[Show abstract][Hide abstract] ABSTRACT: We study the behavior of massless Dirac particles in the vacuum C-metric
spacetime, representing the nonlinear superposition of the Schwarzschild black
hole solution and the Rindler flat spacetime associated with uniformly
accelerated observers. Under certain conditions, the C-metric can be considered
as a unique laboratory to test the coupling between intrinsic properties of
particles and fields with the background acceleration in the full (exact)
strong-field regime. The Dirac equation is separable by using, e.g., a
spherical-like coordinate system, reducing the problem to one-dimensional
radial and angular parts. Both radial and angular equations can be solved
exactly in terms of general Heun functions. We also provide perturbative
solutions to first-order in a suitably defined acceleration parameter, and
compute the acceleration-induced corrections to the particle absorption rate as
well as to the angle-averaged cross section of the associated scattering
problem in the low-frequency limit. Furthermore, we show that the angular
eigenvalue problem can be put in one-to-one correspondence with the analogous
problem for a Kerr spacetime, by identifying a map between these "acceleration"
harmonics and Kerr spheroidal harmonics. Finally, in this respect we discuss
the nature of the coupling between intrinsic spin and spacetime acceleration in
comparison with the well known Kerr spin-rotation coupling.
[Show abstract][Hide abstract] ABSTRACT: The features of equatorial motion of an extended body in Kerr spacetime are
investigated in the framework of the Mathisson-Papapetrou-Dixon model. The body
is assumed to stay at quasi-equilibrium and respond instantly to external
perturbations. Besides the mass, it is completely determined by its spin, the
multipolar expansion being truncated at the quadrupole order, with a
spin-induced quadrupole tensor. The study of the radial effective potential
allows to analytically determine the ISCO shift due to spin and the associated
frequency of the last circular orbit.
[Show abstract][Hide abstract] ABSTRACT: An assessment is made of recent attempts to evaluate how quantum gravity may
affect the anisotropy spectrum of the cosmic microwave background. A
perturbative scheme for the solution of the Wheeler-DeWitt equation has been
found to allow for enhancement of power at large scales, whereas the
alternative predicts a suppression of power at large scales. Both effects are
corrections which, although conceptually interesting, turn out to be too small
to be detected. Another scheme relies upon a Born-Oppenheimer analysis: by
using a perturbative approach to the nonlinear ordinary differential equation
obeyed by the two-point function for scalar fluctuations, a new family of power
spectra have been obtained and studied by the authors.
[Show abstract][Hide abstract] ABSTRACT: An extended body orbiting a compact object undergoes tidal deformations by the background gravitational field. Tidal invariants built up with the Riemann tensor and their derivatives evaluated along the worldline of the body are essential tools to investigate both geometrical and physical properties of the tidal interaction. For example, one can determine the tidal potential in the neighborhood of the body by constructing a body-fixed frame, which requires Fermi-type coordinates attached to the body itself, the latter being in turn related to the spacetime metric and curvature along the considered worldline. Similarly, in an effective field theory description of extended bodies, finite size effects are taken into account by adding to the point mass action certain nonminimal couplings which involve integrals of tidal invariants along the orbit of the body. In both cases such a computation of tidal tensors is required. Here we consider the case of a spinning body also endowed with a nonvanishing quadrupole moment in a Kerr spacetime. The structure of the body is modeled by a multipolar expansion around the ``center-of-mass line'' according to the Mathisson-Papapetrou-Dixon model truncated at the quadrupolar order. The quadrupole tensor is assumed to be quadratic in spin, accounting for rotational deformations. The behavior of tidal invariants of both electric and magnetic type is discussed in terms of gauge-invariant quantities when the body is moving along a circular orbit as well as in the case of an arbitrary (equatorial) motion. The analysis is completed by examining the associated eigenvalues and eigenvectors of the tidal tensors. The limiting situation of the Schwarzschild solution is also explored both in the strong field regime and in the weak field limit.
Physical Review D 04/2015; 91(8). DOI:10.1103/PhysRevD.91.084012 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A general framework is developed to investigate the properties of useful
choices of stationary spacelike slicings of stationary spacetimes whose
congruences of timelike orthogonal trajectories are interpreted as the world
lines of an associated family of observers, the kinematical properties of which
in turn may be used to geometrically characterize the original slicings. On the
other hand properties of the slicings themselves can directly characterize
their utility motivated instead by other considerations like the initial value
and evolution problems in the 3-plus-1 approach to general relativity. An
attempt is made to categorize the various slicing conditions or "time gauges"
used in the literature for the most familiar stationary spacetimes: black holes
and their flat spacetime limit.
International Journal of Geometric Methods in Modern Physics 03/2015; 12(7):150329185646001. DOI:10.1142/S021988781550070X · 0.44 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Continuing our analytic computation of the first-order self-force
contribution to the "geodetic" spin precession frequency of a small spinning
body orbiting a large (non-spinning) body we provide the exact expressions of
the tenth and tenth-and-a-half post-Newtonian terms. We also introduce a new
approach to the analytic computation of self-force regularization parameters
based on a WKB analysis of the radial and angular equations satisfied by the
metric perturbations.
Physical Review D 03/2015; 91(6). DOI:10.1103/PhysRevD.91.064064 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study Weitzenb\"ock's torsion and discuss its properties. Specifically, we
calculate the measured components of Weitzenb\"ock's torsion tensor for a frame
field adapted to static observers in a Fermi normal coordinate system that we
establish along the world line of an arbitrary accelerated observer in general
relativity. A similar calculation is carried out in the standard
Schwarzschild-like coordinates for static observers in the exterior Kerr
spacetime; we then compare our results with the corresponding curvature
components. Our work supports the contention that in the extended general
relativistic framework involving both the Levi-Civita and Weitzenb\"ock
connections, curvature and torsion provide complementary representations of the
gravitational field.
Physical Review D 02/2015; 91(8). DOI:10.1103/PhysRevD.91.084026 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Continuing our analytic computation of the first-order self-force
contribution to Detweiler's redshift variable we provide the exact expressions
of the ninth and ninth-and-a-half post-Newtonian terms.
Physical Review D 02/2015; 91(6). DOI:10.1103/PhysRevD.91.064050 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Motivated by the picture of a thin accretion disc around a black hole, radiating mainly in the direction perpendicular to
its plane, we study the motion of test particles interacting with a test geodesic radiation flux originating in the equatorial
plane of a Schwarzschild space–time and propagating initially in the perpendicular direction. We assume that the interaction
with the test particles is modelled by an effective term corresponding to the Thomson-type interaction which governs the Poynting–Robertson
effect. After approximating the individual photon trajectories adequately, we solve the continuity equation approximately
in order to find a consistent flux density with a certain plausible prescribed equatorial profile. The combined effects of
gravity and radiation are illustrated in several typical figures which confirm that the particles are generically strongly
influenced by the flux. In particular, they are both collimated and accelerated in the direction perpendicular to the disc,
but this acceleration is not enough to explain highly relativistic outflows emanating from some black hole–disc sources. The
model can however be improved in a number of ways before posing further questions which are summarized in concluding remarks.
Monthly Notices of the Royal Astronomical Society 01/2015; 446(3):2317. DOI:10.1093/mnras/stu2242 · 5.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In light of the relativistic precession model, we present here detailed
analyses, extending the ones performed in the Schwarzschild and Kerr
spacetimes. We consider the kilohertz quasi-periodic oscillations in the
Hartle-Thorne spacetime, which describes the gravitational field of a rotating
and deformed object. We derive the analytic formulas for the epicyclic
frequencies in the Hartel-Thorne spacetime and by means of these frequencies we
interpret the kilohertz quasi-periodic oscillations of low-mass X-ray binaries
of the atoll and Z - sources, on the basis of the relativistic precession
model. Particularly we perform analyzes for Z -source: GX 5-1. We show that the
quasi-periodic oscillations data can provide information on the parameters,
namely, the mass, angular momentum and quadrupole moment of the compact objects
in the low-mass X-ray binaries.
Gravitation and Cosmology 12/2014; 20(4). DOI:10.1134/S0202289314040033 · 0.72 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The influence of an arbitrary spin orientation on the quadrupolar structure
of an extended body moving in a Schwarzschild spacetime is investigated. The
body dynamics is described according to the Mathisson-Papapetrou-Dixon model
without any restriction on the motion or simplifying assumption on the
associated spin vector and quadrupole tensor, generalizing previous works. The
equations of motion are solved analytically in the limit of small values of the
characteristic length scales associated with the spin and quadrupole variables
with respect to the characteristic length of the background curvature. The
solution provides all corrections to the circular geodesic on the equatorial
plane taken as the reference trajectory due to both dipolar and quadrupolar
structure of the body as well as the conditions which the nonvanishing
components of the quadrupole tensor must fulfill in order that the problem be
self-consistent.
Physical Review D 12/2014; 91(10). DOI:10.1103/PhysRevD.91.104036 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The motion of a test particle in the gravitational field of a non-spherical
source endowed with both mass and mass quadrupole moment is investigated when a
test radiation field is also present. The background is described by the
Erez-Rosen solution, which is a static spacetime belonging to the Weyl class of
solutions to the vacuum Einstein's field equations, and reduces to the familiar
Schwarzschild solution when the quadrupole parameter vanishes. The radiation
flux has a fixed but arbitrary (non-zero) angular momentum. The interaction
with the radiation field is assumed to be Thomson-like, i.e., the particles
absorb and re-emit radiation, thus suffering for a friction-like drag force.
Such an additional force is responsible for the Poynting-Robertson effect,
which is well established in the framework of Newtonian gravity and has been
recently extended to the general theory of relativity. The balance between
gravitational attraction, centrifugal force and radiation drag leads to the
occurrence of equilibrium circular orbits which are attractors for the
surrounding matter for every fixed value of the interaction strength. The
presence of the quadrupolar structure of the source introduces a further degree
of freedom: there exists a whole family of equilibrium orbits parametrized by
the quadrupole parameter, generalizing previous works. This scenario is
expected to play a role in the context of accretion matter around compact
objects.
Monthly Notices of the Royal Astronomical Society 10/2014; 446(1). DOI:10.1093/mnras/stu2082 · 5.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Tidal interactions have a significant influence on the late dynamics of
compact binary systems, which constitute the prime targets of the upcoming
network of gravitational-wave detectors. We refine the theoretical description
of tidal interactions (hitherto known only to the second post-Newtonian level)
by extending our recently developed analytic self-force formalism, for extreme
mass-ratio binary systems, to the computation of several tidal invariants.
Specifically, we compute, to linear order in the mass ratio and to the
7.5$^{\rm th}$ post-Newtonian order, the following tidal invariants: the square
and the cube of the gravitoelectric quadrupolar tidal tensor, the square of the
gravitomagnetic quadrupolar tidal tensor, and the square of the gravitoelectric
octupolar tidal tensor. Our high-accuracy analytic results are compared to
recent numerical self-force tidal data by Dolan et al. \cite{Dolan:2014pja},
and, notably, provide an analytic understanding of the light ring asymptotic
behavior found by them. We transcribe our kinematical tidal-invariant results
in the more dynamically significant effective one-body description of the tidal
interaction energy. By combining, in a synergetic manner, analytical and
numerical results, we provide simple, accurate analytic representations of the
global, strong-field behavior of the gravitoelectric quadrupolar tidal factor.
A striking finding is that the linear-in-mass-ratio piece in the latter tidal
factor changes sign in the strong-field domain, to become negative (while its
previously known second post-Newtonian approximant was always positive). We,
however, argue that this will be more than compensated by a probable fast
growth, in the strong-field domain, of the nonlinear-in-mass-ratio
contributions in the tidal factor.
Physical Review D 09/2014; 90(12). DOI:10.1103/PhysRevD.90.124037 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The optical medium analogy of a given spacetime was developed decades ago and
has since then been widely applied to different gravitational contexts. Here we
consider the case of a colliding gravitational wave spacetime, generalizing
previous results concerning single gravitational pulses. Given the complexity
of the nonlinear interaction of two gravitational waves in the framework of
general relativity, typically leading to the formation of either horizons or
singularities, the optical medium analogy proves helpful to simply capture some
interesting effects of photon propagation.
General Relativity and Gravitation 08/2014; 46(1). DOI:10.1007/s10714-013-1644-4 · 1.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The equatorial motion of extended bodies in a Kerr spacetime is investigated
in the framework of the Mathisson-Papapetrou-Dixon model, including the full
set of effective components of the quadrupole tensor. The numerical integration
of the associated equations shows the specific role of the mass and current
quadrupole moment components. While most of the literature on this topic is
limited to spin-induced (purely electric) quadrupole tensor, the present
analysis highlights the effect of a completely general quadrupole tensor on the
dynamics. The contribution of the magnetic-type components is indeed related to
a number of interesting features, e.g., enhanced inward/outward spiraling
behavior of the orbit and spin-flip-like effects, which may have observational
counterparts. Finally, the validity limit of the Mathisson-Papapetrou-Dixon
model is also discussed through explicit examples.
[Show abstract][Hide abstract] ABSTRACT: We investigate the dynamics of test particles undergoing friction forces in a Friedmann–Robertson–Walker (FRW) spacetime. The interaction with the background fluid is modeled by introducing a Poynting–Robertson-like friction force in the equations of motion, leading to measurable (at least in principle) deviations of the particle trajectories from geodesic motion. The effect on the peculiar velocities of the particles is investigated for various equations of state of the background fluid and different standard cosmological models. The friction force is found to have major effects on particle motion in closed FRW universes, where it turns the time-asymptotic value (approaching the recollapse) of the peculiar particle velocity from ultra-relativistic (close to light speed) to a co-moving one, i.e., zero peculiar speed. On the other hand, for open or flat universes the effect of the friction is not so significant, because the time-asymptotic peculiar particle speed is largely non-relativistic also in the geodesic case.
European Physical Journal C 08/2014; 73(2). DOI:10.1140/epjc/s10052-013-2334-9 · 5.08 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Some strong field effects on test particle motion associated with the
propagation of a plane electromagnetic wave in the exact theory of general
relativity are investigated. Two different profiles of the associated radiation
flux are considered in comparison, corresponding to either constant or
oscillating electric and magnetic fields with respect to a natural family of
observers. These are the most common situations to be experimentally explored,
and have a well known counterpart in the flat spacetime limit. The resulting
line elements are determined by a single metric function, which turns out to be
expressed in terms of standard trigonometric functions in the case of a
constant radiation flux, and in terms of special functions in the case of
oscillating flux, leading to different features of test particle motion. The
world line deviation between both uncharged and charged particles on different
spacetime trajectories due to the combined effect of gravitational and
electromagnetic forces is studied. The interaction of charged particles with
the background radiation field is also discussed through a general relativistic
description of the inverse Compton effect. Motion as well as deviation effects
on particles endowed with spin are studied too. Special situations may occur in
which the direction of the spin vector change during the interaction, leading
to obsevables effects like spin-flip.
Physical Review D 08/2014; 89(10). DOI:10.1103/PhysRevD.89.104049 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A simple observation about the action for geodesics in a stationary spacetime
with separable geodesic equations leads to a natural class of slicings of that
spacetime whose orthogonal geodesic trajectories represent freely falling
observers. The time coordinate function can then be taken to be the observer
proper time, leading to a unit lapse function. This explains some of the
properties of the original Painlev\'e-Gullstrand coordinates on the
Schwarzschild spacetime and their generalization to the Kerr-Newman family of
spacetimes, reproducible also locally for the G\"odel spacetime. For the static
spherically symmetric case the slicing can be chosen to be intrinsically flat
with spherically symmetric geodesic observers, leaving all the gravitational
field information in the shift vector field.
General Relativity and Gravitation 08/2014; 44(3). DOI:10.1007/s10714-011-1295-2 · 1.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The motion of a massive test particle in a Schwarzschild spacetime surrounded by a perfect fluid with equation of state p
0=wρ
0 is investigated. Deviations from geodesic motion are analyzed as a function of the parameter w, ranging from w=1, which corresponds to the case of massive free scalar fields, down into the so-called “phantom” energy, with w<−1. It is found that the interaction with the fluid leads to capture (escape) of the particle trajectory in the case 1+w>0 (<0), respectively. Based on this result, it is argued that inspection of the trajectories of test particles in the vicinity of a Schwarzschild black hole with matter around may offer a new means of gaining insights into the nature of cosmic matter.
European Physical Journal C 08/2014; 72(3). DOI:10.1140/epjc/s10052-012-1913-5 · 5.08 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The motion of test particles along circular orbits in the vacuum $C$ metric
is studied in the Frenet-Serret formalism. Special orbits and corresponding
intrinsically defined geometrically relevant properties are selectively
studied.