arXiv subjects

Lorenzo Iorio

Publications and source records attributed to Lorenzo Iorio.

At least 19 recordsLinked to original sources

arXiv2026

The measurable impact of the 2pN spin-dependent accelerations on the jet precession of M87$^\ast$

Motivated by recent accurate measurements of disk/jet coprecessions around some galactic supermassive black holes, the accelerations experienced by an uncharged, spinless object in the Kerr metric, written in harmonic coordinates, are analytically calculated up to the formal second post-Newtonian order. To such a level, some new accelerations make their appearance. They are proportional to even and odd powers of the hole's angular momentum. Their counterparts are not known where the primary is a material body. After expressing them in a coordinate-independent, vector form valid for any orientations of the hole's spin axis in space, their orbital effects are perturbatively worked out in terms of the particle's Keplerian orbital elements. The resulting expressions, averaged over one orbital revolution, are valid for generic shapes and inclinations of the orbit. The orbital plane's precession proportional to the first power of the hole's angular momentum and to the reciprocal of the fourth power of the speed of light amounts to about twenty per cent of the corresponding Lense-Thirring effect. The latter is believed to be the cause of the accurately measured disk/jet precessional phenomenology, currently measured to a few per cent accuracy. Although at a lesser extent, also the precession proportional to the second power of the hole's spin and to the reciprocal of the fourth power of the speed of light is measurable. Allowed domains in the parameter space of the jet precession around M87$^\ast$ are displayed.

gr-qc↗

arXiv2026

The no-hair theorems at work in the tidal disruption event AT2020afhd

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.

astro-ph.HE↗

arXiv2026

Has Kronos devoured Planet Nine and its epigones?

The Planet Nine hypothesis encompasses a body of about 5-8 Earth's masses whose orbital plane would be inclined to the ecliptic by one or two tens of degrees and whose perihelion distance would be as large as about 240-385 astronomical units. Recently, a couple of his epigones have appeared: Planet X and Planet Y. The former is a sort of minor version of Planet Nine in that all its physical and orbital parameters would be smaller. Instead, the latter would have a mass ranging from that of Mercury to the Earth's one and semimajor axis within 100-200 astronomical units. By using realistic upper bounds for the orbital precessions of Saturn, one can get insights on their position which, for Planet Nine, appears approximately confined around its aphelion. Planet Y can be just a Mercury-sized object at no less than about 125 astronomical units, while Planet X appears to be ruled out. Dedicated data reductions by modeling such perturber(s) are required to check the present conclusions, to be intended as hints of what might be detectable should planetary ephemerides include them. A probe on the same route of Voyager 1 would be perturbed by Planet Nine by about 20-40 km after some decades.

astro-ph.EP↗

arXiv2026

Can the jet precession of M87$^\ast$ be caused by a distant intermediate-mass black hole?

The long-term rates of change of all the Keplerian orbital elements of a two-body system acted upon by a remote massive pointlike object are analytically worked out, to the Newtonian quadrupolar level, without any restriction either on the orbital eccentricity and inclination of the disturbed pair or the position of the distant perturber. The latter is considered fixed during the average over one orbital revolution of the inner binary by means of which its orbital perturbations are calculated. The results are presented in a compact form that facilitates a straightforward application to the case of the supermassive black hole-or megapyknon-M87$^\ast$. In principle, the presence of another distant intermediate-mass black hole may concur to cause the observed jet precession, assumed tightly coupled with the accretion disk. Such a possibility is ruled out by the exclusion plots in the parameter space obtained with the approach presented here.

gr-qc↗

arXiv2025

Nethotrons: exploring the possibility of measuring relativistic spin precessions, from Earth's satellites to the Galactic Centre

By ``nethotrons'', 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 in a year after about 50 years from conception to completion of data analysis at a cost of 750 million dollars to $0.3$ and $19$ per cent accuracy, respectively. The perspectives to measure them also with long-lived Earth's 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.

gr-qc↗

arXiv2025

The Lense-Thirring effect at work in M87$^\ast$

Recently, the temporal evolution of the angles characterizing the spatial configuration of the jet in the supermassive black hole M87$^\ast$ was measured exhibiting a precessional pattern around the hole's spin axis. It would be due to the dragging induced by the fact that the hole's external spacetime is described by the Kerr metric. Here, it is shown that the Lense-Thirring orbital precessions of a test particle moving about a rotating massive object, calculated perturbatively to the first post-Newtonian order, are able to fully reproduce all the measured features of the jet axis of M87$^\ast$. In particular, by assuming that the latter is aligned with the angular momentum of the accretion disk, modelled as an effective particle moving along a circular orbit, the condition that the absolute value of the predicted Lense-Thirring precessional frequency of the disk agrees with the measured value of $0.56\pm 0.02$ radians per year of the jet's one is satisfied for a range of physically meaningful values of the hole's spin parameter, close to unity, and of the effective disk radius, of the order of just over a dozen gravitational radii. Relying upon such assumptions and results, it is possible to predict that the angle between the hole's spin axis and the jet's one stays constant over the years amounting to $1.16^\circ$, in agreement with its measured value of $1.25^\circ\pm 0.18^\circ$. Furthermore, also the temporal pattern and the amplitudes of the time series of the jet's angles are reproduced by the aforementioned Lense-Thirring precessional model.

gr-qc↗

arXiv2025

Will LAGEOS and LARES 2 succeed in accurately measuring frame-dragging?

The current LAGEOS-LARES 2 experiment aims to accurately measure the general relativistic Lense-Thirring effect in the gravitomagnetic field of the spinning Earth generated by the latter's angular momentum $\boldsymbol{J}$. The key quantity to a priori analytically assess the overall systematic uncertainty is the ratio $\mathcal{R}^{J_2}$ of the sum of the classical precessions of the satellites' nodes $Ω$ induced by the Earth's oblateness $J_2$ to the sum of their post-Newtonian counterparts. $In$ $principle$, if the sum of the inclinations $I$ of both satellites were $exactly$ $180^\circ$, the semimajor axes $a$ and the eccentricities $e$ being $identical$, $\mathcal{R}^{J_2}$ would $exactly$ vanish. Actually, it is $not$ so by a large amount because of the departures of the $real$ satellites' orbital configurations from their $ideal$ ones. Thus, $J_2$ impacts not only directly through its own uncertainty, but also $indirectly$ through the errors in all the other physical and orbital parameters entering $\mathcal{R}^{J_2}$. The consequences of this fact are examined in greater details than done so far in the literature. The Van Patten and Everitt's proposal in 1976 of looking at the sum of the node precessions of two counter-orbiting spacecraft in (low-altitude) circular polar orbits is revamped rebranding it POLAr RElativity Satellites (POLARES). (Abridged)

gr-qc↗

arXiv2025

The no-hair theorems at work in M87$^\ast$

Recently, a perturbative calculation to the first post-Newtonian order has shown that the analytically worked out Lense-Thirring precession of the orbital angular momentum of a test particle following a circular path around a massive spinning primary is able to explain the measured features of the jet precession of the supermassive black hole at the centre of the giant elliptical galaxy M87. It is shown that also the hole's mass quadrupole moment $Q_2$, as given by the no-hair theorems, has a dynamical effect which cannot be neglected, as, instead, done so far in the literature. New allowed regions for the hole's dimensionless spin parameter $a^\ast$ and the effective radius $r_0$ of the accretion disk, assumed tightly coupled with the jet, are obtained by including both the Lense-Thirring and the quadrupole effects in the dynamics of the effective test particle modeling the accretion disk. One obtains that, by numerically integrating the resulting averaged equations for the rates of change of the angles $η$ and $ϕ$ characterizing the orientation of the orbital angular momentum with $a^\ast = +0.98$ and $r_0=14.1$ gravitational radii, it is possible to reproduce, both quantitatively and qualitatively, the time series for them recently measured with the Very Long Baseline Interferometry technique. Instead, the resulting time series produced with $a^\ast = -0.95$ and $r_0=16$ gravitational radii turn out to be out of phase with respect to the observationally determined ones, while maintaining the same amplitudes.

gr-qc↗

arXiv2024

Using the Difference of the Inclinations of a Pair of Counter-Orbiting Satellites to Measure the Lense-Thirring Effect

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 due to the primary's oblateness are identical. Thus, the difference of the inclination shifts of the two orbiters would allow, in principle, to cancel out the classical effects by enhancing the general relativistic ones. The conditions affecting the orbital configurations that must be satisfied for this to occur and possible observable consequences in the field of 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.

gr-qc↗

arXiv2024

Post-Keplerian perturbations of the hyperbolic motion in the field of a rotating massive object. Analysis in terms of osculating and nonosculating (contact) elements

The perturbations of the hyperbolic motion of a test particle due to the general relativistic gravitoelectromagnetic Schwarzschild and Lense-Thirring components of the gravitational field of a rotating massive body are analytically worked out to the first post-Newtonian level in terms of the osculating Keplerian orbital elements. To the Newtonian order, the impact of the quadrupole mass moment of the source is calculated as well. The resulting analytical expressions are valid for a generic orientation in space of both the orbital plane of the probe and the spin axis of the primary, and for arbitrary values of the eccentricity. They are applied to 'Oumuamua, an interstellar asteroid which recently visited our solar system along an unbound heliocentric orbit, and to the Near Earth Asteroid Rendezvous (NEAR) spacecraft during its flyby of the Earth. The calculational approach developed can be straightforwardly extended to any alternative models of gravity as well.

gr-qc↗

arXiv2024

Review of the Gravitomagnetic Clock Effect

The general relativistic gravitomagnetic clock effect, in its simplest form, consists of the non-vanishing difference in the orbital periods of two counter-orbiting objects moving in opposite directions along circular orbits lying in the equatorial plane of a central rotating source. We briefly review both the theoretical and observational aspects of such an intriguing consequence of Einstein's theory of gravitation.

gr-qc↗

arXiv2024

On the Euler-type gravitomagnetic orbital effects in the field of a precessing body

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.

gr-qc↗

arXiv2024

When the anomalistic, draconitic and sidereal orbital periods do not coincide: the impact of post-Keplerian perturbing accelerations

In a purely Keplerian picture, the anomalistic, draconitic and sidereal orbital periods of a test particle orbiting a massive body coincide with each other. Such a degeneracy is removed when a post-Keplerian perturbing acceleration enters the equations of motion yielding generally different corrections to the Keplerian period for the three aforementioned characteristic orbital timescales. They are analytically worked out in the case of the accelerations induced by the general relativistic post-Newtonian gravitoelectromagnetic fields and, to the Newtonian level, by the oblateness of the central body as well. The resulting expressions hold for completely general orbital configurations and spatial orientations of the spin axis of the primary. Astronomical systems characterized by extremely accurate measurements of the orbital periods like, e.g., transiting exoplanets and binary pulsars, may offer potentially viable scenarios for measuring such post--Keplerian features of motion, at least in principle. As an example, the sidereal period of the brown dwarf WD1032 + 011 b is currently known with an uncertainty as small as $\simeq 10^{-5}\,\mathrm{s}$, while its predicted post-Newtonian gravitoelectric correction amounts to $0.07\,\mathrm{s}$; however, the accuracy with which the Keplerian period can be calculated is just 572 s. For the double pulsar PSR J0737-3039, the largest relativistic correction to the anomalistic period amounts to a few tenths of a second, given a measurement error of such a characteristic orbital timescale as small as $\simeq 10^{-6}\,\mathrm{s}$. On the other hand, the Keplerian term can be currently calculated just to a $\simeq 9$ s accuracy. In principle, measuring at least two of the three characteristic orbital periods for the same system independently would allow to cancel out their common Keplerian component provided that their difference is taken.

gr-qc↗

arXiv2024

Measuring a gravitomagentic effect with the triple pulsar PSR J0337+1715

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 $\simeq 0.15$ 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 $\simeq 0.04$ milliarcseconds per year. The mismodelling in the much larger Newtonian periastron rate due to the quadrupolar term of the multipolar expansion of the gravitational potential of a massive ring, whose nominal size for PSR J0337+1715 is $0.17$ degrees per year, might be reduced down to the $\simeq 0.5$ milliarcseconds per year level over the next 10 years. Thus, a first measurement of such a novel form of gravitomagnetism, although challenging, may be somehow feasible in a not too distant future.

gr-qc↗

arXiv2024

Post-Newtonian orbital effects induced by the mass quadrupole and spin octupole moments of an axisymmetric body

The post-Newtonian orbital effects induced by the mass quadrupole and spin octupole moments of an isolated, oblate spheroid of constant density that is rigidly and uniformly rotating on the motion of a test particle are analytically worked out for an arbitrary orbital configuration and without any preferred orientation of the body's spin axis. The resulting expressions are specialized to the cases of (a) equatorial and (b) polar orbits. The opportunity offered by a hypothetical new spacecraft moving around Jupiter along a Juno-like highly elliptical, polar orbit to measure them is preliminarily studied. Although more difficult to be practically implemented, also the case of a less elliptical orbit is considered since it yields much larger figures for the relativistic effects of interest. The possibility of using the S stars orbiting the supermassive black hole in Sgr A$^\ast$ at the Galactic Center as probes to potentially constrain some parameters of the predicted extended mass distribution surrounding the hole by means of the aforementioned orbital effects is briefly examined.

gr-qc↗

arXiv2023

Revisiting the gravitomagnetic clock effect

To the first post-Newtonian order, if two test particles revolve in opposite directions about a massive, spinning body along two circular and equatorial orbits with the same radius, they take different times to return to the reference direction relative to which their motion is measured: it is the so-called gravitomagnetic clock effect. The satellite moving in the same sense of the rotation of the primary is slower, and experiences a retardation with respect to the case when the latter does not spin, while the one circling in the opposite sense of the rotation of the source is faster, and its orbital period is shorter than it would be in the static case. The resulting time difference due to the stationary gravitomagnetic field of the central spinning body is proportional to the angular momentum per unit mass of the latter through a numerical factor which so far has been found to be $4π$. A numerical integration of the equations of motion of a fictitious test particle moving along a circular path lying in the equatorial plane of a hypothetical rotating object by including the gravitomagnetic acceleration to the first post-Newtonian order shows that, actually, the gravitomagnetic corrections to the orbital periods are larger by a factor of $4$ in both the prograde and retrograde cases. Such an outcome, which makes the proportionality coefficient of the gravitomagnetic difference in the orbital periods of the two counter-revolving orbiters equal to $16π$, confirms an analytical calculation recently published in the literature by the present author.

gr-qc↗

arXiv2023

The post-Newtonian motion around an oblate spheroid: the mixed orbital effects due to the Newtonian oblateness and the post-Newtonian mass monopole accelerations

When a test particle moves about an oblate spheroid, it is acted upon, among other things, by two standard perturbing accelerations. One, of Newtonian origin, is due to the quadrupole mass moment $J_2$ of the orbited body. The other one, of the order of $\mathcal{O}\left(1/c^2\right)$, is caused by the static, post-Newtonian field arising solely from the mass of the central object. Both of them concur to induce \textrm{indirect}, \textrm{mixed} orbital effects of the order of $\mathcal{O}\left(J_2/c^2\right)$. They are of the same order of magnitude of the \textrm{direct} ones induced by the post-Newtonian acceleration arising in presence of an oblate source, not treated here. We calculate these less known features of motion in their full generality in terms of the osculating Keplerian orbital elements. Subtleties pertaining the correct calculation of their mixed net \textrm{precessions} per orbit to the full order of $\mathcal{O}\left(J_2/c^2\right)$ are elucidated. The obtained results hold for arbitrary orbital geometries and for any orientation of the body's spin axis $\mathbf{\hat{k}}$ in space. The method presented is completely general, and can be extended to any pair of post-Keplerian accelerations entering the equations of motion of the satellite, irrespectively of their physical nature.

gr-qc↗

arXiv2023

Is it possible to measure the Lense-Thirring orbital shifts of the short-period S-star S4716 orbiting Sgr A$^\ast$?

The maximal values of the general relativistic Lense-Thirring (LT) orbital shifts $ΔI^\mathrm{LT},\,ΔΩ^\mathrm{LT}$ and $Δω^\mathrm{LT}$ of the inclination $I$, the longitude of the ascending node $Ω$ and the perinigricon $ω$ of the recently discovered star S4716, which has the shortest orbital period $\left(P_\mathrm{b}=4.02\,\mathrm{yr}\right)$ of all the S-stars that orbit the supermassive black hole (SMBH) in Sgr A$^\ast$, are of the order of $\simeq 5-16$ arcseconds per revolution $\left(^{\prime\prime}\,\mathrm{rev}^{-1}\right)$. Given the current error $σ_ω= 0.02^\circ$ in determining $ω$, which is the most accurate orbital parameter of S4716 among all those affected by the SMBH's gravitomagnetic field through its angular momentum ${\boldsymbol{J}}_\bullet$, about 48 yr would be needed to reduce $σ_ω$ to $\simeq 10\%$ of the cumulative LT perinigricon shift over the same time span. Measuring $ΔI^\mathrm{LT}$ and $ΔΩ^\mathrm{LT}$ to the same level of accuracy would take even much longer. Instead, after just 16 yr, a per cent measurement of the larger gravitoelectric (GE) Schwarzschild-like perinigricon shift $Δω^\mathrm{GE}$, which depends only on the SMBH's mass $M_\bullet$, would be possible. On the other hand, the uncertainties in the physical and orbital parameters entering $Δω^\mathrm{GE}$ would cause a huge systematic bias of $Δω^\mathrm{LT}$ itself. The SMBH's quadrupole mass moment $Q_2^\bullet$ induces orbital shifts as little as $\simeq 0.01-0.05\,^{\prime\prime}\,\mathrm{rev}^{-1}$.

gr-qc↗