Orbital Effects of a Time-Dependent Pioneer-Like Anomalous Acceleration
L. Iorio, Orbital Effects of a Time-Dependent Pioneer-Like Anomalous Acceleration, Modern Physics Letters A, vol. 27, no. 12, id. 1250071, 2012
We work out the impact that the recently determined time-dependent component of the
Pioneer Anomaly (PA), if... more
We work out the impact that the recently determined time-dependent component of the
Pioneer Anomaly (PA), if interpreted as an additional exotic acceleration of gravitational
origin with respect to the well-known PA-like constant one, may have on the orbital
motions of some planets of the solar system. By assuming that it points towards the
Sun, it turns out that both the semi-major axis a and the eccentricity e of the orbit of
a test particle would experience secular variations. For Saturn and Uranus, for which
modern data records cover at least one full orbital revolution, such predicted anomalies
are up to 2–3 orders of magnitude larger than the present-day accuracies in empirical
determinations of their orbital parameters from the usual orbit determination procedures
in which the PA was not modeled. Given the predicted huge sizes of such hypothetical
signatures, it is unlikely that their absence from the presently available processed data
can be attributable to an “absorption” for them in the estimated parameters caused by
the fact that they were not explicitly modeled. The magnitude of a constant PA-type
acceleration at 9.5 au cannot be larger than 9 × 10−15 m s−2 according to the latest
observational results for the perihelion precession of Saturn.
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Seen by: General relativistic spin-orbit and spin–spin effects on the motion of rotating particles in an external gravitational field
L. Iorio, General relativistic spin-orbit and spin–spin effects on the motion of rotating particles in an external gravitational field, General Relativity and Gravitation, vol. 44, no. 3, pp. 719-736, 2012
We analytically compute the orbital effects induced on the motion of a spinning particle geodesically traveling around... more We analytically compute the orbital effects induced on the motion of a spinning particle geodesically traveling around a central rotating body by the general relativistic two-body spin–spin and spin-orbit leading-order interactions. Concerning the spin-orbit term, we compute the long-term variations due to the particle’s spin by finding secular precessions for the inclination I of the particle’s orbit, its longitude of the ascending node Ω and the longitude of pericenter . Moreover, we generalize the well-known Lense-Thirring precessions to a generic orientation of the source’s angular momentum by obtaining an entirely new effect represented by a secular precession of I, and additional secular precessions of Ω and as well. The spin–spin interaction is responsible of gravitational effects à la Stern-Gerlach consisting of secular precessions of I and the mean anomaly . Such results are obtained without resorting to any approximations either in the particle’s eccentricity e or in its inclination I; moreover, no preferred orientations of both the system’s angular momenta are adopted. Their generality allows them to be applied to a variety of astronomical and astrophysical scenarios like, e.g., the Sun and its planets and the double pulsar PSR J0737-3039A/B. It turns out that the orbital precessions caused by the spin–spin and the spin-orbit perturbations due to the less massive body are below the current measurability level, especially for the solar system and the Stern-Gerlach effects. Concerning the solar Lense-Thirring precessions, the slight misalignment of the solar equator with respect to the ecliptic reduces the gravitomagnetic node precession of Mercury down to a 0.08 mas per century level with respect to the standard value of 1 mas per century obtained by aligning the z axis with the Sun’s angular momentum. The new inclination precession is as large as 0.06 mas per century, while the perihelion’s rate remains substantially unchanged, amounting to −2 mas per century. Further studies may be devoted to the extrasolar planets which exhibit a rich variety of orbital and rotational configurations.
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A Gedankenexperiment in Gravitation
In this paper we consider a thought experiment involving the effect of gravitation on an ideal scale containing a... more In this paper we consider a thought experiment involving the effect of gravitation on an ideal scale containing a photon. If the tidal forces inherent to a gravitational field are neglected, then one is led to scenario which seems to bring about perpetual motion violating the first and second principle of thermodynamics. The tidal effects of gravity must neccessarily be included in order to obtain a consistent physical theory. As a result, Albert Einstein's thought experiments according to which the physical effects of inertia in an accelerated reference frame are equivalent to the effects of gravity in a frame at rest on the surface of a massive body must be reconsidered, since linearly accelerated frames do not produce tidal effects. We argue that the equivalence between inertial effects and gravitation can be restored for rotating frames and in this context a relation with the possible nature of quantum gravity is conjectured.
Constraints on the location of a putative distant massive body in the Solar System from recent planetary data
L. Iorio, Constraints on the location of a putative distant massive body in the Solar System from recent planetary data, Celestial Mechanics and Dynamical Astronomy, vol. 112, no. 2, pp. 117-130, 2012.
We analytically work out the long-term variations caused on the motion of a planet orbiting a star by a very distant,... more We analytically work out the long-term variations caused on the motion of a planet orbiting a star by a very distant, pointlike massive object X. Apart from the semi-major axis a, all the other Keplerian osculating orbital elements experience long-term variations which are complicated functions of the orbital configurations of both the planet itself and of X. We infer constraints on the minimum distance d X at which X may exist by comparing our prediction of the long-term variation of the longitude of the perihelion to the latest empirical determinations of the corrections to the standard Newtonian/Einsteinian secular precessions of several solar system planets recently estimated by independent teams of astronomers. We obtain the following approximate lower bounds on d X for the assumed masses of X quoted in brackets: 150–200 au (Mars), 250–450 au (07m), 3500–4500 au (4 m Jup).
Groundstate splitting around rotating mini-blackholes
by Frank Witte
A working paper from 2008 together with Ivo Sturm (grad student). It represents the first approximate calculation of boundstate energies of spin 1/2 fermions around a rotating blackhole.
In this letter we present the result of a spin-dependent groundstate-energy calculation for fermionic boundstates in... more In this letter we present the result of a spin-dependent groundstate-energy calculation for fermionic boundstates in the spacetime around a rotating blackhole. Using a slow rotation approximation and a minimax variational approach we find boundstate energies of 0 to 5 percent of the fermions flatspace restmass. The groundstate displays a spin-dependent splitting with an energy difference of about 10 percent of the binding energy. For a dilute gas of primordial mini blackholes with gravitationally bound electrons spin-flip transitions could possibly give rise to observable signatures in the observed soft X-ray spectrum for sources at cosmological distances.
Impact of a Pioneer/Rindler-type acceleration on the Oort Cloud
L. Iorio, Impact of a Pioneer/Rindler-type acceleration on the Oort Cloud, Monthly Notices of the Royal Astronomical Society, vol. 419, no. 3, pp. 2226–2232, 2012
According to a recent modified model of gravity at large distances, a radial constant and
uniform... more
According to a recent modified model of gravity at large distances, a radial constant and
uniform extra-acceleration ARin = ARin ˆr of Rindler type acts upon a test particle p in the
static field of a central mass M if certain conditions are satisfied. Among other things, it was
proposed as a potentially viable explanation of a part of the Pioneer anomaly. We study the
impact that an anomalous Rindler-type term as large as |ARin| ∼ 10−10 ms−2 may have on the
the orbital dynamics of a typical object of the Oort Cloud whose self-energy is quite smaller
than its putative Rindler energy. By taking a typical comet moving along a highly eccentric
and inclined orbit throughout the expected entire extension of the Oort Cloud (∼0.02–1 pc), it
turns out that the addition of an outward Rindler-like acceleration, that is, for ARin > 0, does
not allow bound orbits. Instead, if ARin < 0, the resulting numerically integrated trajectory
is limited in space, but it radically differs from the standard Keplerian ellipse. In particular,
the heliocentric distance of the comet gets markedly reduced and experiences high-frequency
oscillations, its speed is increased, and the overall pattern of the trajectory is quite isotropic.
As a consequence, the standard picture of the Oort Cloud is radically altered since its modified
orbits are much less sensitive to the disturbing actions of the Galactic tide and nearby passing
stars whose effects, in the standard scenario, are responsible for the phenomenology on which
our confidence in the existence of the cloud itself is based. The present analysis may be
supplemented in future by further statistical Monte Carlo type investigations by randomly
varying the initial conditions of the comets.
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Perturbed stellar motions around the rotating black hole in Sgr A* for a generic orientation of its spin axis
L. Iorio, Perturbed stellar motions around the rotating black hole in Sgr A* for a generic orientation of its spin axis, Physical Review D, vol. 84, issue 12, id. 124001, 2011.
Empirically determining the averaged variations of the orbital parameters of the stars orbiting the Supermassive Black... more Empirically determining the averaged variations of the orbital parameters of the stars orbiting the Supermassive Black Hole (SBH) hosted by the Galactic center (GC) in Sgr A* is, in principle, a valuable tool to test the General Theory of Relativity (GTR), in regimes far stronger than those tested so far, and certain key predictions of it like the “no-hair” theorems. We analytically work out the long-term variations of all the six osculating Keplerian orbital elements of a test particle orbiting a nonspherical, rotating body with quadrupole moment Q2 and angular momentum S for a generic spatial orientation of its spin axis k̂. This choice is motivated by the fact that, basically, we do not know the position in the sky of the spin axis of the SBH in Sgr A* with sufficient accuracy. We apply our results to S2, which is the closest star discovered so far having an orbital period Pb=15.98 yr, and to a hypothetical closer star X with Pb=0.5 yr. Our calculations are quite general, not being related to any specific parameterization of k̂, and can be applied also to astrophysical binary systems, stellar planetary systems, and planetary satellite geodesy in which different reference frames, generally not aligned with the primary’s rotational axis, are routinely used.
Some considerations on the present-day results for the detection of frame-dragging after the final outcome of GP-B
L. Iorio, Some considerations on the present-day results for the detection
of frame-dragging after the final outcome of GP-B, Europhysics Letters, vol. 96, no. 3, id. 30001, 2011
The cancellation of the first even zonal harmonic coefficient J2 from the linear
combination f(2L) of the nodes ... more
The cancellation of the first even zonal harmonic coefficient J2 from the linear
combination f(2L) of the nodes of LAGEOS and LAGEOS II used in the latest tests of the
Lense-Thirring effect cannot be perfect, contrary to what assumed so far. It is so also because of
the uncertainties in the spatial orientation of the terrestrial spin axis ˆk . As a consequence of above,
the coefficient c1 entering f(2L), which is not a solve-for parameter being, instead, theoretically
computed from the analytical expressions of the classical node precessions ˙ J2 due to J2, is, on
average, uncertain at a 10−8 level over multi-decadal time spans ΔT comparable to those used in
the data analyses performed so far. A further ≃ 20% systematic uncertainty, thus, occurs. The shift
ΔLT due to the gravitomagnetic frame-dragging on the station-spacecraft range is numerically
computed over ΔT =15 d and ΔT =1 y. The need to look at such a directly observable quantity is
highlighted, along with some critical remarks concerning the methodology used so far to measure
the Lense-Thirring effect with the LAGEOS satellites. Suggestions for a different, more trustable
and reliable approach are offered.
Observational constraints on spatial anisotropy of G from orbital motions
L. Iorio, Observational constraints on spatial anisotropy of G from orbital motions. Classical and Quantum Gravity, vol. 28, no. 22, id. 225027, 2011
A phenomenological anisotropic variation ΔG/G of the Newtonian gravitational coupling parameter G, if real, would... more A phenomenological anisotropic variation ΔG/G of the Newtonian gravitational coupling parameter G, if real, would affect the orbital dynamics of a two-body gravitationally bound system in a specific way. We analytically work out the long-term effects that such a putative modification of the usual Newtonian inverse-square law would induce on the trajectory of a test particle orbiting a central mass. Without making any a priori simplifying assumptions concerning the orbital configuration of the test particle, it turns out that its osculating semi-major axis a, eccentricity e, pericenter piv and mean anomaly $\mathcal {M}$ undergo long-term temporal variations, while the inclination I and the node Ω are left unaffected. Moreover, the radial and the transverse components of the position and the velocity vectors r and v of the test particle, experience non-vanishing changes per orbit, contrary to the out-of-plane ones. Then, we compute our theoretical predictions for some of the major bodies of the solar system by orienting the gradient of G(r) toward the Galactic center and keeping it fixed over the characteristic timescales involved. By comparing our calculation to the latest observational determinations for the same bodies, we infer ΔG/G ≤ 10−17 over about 1 AU. Finally, we consider also the supermassive black hole hosted by the Galactic center in Sgr A* and the main sequence star S2 orbiting it in about 16 years, obtaining just ΔG/G ≤ 10−2 over 1 KAU.
Gravitomagnetism and the Earth–Mercury range
L. Iorio, Gravitomagnetism and the Earth–Mercury range, Advances in Space Research, vol. 48, no. 8, pp. 1403–1410, 2011
We numerically work out the impact of the general relativistic Lense–Thirring effect on the Earth–Mercury range caused... more
We numerically work out the impact of the general relativistic Lense–Thirring effect on the Earth–Mercury range caused by the
gravitomagnetic field of the rotating Sun. The peak-to-peak nominal amplitude of the resulting time-varying signal amounts to
17.5 m over a temporal interval Dt = 2 yr. Future interplanetary laser ranging facilities should reach a cm-level in ranging to Mercury
over comparable timescales; for example, the BepiColombo mission, to be launched in 2014, should reach a 4.5–10 cm level over
1-8 yr. We looked also at other Newtonian (solar quadrupole mass moment, ring of the minor asteroids, Ceres, Pallas, Vesta, Trans-
Neptunian Objects) and post-Newtonian (gravitoelectric Schwarzschild solar field) dynamical effects on the Earth–Mercury range. They
act as sources of systematic errors for the Lense–Thirring signal which, in turn, if not properly modeled, may bias the recovery of some
key parameters of such other dynamical features of motion. Their nominal peak-to-peak amplitudes are as large as 4 10^5 m (Schwarzschild),
300 m (Sun’s quadrupole), 81 m (Ceres, Pallas, Vesta), 4 m (ring of minor asteroids), 80 cm (Trans-Neptunian
Objects). Their temporal patterns are different with respect to that of the gravitomagnetic signal.
Gravitomagnetism and Gravitational Waves
L. Iorio, C. Corda, Gravitomagnetism and Gravitational Waves, The Open Astronomy Journal, vol. 4, Suppl. 1-M5, pp. 84-97, 2011
After extensively reviewing general relativistic gravitomagnetism, both historically and phenomenologically,
we... more
After extensively reviewing general relativistic gravitomagnetism, both historically and phenomenologically,
we review in detail the so-called magnetic components of gravitational waves (GWs), which have to be taken into account
in the context of the total response functions of interferometers for GWs propagating from arbitrary directions. Following
the more recent approaches of this important issue, the analysis of such magnetic components will be reviewed in both of
standard General Theory of Relativity (GTR) and Scalar Tensor Gravity. Thus, we show in detail that such a magnetic
component becomes particularly important in the high-frequency portion of the range of ground based interferometers for
GWs which arises from the two different theories of gravity. Our reviewed results show that if one neglects the magnetic
contribution to the gravitational field of a GW, approximately 15% of the potential observable signal could, in principle,
be lost.
Cosmic Acceleration from Topological Considerations: Branes Filled by Scalar Field Dark Matter
by Miguel Ángel García Aspeitia
Following a previous work [Gen. Rel. Grav. \textbf{43} (2011)], we further study the behavior of a real scalar field... more
Following a previous work [Gen. Rel. Grav. \textbf{43} (2011)], we further study the behavior of a real scalar field in a hidden brane in a configuration of two branes embedded in a five dimensional bulk.
We find an expression for the equation of state for this scalar field in the visible brane in terms of the
fields of the hidden one. Additionally, we investigated
the perturbations produced by this scalar field in the visible brane with the aim to study their dynamical properties.
Our results show that if the kinetic energy of the scalar field dominates during the early universe the perturbed scalar field could mimic the observed dynamics for the dark matter in the standard paradigm. Thus, the scalar field
dark matter hypothesis in the context of braneworld theory could be an interesting alternative to the
nature of dark matter in the Universe.
Black Holes or Eternally Collapsing Objects: A Review of 90 Years of Misconceptions
by Abhas Mitra
Focus on Black Hole Research, edited by Paul V. Kreitler. ISBN 1-59454-460-3. Published by Nova Science Publishers, Inc., New York, NY USA, 2006, p.1