On Mössbauer rotor effect, clock synchronization and third postulate of relativity

The treatment of the coordinate systems is briefly reviewed in the Newtonian mechanics, in the special theory of relativity, and in the general relativistic theory, respectively. Some reference frames and coordinate systems proposed within the general relativistic framework are introduced. With use of the ideas on which these coordinate systems are based, the proper reference frame comoving with a system of mass-points is defined as a general relativistic extension of the relative coordinate system in the Newtonian mechanics. The coordinate transformation connecting this and the background coordinate systems is presented explicitly in the post-Newtonian formalism. The conversion formulas of some physical quantities caused by this coordirate transformation are discussed. The concept of the rotating coordinate system is reexamined within the relativistic framework. A modification of the introduced proper reference frame is proposed as the basic coordinate system in the astrometry. The relation between the solar system barycentric coordinate system and the terrestrial coordinate system is given explicitly.

Context. The energy equilibrium between the corona and the underlying disk in a two-phase accretion flow sets a lower limit on the achievable photon index. A slab coronal geometry may not adequately explain the hard state observations of X-ray binaries (XRBs). Aims. We incorporated energy feedback to the accretion disk resulting from illumination by an extended corona, and vice versa. The interaction between these two components makes it possible to find an energetically self-consistent equilibrium solution for a given disk–corona system. Methods. We upgraded the existing Monte Carlo radiative transfer code, MONK, to incorporate the interaction between the disk and the extended corona within the general relativistic framework. We introduced an albedo parameter to specify the fraction of the incident flux that is reflected by the disk, while the remainder is absorbed and added to the intrinsic dissipation. Reflection was modeled assuming a semi-infinite electron atmosphere. For a given disk–corona system, Comptonization by the corona and disk illumination are iteratively computed to reach equilibrium, under the constraint that the total observed luminosity equals the total available accretion power. Results. We find global equilibrium solutions not only for the hard state but also for intermediate states, with partial contributions from the disk and from the corona. A higher black hole spin, higher coronal temperature, and higher albedo all lead to harder spectra. For typical coronal temperatures and disk albedos, the lowest achievable photon index with a static slab corona fully covering the disk is approximately 1.7−1.8. Under the assumption of a spatially uniform, extended slab corona, energy must flow from the inner to the outer annuli if local equilibrium is imposed between the disk and the corona at each radial annulus, in addition to the global equilibrium condition. Conclusions. With the upgraded version of MONK, we are now able to achieve global energy equilibrium for a given disk–corona system. This approach holds significant potential for constraining the coronal geometry using not only the observed flux, but also polarization. A static slab does not appear to be a favorable coronal geometry for the hard state of X-ray binaries, even when global energy balance between the disk and corona is taken into account. In future work, we will explore truncated disk geometries and outflowing coronae as potential alternatives.

We calculate the first dynamical evolutions of merging black hole-neutron star binaries that construct the combined black hole-neutron star spacetime in a general relativistic framework. We treat the metric in the conformal flatness approximation, and assume that the black hole mass is sufficiently large compared to that of the neutron star so that the black hole remains fixed in space. Using a spheroidal spectral methods solver, we solve the resulting field equations for a neutron star orbiting a Schwarzschild black hole. The matter is evolved using a relativistic, Lagrangian, smoothed particle hydrodynamics (SPH) treatment. We take as our initial data recent quasiequilibrium models for synchronized neutron star polytropes generated as solutions of the conformal thin-sandwich (CTS) decomposition of the Einstein field equations. We are able to construct from these models relaxed SPH configurations whose profiles show good agreement with CTS solutions. Our adiabatic evolution calculations for neutron stars with low-compactness show that mass transfer, when it begins while the neutron star orbit is still outside the innermost stable circular orbit, is more unstable than is typically predicted by analytical formalisms. This dynamical mass loss is found to be the driving force in determining the subsequent evolution of the binary orbit and the neutron star, which typically disrupts completely within a few orbital periods. The majority of the mass transferred onto the black hole is accreted promptly; a significant fraction ($\ensuremath{\sim}30%$) of the mass is shed outward as well, some of which will become gravitationally unbound and ejected completely from the system. The remaining portion forms an accretion disk around the black hole, and could provide the energy source for short-duration gamma-ray bursts.

We study nonradial oscillations of neutron stars with superfluid baryons, in a general relativistic framework, including finite temperature effects. Using a perturbative approach, we derive the equations describing stellar oscillations, which we solve by numerical integration, employing different models of nucleon superfluidity, and determining frequencies and gravitational damping times of the quasinormal modes. As expected by previous results, we find two classes of modes, associated to superfluid and non-superfluid degrees of freedom, respectively. We study the temperature dependence of the modes, finding that at specific values of the temperature, the frequencies of the two classes of quasinormal modes show avoided crossings, and their damping times become comparable. We also show that, when the temperature is not close to the avoided crossings, the frequencies of the modes can be accurately computed by neglecting the coupling between normal and superfluid degrees of freedom. Our results have potential implications on the gravitational wave emission from neutron stars.

We investigate the structure of gravitational self-interactions of coherently oscillating axions in the general relativistic framework. A generic action for a massive scalar field in the Friedmann-Robertson-Walker background is first introduced based on the effective field theory approach to cosmological perturbations. Using the obtained setup, we evaluate the effective gravitational interaction of the massive scalar field, i.e. scalar quartic interactions mediated by metric perturbations. Applying the results to the system of dark matter axions, we estimate their self-interaction rate and discuss its implications for the axion Bose-Einstein condensate dark matter scenario. Leading contributions for the gravitational interactions of axions are given by the process mediated by the dynamical graviton field, which is essentially the Newtonian potential induced by fluctuations of the background fluids. We find that it leads to the same order of magnitude for the interaction rate of dark matter axions in the condensed regime, compared with the results of previous studies using the Newtonian approximation.

Electron–positron pairs in physics and astrophysics: From heavy nuclei to black holes

Relativistic effects in the synchronization of clocks with a radio interferometer with an extremely long baseline

We have modelled a neutral non-homogeneous anisotropic stellar compact object with two distinct equations of state in general relativity framework. We have considered the macroscopic features of a general relativistic gravitating compact object. The equation of state is quadratic in the core and linear in the envelope. There is smooth matching between the core, envelope and the vacuum exterior regions. We found the masses, radii and compactness of some compact objects such PSR J1614-2230, PSR J1903+0327, Vela X-1, SMC-X-1, Cen X-3; which are in agreement with previous investigations. The gravitational potentials and the matter variables are well behaved throughout the stellar structure. We present in particular the variation of the radius in the core and the envelope of the star by changing some parameters values. Physical features of the pulsars PSR J1614-2230 are presented in more details. It observed that the radial pressure in the core is higher than the radial pressure in the envelope. The investigation reveals that the model is physically relevant for the study of observed compact stars.

Coordinate velocity and desynchronization of clocks

In this study, our aim is to generate the new anisotropic solution for compact stellar configurations with the help of Buchdahl geometry. We used the Buchdahl metric potential [J. Astrophys. Astron. 3, 325 (1982)] to deal with the field equations in general relativity framework. To get the constant parameters, the exterior Schwarzschild de Sitter solution is linked to the interior solution at the boundary. We discuss the behavior of density, radial and tangential pressure for the present model. We take the star candidates 4U 1820-30, PSR J1903+327, 4U 1608-52, 4U 1538-52 and HerX-1 to complete our analysis. The proposed compact stars equilibrium and stability states are analyzed using the Tolman-Oppenheimer-Volkoff equation, causality condition, adiabatic index and Harrison-Zeldovich-Novikov Criterion, respectively. It is noticed that our proposed model is suitable and provides viable results with Buchdahl geometry.

For numerical integration of the geocentric equations of motion of Earth satellites in the general relativity framework one may choose now between rather simple equations involving in their relativistic dynamical part only the Earth-induced terms and very complicated equations taking into account the relativistic third-body action. However, it is possible quite easily to take into account the relativistic indirect third-body perturbations and to neglect much lesser direct third-body perturbations. Such approach is based on the use of the Newtonian third-body perturbations in geocentric variables with expressing them in the relativistic manner in terms of the barycentric arguments. Together with it, to extend the known results for the spheroid model of the Earth, the Earth-induced terms are treated in great detail by including the non-spin part of the Earth vector-potential and the Earth triaxial non-sphericity.

In this article, we investigate the properties of neutron stars within the braneworld model, employing six distinct piece-wise polytropic equation of states. These equation of states satisfy observational constraints put by GW170817 event and pulsar observations (PSR J0740 and PSR J0030) within general relativity framework. Our primary goal is to assess whether these equation of states, in conjunction with the braneworld framework, can accommodate more massive neutron stars, as suggested by the GW190814 observation, while remaining consistent with established observational constraints. The brane tension parameter significantly affects the mass-radius and mass-tidal deformability relations, particularly for neutron stars with masses exceeding the canonical value. We establish strong constraints on the brane tension by comparing the canonical neutron star radius and tidal deformability with the results from the braneworld model, a stringent lower bound on the brane tension, $$\lambda > 2 \times 10^{37} \, \text{ dyne/cm } ^2 $$ λ > 2 × 10 37 dyne/cm 2 . Our results demonstrate that the braneworld model allows for the existence of neutron stars with masses greater than those predicted by General Relativity, in agreement with the GW190814 observation, and highlight the significant role of brane tension in shaping the properties of neutron stars.

Salient features of the Hafele-Keating test of relativistic clock-rate changes are presented; these changes were for cesium atomic clocks which had been flown around the world, once eastward and once westward, on approximately equatorial paths. An inconsistency for an earth observer, between equal energy but different time rates for eastward and westward moving clocks, is shown to be removed if the Sagnac effect is taken into account in the synchronization of clocks in the earth reference system. Also, it is shown that an atomic clock's directional relativistic loss (gain) for an eastward (westward) circumpolar journey is velocity independent. The observed relativistic time effects may be derived as general-relativistic changes, leaving the question of special-relativistic kinetic effects on a macroscopic clock an open one empirically.

In special and general relativity the synchronization convention of distant clocks may be simulated with a mathematical definition of global non-inertial frames (the only ones existing in general relativity due to the equivalence principle) with well-defined instantaneous 3-spaces. For asymptotically Minkowskian Einstein space-times this procedure can be used at the Hamiltonian level in the York canonical basis, where it is possible for the first time to disentangle tidal gravitational degrees of freedom from gauge inertial ones. The most important inertial effect connected with clock synchronization is the York time {}^3K(\tau, \sigma^r), not existing in Newton gravity. This fact opens the possibility to describe some aspects of {\it darkness} as a relativistic inertial effect in Einstein gravity by means of a Post-Minkowskian reformulation of the Celestial Reference System ICRS.

Fatigue of short fiber thermoplastic composites: A review of recent experimental results and analysis