Search Results (32)

General relativity is often perceived by undergraduate and advanced high-school students as conceptually and mathematically inaccessible. This paper does not provide new results in gravitation but rather introduces a lucid pedagogical framework for understanding gravitomagnetic effects in rotating systems. Starting from the Langevin metric, which describes flat spacetime in a uniformly rotating reference frame, the paper considers an apparent paradox: two clocks moving with identical velocities in an inertial frame but located at different radii on a rotating platform. While the equality of proper time of the clocks is expected in the inertial frame, its reconstruction in the rotating frame is not immediately transparent. It is shown here that this equality emerges from an exact compensation between three distinct contributions: a centrifugal potential term, a kinematic time dilation term, and a velocity-dependent term being formally analogous to a gravitomagnetic potential. The explicit identification and interpretation of these contributions constitute the pedagogical significance of this paper. Although the consideration presented is performed in flat spacetime, the formal analogy with gravitomagnetic effects provides students with an accessible pathway to more advanced concepts such as frame-dragging and the Sagnac effect, while highlighting the importance of velocity-dependent interactions in relativistic physics. Full article

Recently, the coprecession of both the accretion disk and the jet formed following the tidal disruption event associated with the optical transient AT2020afhd, driven by a supermassive black hole of almost ten million solar masses, were independently measured in both the X and radio bands, respectively, showing a periodicity of nearly 20 days over about 300 days. An analytical model of the general relativistic gravitomagnetic Lense-Thirring precession of the effective orbit of a fictitious test particle revolving about a spinning primary can explain the observed precessional features. It yields allowed regions in the system’s parameter space which, as far as the hole’s dimensionless spin parameter is concerned, are essentially in agreement with those obtained in the literature with general relativistic magnetohydrodynamic simulations. The present analytical approach can be extended to include the precession due to the hole’s quadrupole mass moment as well. It breaks the degeneracy in the allowed regions occurring for negative and positive values of the spin parameter when only the Lense-Thirring effect is considered. The best estimate for the hole’s mass yields the range 0.185–0.215 for the dimensionless spin parameter. Using the same strategy with the gravitomagnetic frequency for an extended disk of finite size with a parameterized power-law mass density yields to distinct, generally non-overlapping allowed regions for each value of the power-law index adopted. Some of the assumptions on which this work is based are critically examined. Full article

By “nethotron”, from the ancient Greek verb for “to spin”, it is meant here a natural or artificial rotating object, like a pulsar or an artificial satellite, whose rotational axis is cumulatively displaced by the post-Newtonian static (gravitoelectric) and stationary (gravitomagnetic) components of the gravitational field of some massive body around which it freely moves. Until now, both relativistic effects have been measured only by the dedicated space-based mission Gravity Probe B in the terrestrial environment. It detected the gravitoelectric de Sitter and gravitomagnetic Pugh–Schiff spin precessions of four superconducting gyroscopes accumulated within a year after about 50 years from conception to completion of data analysis at a cost of 750 million US dollars to $0.3$ and 19 percent accuracy, respectively. The perspectives to measure them with Earth’s long-lived laser-ranged geodetic satellites, like those of the LAGEOS family or possibly one or more of them to be built specifically from scratch, and pulsars orbiting the supermassive black hole in the Galactic Centre, yet to be discovered, are preliminarily investigated. The double pulsar PSR J0737-3039A/B is examined as well. Full article

In order to properly describe the gravity interactions, including the mass currents, in gravitomagnetism, we construct four Maxwell-type gravitational equations that are shown to be analogs of the Maxwell equations in electromagnetism. Next, exploiting the Maxwell-type gravitational equations, we explicitly predict the mass magnetic fields for both the isolated system of the spinning Moon orbiting the spinning Earth and that of the Sun and solar system planets orbiting the spinning Sun, whose phenomenological values have not been evaluated in the preceding Newtonian gravity formalisms. In gravitomagnetism, we also phenomenologically investigate the mass magnetic general relativity (GR) forces associated with the mass magnetic fields, finding that they are extremely small but non-vanishing compared to the corresponding mass electric Newtonian forces. Moreover, the directions of the mass magnetic GR forces for the solar system planets, except Venus and Uranus, are shown to be anti-parallel to those of their mass electric Newtonian forces. Next, we investigate the mass magnetic dipole moment related to the B ring of Saturn to evaluate ${\overrightarrow{m}}_M\left(Ring\right)=-1.141\times {10}^4{\mathrm{m}}^3{\mathrm{s}}^{-1}\widehat{\omega }$, with $\widehat{\omega }$ being the unit vector along the axis direction of the spinning B ring. The predicted value of ${\overrightarrow{m}}_M\left(Ring\right)$ is shown to be directly related to the Cassini data on the total mass of the rings of Saturn. Full article

Let two test particles A and B, revolving about a spinning primary along ideally identical orbits in opposite directions, be considered. From the general expressions of the precessions of the orbital inclination induced by the post-Newtonian gravitomagnetic and Newtonian quadrupolar fields of the central object, it turns out that the Lense–Thirring inclination rates of A and B are equal and opposite, while the Newtonian ones oblateness are identical, due to the primary’s oblateness. Thus, the differences in the inclination shifts of the two orbiters would allow, in principle, for the classical effects to be cancelled out by enhancing the general relativistic ones. The conditions affecting the orbital configurations that must be satisfied for this to occur and possible observable consequences regarding the Earth are investigated. In particular, a scenario involving two spacecraft in polar orbits, branded POLAr RElativity Satellites (POLARES) and reminiscent of an earlier proposal by Van Patten and Everitt in the mid-1970s, is considered. A comparison with the ongoing experiment with the LAser GEOdynamics Satellite (LAGEOS) and LAser RElativity Satellite (LARES) 2 is made. Full article

To the first post–Newtonian order, the gravitational action of mass–energy currents is encoded by the off–diagonal gravitomagnetic components of the spacetime metric tensor. If they are time–dependent, a further acceleration enters the equations of motion of a moving test particle. Let the source of the gravitational field be an isolated, massive body rigidly rotating whose spin angular momentum experiences a slow precessional motion. The impact of the aforementioned acceleration on the orbital motion of a test particle is analytically worked out in full generality. The resulting averaged rates of change are valid for any orbital configuration of the satellite; furthermore, they hold for an arbitrary orientation of the precessional velocity vector of the spin of the central object. In general, all the orbital elements, with the exception of the mean anomaly at epoch, undergo nonvanishing long–term variations which, in the case of the Juno spacecraft currently orbiting Jupiter and the double pulsar PSR J0737–3039 A/B turn out to be quite small. Such effects might become much more relevant in a star–supermassive black hole scenario; as an example, the relative change of the semimajor axis of a putative test particle orbiting a Kerr black hole as massive as the one at the Galactic Centre at, say, 100 Schwarzschild radii may amount up to about $7\%$ per year if the hole’s spin precessional frequency is $10\%$ of the particle’s orbital one. Full article

We calculate the metric of a self-gravitating and collapsing infinitely thin spherical shell in the weak-field and slow-motion limits, and we demonstrate that Birkhoff’s theorem is not consistent with the theory of the post-Newtonian approximation. More importantly, it is illustrated that performing a coordinate transformation in solving Einstein field equations may change the matter energy-momentum tensor, making the resultant solution not correspond to the original problem. Full article

To the first post-Newtonian order, the orbital angular momentum of the fast-revolving inner binary of the triple system PSR J0337+1715, made of a millisecond pulsar and a white dwarf, induces an annular gravitomagnetic field which displaces the line of apsides of the slower orbit of the other, distant white dwarf by $-1.2$ milliarcseconds per year. The current accuracy in determining the periastron of the outer orbit is $63.9$ milliarcseconds after 1.38 years of data collection. By hypothesizing a constant rate of measurement of the pulsar’s times of arrivals over the next 10 years, assumed equal to the present one, it can be argued that the periastron will be finally known to a ≃$0.15$ milliarcseconds level, while its cumulative gravitomagnetic retrograde shift will be as large as $-12$ milliarcseconds. The competing post-Newtonian gravitolectric periastron advance due to the inner binary’s masses, nominally amounting to $74.3$ milliarcseconds per year, can be presently modelled to an accuracy level as good as ≃$0.04$ milliarcseconds per year. The mismodeling in the much larger Newtonian periastron rate due to the quadrupolar term of the multipolar expansion of the gravitational potential of a massive ring representing the inner binary, whose nominal size for PSR J0337+1715 is $0.17$ degrees per year, might be reduced down to the ≃$0.5$ milliarcseconds per year level over the next 10 years. Thus, a first measurement of such a novel form of gravitomagnetism, although undoubtedly challenging, might be, perhaps, feasible in a not too distant future. Full article

The coupling of intrinsic spin with the nonlinear gravitomagnetic fields of Gödel-type spacetimes is studied. We work with Gödel-type universes in order to show that the main features of spin-gravity coupling are independent of causality problems of the Gödel universe. The connection between the spin–gravitomagnetic field coupling and Mathisson’s spin-curvature force is demonstrated in the Gödel-type universe. That is, the gravitomagnetic Stern–Gerlach force due to the coupling of spin with the gravitomagnetic field reduces in the appropriate correspondence limit to the classical Mathisson spin-curvature force. Full article

The perspectives of detecting the general relativistic gravitomagnetic Lense–Thirring effect on the orbits of the Galilean moons of Jupiter induced by the angular momentum $\mathit{S}$ of the latter are preliminarily investigated. Numerical integrations over one century show that the expected gravitomagnetic signatures of the directly observable right ascension $\alpha$ and declination $\delta$ of the satellites are as large as tens of arcseconds for Io, while for Callisto they drop to the ≃$0.2\mathrm{arcseconds}$ level. Major competing effects due to the mismodeling in the zonal multipoles $J_{\mathsf{\ell }},\mathsf{\ell }=2,3,4,\dots$ of the Jovian non-spherically symmetric gravity field and in the Jupiter’s spin axis $\widehat{\mathit{k}}$ should have a limited impact, especially in view of the future improvements in determining such parameters expected after the completion of the ongoing Juno mission in the next few years. On the other hand, the masses of the satellites, responsible of their mutual $N$-body perturbations, should be known better than now. Such a task should be accomplished with the future JUICE and Clipper missions to the Jovian system. Present-day accuracy in knowing the orbits of the Jovian Galilean satellites is of the order of 10 milliarcseconds, to be likely further improved thanks to the ongoing re-reduction of old photographic plates. This suggests that, in the next future, the Lense–Thirring effect in the main Jovian system of moons might be detectable with dedicated data reductions in which the gravitomagnetic field is explicitly modeled and solved-for. Full article

The new geodetic satellite LARES 2, cousin of LAGEOS and sharing with it almost the same orbital parameters apart from the inclination, displaced by 180 deg, was launched last year. Its proponents suggest using the sum of the nodes of LAGEOS and of LARES 2 to measure the sum of the Lense–Thirring node precessions independently of the systematic bias caused by the even zonal harmonics of the geopotential, claiming a final ≃0.2 percent total accuracy. In fact, the actual orbital configurations of the two satellites do not allow one to attain the sought for mutual cancellation of their classical node precessions due to the Earth’s quadrupole mass moment, as their sum is still ≃5000 times larger than the added general relativistic rates. This has important consequences. One is that the current uncertainties in the eccentricities and the inclinations of both satellites do not presently allow the stated accuracy goal to be met, needing improvements of 3–4 orders of magnitude. Furthermore, the imperfect knowledge of the Earth’s angular momentum S impacts the uncancelled sum of the node precessions, from 150 to 4900 percent of the relativistic signal depending on the uncertainty assumed in S. It is finally remarked that the real breakthrough in reliably testing the gravitomagnetic field of the Earth would consist in modeling it and simultaneously estimating one or more dedicated parameter(s) along with other ones characterising the geopotential, as is customarily performed for any other dynamical feature. Full article

We analyze neutrino emission channels in energetic ($\gtrsim {10}^{52}$ erg) long gamma-ray bursts within the binary-driven hypernova model. The binary-driven hypernova progenitor is a binary system composed of a carbon-oxygen star and a neutron star (NS) companion. The gravitational collapse leads to a type Ic supernova (SN) explosion and triggers an accretion process onto the NS. For orbital periods of a few minutes, the NS reaches the critical mass and forms a black hole (BH). Two physical situations produce MeV neutrinos. First, during the accretion, the NS surface emits neutrino–antineutrino pairs by thermal production. We calculate the properties of such a neutrino emission, including flavor evolution. Second, if the angular momentum of the SN ejecta is high enough, an accretion disk might form around the BH. The disk’s high density and temperature are ideal for MeV-neutrino production. We estimate the flavor evolution of electron and non-electron neutrinos and find that neutrino oscillation inside the disk leads to flavor equipartition. This effect reduces (compared to assuming frozen flavor content) the energy deposition rate of neutrino–antineutrino annihilation into electron–positron ($e^{+}{e}^{-}$) pairs in the BH vicinity. We then analyze the production of GeV-TeV neutrinos around the newborn black hole. The magnetic field surrounding the BH interacts with the BH gravitomagnetic field producing an electric field that leads to spontaneous $e^{+}{e}^{-}$ pairs by vacuum breakdown. The $e^{+}{e}^{-}$ plasma self-accelerates due to its internal pressure and engulfs protons during the expansion. The hadronic interaction of the protons in the expanding plasma with the ambient protons leads to neutrino emission via the decay chain of $\pi$-meson and $\mu$-lepton, around and far from the black hole, along different directions. These neutrinos have energies in the GeV-TeV regime, and we calculate their spectrum and luminosity. We also outline the detection probability by some current and future neutrino detectors. Full article

In a basis of the space-time coordinate frame four quaternions discovered by Hamilton can be used. For subsequent reproduction of the coordinate frame these four quaternions are expanded to four 4 × 4 matrices with real-valued matrix coefficients −0 and 1. This group set is isomorphic to the SU(2) group. Such a matrix basis introduces extra six degrees of freedom of matter motion in space-time. There are three rotations about three space axes and three boosts along these axes. Next one declares the differential generating operators acting on the energy-momentum density tensor written in the above quaternion basis. The subsequent actions of this operator together with its transposed one on the above tensor lead to the emergence of the gravitomagnetic equations that are like the Maxwell equations. Wave equations extracted from the gravitomagnetic ones describe the propagation of energy density waves and their vortices through space. The Dirac equations and their reduction to two equations with real-valued functions, the quantum Hamilton-Jacobi equations and the continuity equations, are considered. The Klein-Gordon equations arising on the mass shell hints to the alternation of the paired fermion fields and boson ones. As an example, a Feynman diagram of an electron–positron time crystal is illustrated. Full article

We discuss the polarization of gravitational radiation within the standard framework of linearized general relativity. The recent experimental discovery of gravitational waves provides the impetus to revisit the implications of the spin-rotation-gravity coupling for polarized gravitational radiation; therefore, we consider the coupling of the helicity of gravitational waves to the rotation of an observer or the gravitomagnetic field of a rotating astronomical source. Observational possibilities regarding polarization-dependent effects in connection with future gravitational wave detectors are briefly explored. Full article

Extrasolar circumbinary planets are so called because they orbit two stars instead of just one; to date, an increasing number of such planets have been discovered with a variety of techniques. If the orbital frequency of the hosting stellar pair is much higher than the planetary one, the tight stellar binary can be considered as a matter ring current generating its own post-Newtonian stationary gravitomagnetic field through its orbital angular momentum. It affects the orbital motion of a relatively distant planet with Lense-Thirring-type precessional effects which, under certain circumstances, may amount to a significant fraction of the static, gravitoelectric ones, analogous to the well known Einstein perihelion precession of Mercury, depending only on the masses of the system’s bodies. Instead, when the gravitomagnetic field is due solely to the spin of each of the central star(s), the Lense-Thirring shifts are several orders of magnitude smaller than the gravitoelectric ones. In view of the growing interest in the scientific community about the detection of general relativistic effects in exoplanets, the perspectives of finding new scenarios for testing such a further manifestation of general relativity might be deemed worth of further investigations. Full article