Relativistic Langevin Equation derived from a particle-bath Lagrangian

We show how a relativistic Langevin equation can be derived from a Lorentz-covariant version of the Caldeira-Leggett particle-bath Lagrangian. In one of its limits, we identify the obtained equation with the Langevin equation used in contemporary extensions of statistical mechanics to the near-light-speed motion of a tagged particle in non-relativistic dissipative fluids. The proposed framework provides a more rigorous and first-principles form of the weakly-relativistic and partially-relativistic Langevin equations often quoted or postulated as ansatz in previous works. We then refine the aforementioned results to obtain a generalized Langevin equation valid for the case of both fully-relativistic particle and bath, using an analytical approximation obtained from numerics where the Fourier modes of the bath are systematically replaced with covariant plane-wave forms with a length-scale relativistic correction that depends on the space-time trajectory in a parabolic way. We discuss the implications of the apparent breaking of space-time translation and parity invariance, showing that these effects are not necessarily in contradiction with the assumptions of statistical mechanics. The intrinsically non-Markovian character of the fully relativistic generalised Langevin equation derived here, and of the associated fluctuation-dissipation theorem, is also discussed.

A novel mechanism for probing the Planck scale

The Planck or the quantum gravity scale, being $16$ orders of magnitude greater than the electroweak scale, is often considered inaccessible by current experimental techniques. However, it was shown recently by one of the current authors that quantum gravity effects via the Generalized Uncertainty Principle affects the time required for free wavepackets to double their size, and this difference in time is at or near current experimental accuracies [1,2]. In this work, we make an important improvement over the earlier study, by taking into account the leading order relativistic correction, which naturally appears in the sytems under consideration, due to the significant mean velocity of the travelling wavepackets. Our analysis shows that although the relativistic correction adds nontrivial modifications to the results of [1,2], the earlier claims remain intact and are in fact strengthened. We explore the potential for these results being tested in the laboratory.

Bc → J/ψ tensor form factors at large momentum recoil

We present a next-to-leading order (NLO) relativistic correction to [Formula: see text] tensor form factors within nonrelativistic QCD (NRQCD). We also consider complete Dirac bilinears [Formula: see text] with [Formula: see text] matrices [Formula: see text] in the [Formula: see text] transition. The relation among different current form factors is given and it shows that symmetries emerge in the heavy bottom quark limit. For a phenomenological extension, we propose to extract the long-distance matrix elements (LDMEs) for [Formula: see text] meson from the recent HPQCD lattice data and the NLO form factors at large momentum recoil.

Relativistic synchronization of onboard clocks of navigation space vehicles with the aid of intersatellite measurements

The problem of the synchronization of onboard clocks of navigation satellites has considered from a relativistic point of view using the concept of “coordinate simultaneity”. This concept allows an unambiguous interpretation of the synchronization results within the framework of general relativity. The algorithm of intersatellite measurements processing has formulated in terms of a proper time of a space vehicle and the coordinate time of a reference frame. Rules of transformation between coordinate and proper time scales have indicated. An analytical expression has obtained for the periodic relativistic correction to the estimated value of the relative clock drift. This correction has expressed in terms of the coordinate time of a ground observer. The value of this correction exceeds the acceptable synchronization error and should be taken into account for the inter-satellite measurements processing. The error of the relativistic correction determination has calculated. This error provides an upper limit for the period of uploading of ephemeris data on the board of the space vehicle.

Lense–Thirring precession and gravito–gyromagnetic ratio

The geodesics of bound spherical orbits i.e. of orbits performing Lense–Thirring precession, are obtained in the case of the $$\varLambda $$ Λ term within the gravito-electromagnetic formalism. It is shown that the presence of the $$\varLambda $$ Λ -term in the equations of gravity leads to both relativistic and non-relativistic corrections in the equations of motion. The contribution of the $$\varLambda $$ Λ -term in the Lense–Thirring precession is interpreted as an additional relativistic correction and the gravito–gyromagnetic ratio is defined.

Gravitational radiation by magnetic field: application to millisecond magnetars

ABSTRACT We investigate the direct contribution of the magnetic field to the gravitational wave (GW) generation. To do so, we study the post-Newtonian (PN) energy–momentum tensor of the magnetized fluid and the PN expansion of the gravitational potential in the wave zone. We show that the magnetic field appears even in the first PN order of the multipole moment tensor. Then, we find an explicit relativistic correction containing the magnetic field contribution to the well-known quadrupole formula. As an application of this derivation, we find that the B-field part of the GWs released in the early stages of a millisecond magnetar’s life can be as much as one-hundredth of the signals due to the deformed rotating neutron stars. We show that although the event rate of this system is small, the signal would lie in the sensitivity range of the next generation of detectors.

Relativistic calculations of R(D(∗)), R(Ds(∗)), R(ηc) and R(J/ψ)

Recently, the deviation of the ratios [Formula: see text], [Formula: see text] and [Formula: see text] have been found between experimental data and the Standard Model predictions, which may be the hint of new physics. In this work, we calculate these ratios within the Standard Model by using the improved instantaneous Bethe–Salpeter method. The emphasis is pad to the relativistic correction of the form factors. The results are [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], which are consistent with predictions of other models and the experimental data. The semileptonic decay rates and corresponding form factors at zero recoil are also given.

A universal formula for the relativistic correction to the mutual friction coupling time-scale in neutron stars

ABSTRACT Vortex-mediated mutual friction governs the coupling between the superfluid and normal components in neutron star interiors. By, for example, comparing precise timing observations of pulsar glitches with theoretical predictions it is possible to constrain the physics in the interior of the star, but to do so an accurate model of the mutual friction coupling in general relativity is needed. We derive such a model directly from Carter’s multifluid formalism, and study the vortex structure and coupling time-scale between the components in a relativistic star. We calculate how general relativity modifies the shape and the density of the quantized vortices and show that, in the quasi-Schwarzschild coordinates, they can be approximated as straight lines for realistic neutron star configurations. Finally, we present a simple universal formula (given as a function of the stellar compactness alone) for the relativistic correction to the glitch rise-time, which is valid under the assumption that the superfluid reservoir is in a thin shell in the crust or in the outer core. This universal relation can be easily employed to correct, a posteriori, any Newtonian estimate for the coupling time-scale, without any additional computational expense.

Relativistic SZ temperature scaling relations of groups and clusters derived from the BAHAMAS and MACSIS simulations

ABSTRACT The Sunyaev–Zeldovich (SZ) effect has long been recognized as a powerful cosmological probe. Using the BAHAMAS and MACSIS simulations to obtain ${\gt }10\, 000$ simulated galaxy groups and clusters, we compute three temperature measures and quantify the differences between them. The first measure is related to the X-ray emission of the cluster, while the second describes the non-relativistic thermal SZ (tSZ) effect. The third measure determines the lowest order relativistic correction to the tSZ signal, which is seeing increased observational relevance. Our procedure allows us to accurately model the relativistic SZ (rSZ) contribution and we show that a ${\gtrsim}10\!-\!40{{\ \rm per\ cent}}$ underestimation of this rSZ cluster temperature is expected when applying standard X-ray relations. The correction also exhibits significant mass and redshift evolution, as we demonstrate here. We present the mass dependence of each temperature measure alongside their profiles and a short analysis of the temperature dispersion as derived from the aforementioned simulations. We also discuss a new relation connecting the temperature and Compton-y parameter, which can be directly used for rSZ modelling. Simple fits to the obtained scaling relations and profiles are provided. These should be useful for future studies of the rSZ effect and its relevance to cluster cosmology.