42 research outputs found
Stable Bound Orbits in Six-dimensional Myers-Perry Black Holes
The existence of stable bound orbits of test particles is one of the most
characteristic properties in black hole spacetimes. In higher-dimensional black
holes, due to the dimensionality of gravity, there is no stable bound orbit
balanced by Newtonian gravitational monopole force and centrifugal force as in
the same mechanism of the four-dimensional Kerr black hole case. In this paper,
however, the existence of stable bound orbits of massive and massless particles
is shown in six-dimensional singly spinning Myers-Perry black holes with a
value of the spin parameter larger than a critical value. The innermost stable
circular orbits and the outermost stable bound orbit are found on the
rotational axis.Comment: 15 pages, 6 figure
Construction of test Maxwell fields with scale symmetry
Geometrical symmetry in a spacetime can generate test solutions to the
Maxwell equation. We demonstrate that the source-free Maxwell equation is
satisfied by any generator of spacetime self-similarity---a proper homothetic
vector---identified with a vector potential of the Maxwell theory. The test
fields obtained in this way share the scale symmetry of the background.Comment: 4 page
Gravitational two solitons in Levi-Civita spacetime
Applying the Pomeransky inverse scattering method to the four-dimensional
vacuum Einstein equations and using the Levi-Civita solution as a seed, we
construct a two-soliton solution with cylindrical symmetry. In our previous
work, we constructed the one-soliton solution with a real pole and showed that
the singularities that the Levi-Civita background has on an axis can be removed
by the choice of certain special parameters, but it still has unavoidable null
singularities, as usual one-solitons do. In this work, we show that for the
two-soliton solutions, any singularities can be removed by suitable
parameter-setting and such solutions describe the propagation of gravitational
wave packets. Moreover, in terms of the two-soliton solutions, we mention a
time shift phenomenon, the coalescence and the split of solitons as the
nonlinear effect of gravitational waves.Comment: 17 pages, 4 figures, version to be published in Classical and Quantum
Gravit
Gravitational solitons in Levi-Civita spacetime
Applying the Pomeransky inverse scattering method to the four-dimensional
vacuum Einstein equation and using the Levi-Civita solution for a seed, we
construct a cylindrically symmetric single-soliton solution. Although the
Levi-Civita spacetime generally includes singularities on its axis of symmetry,
it is shown that for the obtained single-soliton solution, such singularities
can be removed by choice of certain special parameters. This single-soliton
solution describes propagation of nonlinear cylindrical gravitational shock
wave pulses rather than solitonic waves. By analyzing wave amplitudes and
time-dependence of polarization angles, we provides physical description of the
single-soliton solution.Comment: 14 page
The essence of the Blandford-Znajek process
From a spacetime perspective, the dynamics of magnetic field lines of
force-free electromagnetic fields can be rewritten into a quite similar form
for the dynamics of strings, i.e., dynamics of "field sheets". Using this
formalism, we explicitly show that the field sheets of stationary and
axisymmetric force-free electromagnetic fields have identical intrinsic
properties to the world sheets of rigidly rotating Nambu-Goto strings. Thus, we
conclude that the Blandford-Znajek process is kinematically identical to an
energy-extraction mechanism by the Nambu-Goto string with an effective magnetic
tension.Comment: 15 pages, 3 figures; v2: references added; v3: published version in
PTE
Chaos in a generalized Euler's three-body problem
Euler's three-body problem is the problem of solving for the motion of a
particle moving in a Newtonian potential generated by two point sources fixed
in space. This system is integrable in the Liouville sense. We consider the
Euler problem with the inverse-square potential, which can be seen as a natural
generalization of the three-body problem to higher-dimensional Newtonian
theory. We identify a family of stable stationary orbits in the generalized
Euler problem. These orbits guarantee the existence of stable bound orbits.
Applying the Poincar\'e map method to these orbits, we show that stable bound
chaotic orbits appear. As a result, we conclude that the generalized Euler
problem is nonintegrable.Comment: 11 pages, 2 figure
Scale invariance and constants of motion
Scale invariance in the theory of classical mechanics can be induced from the
scale invariance of background fields. In this paper we consider the relation
between the scale invariance and the constants of particle motion in a
self-similar spacetime, only in which the symmetry is well-defined and is
generated by a homothetic vector. Relaxing the usual conservation condition by
the Hamiltonian constraint in a particle system, we obtain a conservation law
holding only on the constraint surface in the phase space. By the conservation
law, we characterize constants of motion associated with the scale invariance
not only for massless particles but for massive particles and classify the
condition for the existence of the constants of motion. Furthermore, we find
the explicit form of the constants of motion by solving the conservation
equations.Comment: 9 pages; v2:published version in PTE
Stable Bound Orbits of Massless Particles around a Black Ring
We study the geodesic motion of massless particles in singly rotating black
ring spacetimes. We find stable stationary orbits of massless particles in
toroidal spiral shape in the case that the thickness parameter of a black ring
is less than a critical value. Furthermore, there exist nonstationary massless
particles bounded in a finite region outside the horizon. This is the first
example of stable bound orbits of massless particles around a black object.Comment: 16 pages, 12 figure
Killing Tensors and Conserved Quantities of a Relativistic Particle in External Fields
We generalize Killing equations to a test particle system which is subjected
to external force. We relax the conservation condition by virtue of
reparametrization invariance of a particle orbit. As a result, we obtain
generalized Killing equations which have hierarchical structure on the top of
which a conformal Killing equation exists.Comment: Proceedings of the 12th Marcel Grossmann Meeting on General
Relativity (MG 12), Paris, France, 12-18 Jul 200
Stable circular orbits in higher-dimensional multi-black hole spacetimes
We consider the dynamics of particles, particularly focusing on circular
orbits in the higher-dimensional Majumdar-Papapetrou (MP) spacetimes with two
equal mass black holes. It is widely known that in the 5D
Schwarzschild-Tangherlini and Myers-Perry backgrounds, there are no stable
circular orbits. In contrast, we show that in the 5D MP background, stable
circular orbits can always exist when the separation of two black holes is
large enough. More precisely, for a large separation, stable circular orbits
exist from the vicinity of horizons to infinity; for a medium one, they appear
only in a certain finite region bounded by the innermost stable circular orbit
and the outermost stable circular orbit outside the horizons; for a small one,
they do not appear at all. Moreover, we show that in MP spacetimes in more than
5D, they do not exist for any separations.Comment: 22 pages, 4 figures; v2: minor revisions, add references; v3:
published versio