarzschild-Droste black holes. In the Extreme Mass Ratio Inspiral, the determination of the orbital evolution demands that the motion of the small mass be continuously corrected by the self-force, i.e. the self-consistent evolution. At each of the integration steps, the self-force must be computed over an adequate number of modes; further, a differential-integral system of general relativistic equations is to be solved and the outputs regularised for suppressing divergences. Finally, for the provision of the computational power, parallelisation is under examination.Comment: IX Lisa Conference (held the 21-25 May 2012 in Paris) Proceedings by the Astronomical Society of the Pacific Conference Seri

Gauge dependence and self-force from Galilean to Einsteinian free fall, compact stars falling into black holes, Hawking radiation and the Pisa tower at the general relativity centennial

(Short abstract). In Galilean physics, the universality of free fall implies an inertial frame, which in turns implies that the mass m of the falling body is omitted. Otherwise, an additional acceleration proportional to m/M would rise either for an observer at the centre of mass of the system, or for an observer at a fixed distance from the centre of mass of M. These elementary, but overlooked, considerations fully respect the equivalence principle and the identity of an inertial or a gravitational pull for an observer in the Einstein cabin. They value as fore-runners of the self-force and gauge dependency in general relativity. The approximate nature of Galilei's law of free fall is explored herein. When stepping into general relativity, we report how the geodesic free fall into a black hole was the subject of an intense debate again centred on coordinate choice. Later, we describe how the infalling mass and the emitted gravitational radiation affect the free fall motion of a body. The general relativistic self-force might be dealt with to perfectly fit into a geodesic conception of motion. Then, embracing quantum mechanics, real black holes are not classical static objects any longer. Free fall has to handle the Hawking radiation, and leads us to new perspectives on the varying mass of the evaporating black hole and on the varying energy of the falling mass. Along the paper, we also estimate our findings for ordinary masses being dropped from a Galilean or Einsteinian Pisa-like tower with respect to the current state of the art drawn from precise measurements in ground and space laboratories, and to the constraints posed by quantum measurements. The appendix describes how education physics and high impact factor journals discuss the free fall. Finally, case studies conducted on undergraduate students and teachers are reviewed

Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem

In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics, there are theorems which have been proposed for proving the non-existence of entropy in the latter sense. We explicate, clarify and extend the proofs of these theorems to some standard matter (scalar and electromagnetic) field theories in curved spacetime, and then we show why these proofs fail in general relativity; due to properties of the gravitational Hamiltonian and phase space measures, the second law of thermodynamics holds. As a concrete application, we focus on the consequences of these results for the gravitational two-body problem, and in particular, we prove the non-compactness of the phase space of perturbed Schwarzschild-Droste spacetimes. We thus identify the lack of recurring orbits in phase space as a distinct sign of dissipation and hence entropy production.Comment: 39 pages, 3 figures; v2: version to appear in Phys. Rev. D, references adde

Questioning the H0H_0 tension via the look-back time

The Hubble tension is investigated taking into account the cosmological look-back time. Specifically, considering a single equation, widely used in standard cosmology, it is possible to recover both values of the Hubble constant $H_0$ reported by the SH0ES and Planck collaborations: the former is obtained through cosmological ladder methods (e.g. Cepheids, Supernovae Type IA) and the latter through measurements of the Cosmic Microwave Background. Also, other values obtained in the literature are achieved with the same approach. We conclude that the Hubble tension can be removed if the look-back time is correctly referred to the redshift where the measurement is performed.Comment: 8 pages, 1 figure, accepted for publication in Physics of the Dark Univers