5,885 research outputs found
Euler characteristics of moduli spaces of curves
Let Mgn be the moduli space of n-pointed Riemann surfaces of genus g. Denote by Mgn the Deligne-Mumford compactification of Mgn. In the present paper, we calculate the orbifold and the ordinary Euler characteristic of Mgn for any g and n such that n > 2-2g
Geometric transport along circular orbits in stationary axisymmetric spacetimes
Parallel transport along circular orbits in orthogonally transitive
stationary axisymmetric spacetimes is described explicitly relative to Lie
transport in terms of the electric and magnetic parts of the induced
connection. The influence of both the gravitoelectromagnetic fields associated
with the zero angular momentum observers and of the Frenet-Serret parameters of
these orbits as a function of their angular velocity is seen on the behavior of
parallel transport through its representation as a parameter-dependent Lorentz
transformation between these two inner-product preserving transports which is
generated by the induced connection. This extends the analysis of parallel
transport in the equatorial plane of the Kerr spacetime to the entire spacetime
outside the black hole horizon, and helps give an intuitive picture of how
competing "central attraction forces" and centripetal accelerations contribute
with gravitomagnetic effects to explain the behavior of the 4-acceleration of
circular orbits in that spacetime.Comment: 33 pages ijmpd latex article with 24 eps figure
Kerr metric, static observers and Fermi coordinates
The coordinate transformation which maps the Kerr metric written in standard
Boyer-Lindquist coordinates to its corresponding form adapted to the natural
local coordinates of an observer at rest at a fixed position in the equatorial
plane, i.e., Fermi coordinates for the neighborhood of a static observer world
line, is derived and discussed in a way which extends to any uniformly
circularly orbiting observer there.Comment: 15 page latex iopart class documen
Circular holonomy in the Taub-NUT spacetime
Parallel transport around closed circular orbits in the equatorial plane of
the Taub-NUT spacetime is analyzed to reveal the effect of the gravitomagnetic
monopole parameter on circular holonomy transformations. Investigating the
boost/rotation decomposition of the connection 1-form matrix evaluated along
these orbits, one finds a situation that reflects the behavior of the general
orthogonally transitive stationary axisymmetric case and indeed along Killing
trajectories in general.Comment: 9 pages, LaTeX iopart class, no figure
Teukolsky Master Equation: De Rham wave equation for the gravitational and electromagnetic fields in vacuum
A new version of the Teukolksy Master Equation, describing any massless field
of different spin in the Kerr black hole, is presented here in
the form of a wave equation containing additional curvature terms. These
results suggest a relation between curvature perturbation theory in general
relativity and the exact wave equations satisfied by the Weyl and the Maxwell
tensors, known in the literature as the de Rham-Lichnerowicz Laplacian
equations. We discuss these Laplacians both in the Newman-Penrose formalism and
in the Geroch-Held-Penrose variant for an arbitrary vacuum spacetime.
Perturbative expansion of these wave equations results in a recursive scheme
valid for higher orders. This approach, apart from the obvious implications for
the gravitational and electromagnetic wave propagation on a curved spacetime,
explains and extends the results in the literature for perturbative analysis by
clarifying their true origins in the exact theory.Comment: 30 pages. No figures. Used PTP macros. To appear on Prog. Theor.
Phys., Vol. 107, No. 5, May 200
Towards a closed differential aging formula in special relativity
It is well known that the Lorentzian length of a timelike curve in Minkowski
spacetime is smaller than the Lorentzian length of the geodesic connecting its
initial and final endpoints. The difference is known as the 'differential
aging' and its calculation in terms of the proper acceleration history of the
timelike curve would provide an important tool for the autonomous spacetime
navigation of non-inertial observers. I give a solution in 3+1 dimensions which
holds whenever the acceleration is decomposed with respect to a lightlike
transported frame (lightlike transport will be defined), the analogous and more
natural problem for a Fermi-Walker decomposition being still open.Comment: Latex2e, 6 pages, 1 figure, uses psfrag. Contribution to the
Proceedings of The Spanish Relativity Meeting (ERE 2006), Palma de Mallorca,
Spain September 4-8, 200
Spinning particles in Schwarzschild-de Sitter space-time
After considering the reference case of the motion of spinning test bodies in
the equatorial plane of the Schwarzschild space-time, we generalize the results
to the case of the motion of a spinning particle in the equatorial plane of the
Schwarzschild-de Sitter space-time. Specifically, we obtain the loci of turning
points of the particle in this plane. We show that the cosmological constant
affect the particle motion when the particle distance from the black hole is of
the order of the inverse square root of the cosmological constant.Comment: 8 pages, 5 eps figures, submitted to Gen.Rel.Gra
Spinning test particles and clock effect in Schwarzschild spacetime
We study the behaviour of spinning test particles in the Schwarzschild
spacetime. Using Mathisson-Papapetrou equations of motion we confine our
attention to spatially circular orbits and search for observable effects which
could eventually discriminate among the standard supplementary conditions
namely the Corinaldesi-Papapetrou, Pirani and Tulczyjew. We find that if the
world line chosen for the multipole reduction and whose unit tangent we denote
as is a circular orbit then also the generalized momentum of the
spinning test particle is tangent to a circular orbit even though and
are not parallel four-vectors. These orbits are shown to exist because the spin
induced tidal forces provide the required acceleration no matter what
supplementary condition we select. Of course, in the limit of a small spin the
particle's orbit is close of being a circular geodesic and the (small)
deviation of the angular velocities from the geodesic values can be of an
arbitrary sign, corresponding to the possible spin-up and spin-down alignment
to the z-axis. When two spinning particles orbit around a gravitating source in
opposite directions, they make one loop with respect to a given static observer
with different arrival times. This difference is termed clock effect. We find
that a nonzero gravitomagnetic clock effect appears for oppositely orbiting
both spin-up or spin-down particles even in the Schwarzschild spacetime. This
allows us to establish a formal analogy with the case of (spin-less) geodesics
on the equatorial plane of the Kerr spacetime. This result can be verified
experimentally.Comment: IOP macros, eps figures n. 2, to appear on Classical and Quantum
gravity, 200
Gravitomagnetism in the Kerr-Newman-Taub-NUT spacetime
We study the motion of test particles and electromagnetic waves in the
Kerr-Newman-Taub-NUT spacetime in order to elucidate some of the effects
associated with the gravitomagnetic monopole moment of the source. In
particular, we determine in the linear approximation the contribution of this
monopole to the gravitational time delay and the rotation of the plane of the
polarization of electromagnetic waves. Moreover, we consider "spherical" orbits
of uncharged test particles in the Kerr-Taub-NUT spacetime and discuss the
modification of the Wilkins orbits due to the presence of the gravitomagnetic
monopole.Comment: 12 pages LaTeX iopart style, uses PicTex for 1 Figur
Stability of circular orbits of spinning particles in Schwarzschild-like space-times
Circular orbits of spinning test particles and their stability in
Schwarzschild-like backgrounds are investigated. For these space-times the
equations of motion admit solutions representing circular orbits with particles
spins being constant and normal to the plane of orbits. For the de Sitter
background the orbits are always stable with particle velocity and momentum
being co-linear along them. The world-line deviation equations for particles of
the same spin-to-mass ratios are solved and the resulting deviation vectors are
used to study the stability of orbits. It is shown that the orbits are stable
against radial perturbations. The general criterion for stability against
normal perturbations is obtained. Explicit calculations are performed in the
case of the Schwarzschild space-time leading to the conclusion that the orbits
are stable.Comment: eps figures, submitted to General Relativity and Gravitatio
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