104 research outputs found
Stability study of a model for the Klein-Gordon equation in Kerr spacetime
The current early stage in the investigation of the stability of the Kerr
metric is characterized by the study of appropriate model problems.
Particularly interesting is the problem of the stability of the solutions of
the Klein-Gordon equation, describing the propagation of a scalar field of mass
in the background of a rotating black hole. Rigorous results proof the
stability of the reduced, by separation in the azimuth angle in Boyer-Lindquist
coordinates, field for sufficiently large masses. Some, but not all, numerical
investigations find instability of the reduced field for rotational parameters
extremely close to 1. Among others, the paper derives a model problem for
the equation which supports the instability of the field down to .Comment: Updated version, after minor change
Nucleation mechanism for the direct graphite-to-diamond phase transition
Graphite and diamond have comparable free energies, yet forming diamond from
graphite is far from easy. In the absence of a catalyst, pressures that are
significantly higher than the equilibrium coexistence pressures are required to
induce the graphite-to-diamond transition. Furthermore, the formation of the
metastable hexagonal polymorph of diamond instead of the more stable cubic
diamond is favored at lower temperatures. The concerted mechanism suggested in
previous theoretical studies cannot explain these phenomena. Using an ab initio
quality neural-network potential we performed a large-scale study of the
graphite-to-diamond transition assuming that it occurs via nucleation. The
nucleation mechanism accounts for the observed phenomenology and reveals its
microscopic origins. We demonstrated that the large lattice distortions that
accompany the formation of the diamond nuclei inhibit the phase transition at
low pressure and direct it towards the hexagonal diamond phase at higher
pressure. The nucleation mechanism proposed in this work is an important step
towards a better understanding of structural transformations in a wide range of
complex systems such as amorphous carbon and carbon nanomaterials
Two binary stars gravitational waves - homotopy perturbation method
Homotopy perturbation is one of the newest methods for numerical analysis of
deferential equations. We have used for solving wave equation around a black
hole. Our conclusions have this method far reaching consequences for comparison
of theoritical physics and experimental physics.Comment: The manuscript considers the important problem of solve equation wave
around a black hole. We have solved that by using Homotopy perturbation
methods. Homotopy perturbation is one of the newest methods for numerical
analysis of deferential equations. Our conclusions have far reaching
consequences for comparison of theoritical physics and experimental physic
On the horizon instability of an extreme Reissner-Nordstrom black hole
Aretakis has proved that a massless scalar field has an instability at the
horizon of an extreme Reissner-Nordstr\"om black hole. We show that a similar
instability occurs also for a massive scalar field and for coupled linearized
gravitational and electromagnetic perturbations. We present numerical results
for the late time behaviour of massless and massive scalar fields in the
extreme RN background and show that instabilities are present for initial
perturbations supported outside the horizon, e.g.\ an ingoing wavepacket. For a
massless scalar we show that the numerical results for the late time behaviour
are reproduced by an analytic calculation in the near-horizon geometry. We
relate Aretakis' conserved quantities at the future horizon to the
Newman-Penrose conserved quantities at future null infinity.Comment: 44 pages, 19 figure
Quasi-Normal Modes of Stars and Black Holes
Perturbations of stars and black holes have been one of the main topics of
relativistic astrophysics for the last few decades. They are of particular
importance today, because of their relevance to gravitational wave astronomy.
In this review we present the theory of quasi-normal modes of compact objects
from both the mathematical and astrophysical points of view. The discussion
includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om,
Kerr and Kerr-Newman) and relativistic stars (non-rotating and
slowly-rotating). The properties of the various families of quasi-normal modes
are described, and numerical techniques for calculating quasi-normal modes
reviewed. The successes, as well as the limits, of perturbation theory are
presented, and its role in the emerging era of numerical relativity and
supercomputers is discussed.Comment: 74 pages, 7 figures, Review article for "Living Reviews in
Relativity
Physics, Astrophysics and Cosmology with Gravitational Waves
Gravitational wave detectors are already operating at interesting sensitivity
levels, and they have an upgrade path that should result in secure detections
by 2014. We review the physics of gravitational waves, how they interact with
detectors (bars and interferometers), and how these detectors operate. We study
the most likely sources of gravitational waves and review the data analysis
methods that are used to extract their signals from detector noise. Then we
consider the consequences of gravitational wave detections and observations for
physics, astrophysics, and cosmology.Comment: 137 pages, 16 figures, Published version
<http://www.livingreviews.org/lrr-2009-2
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress in characteristic
evolution is traced from the early stage of 1D feasibility studies to 2D
axisymmetric codes that accurately simulate the oscillations and gravitational
collapse of relativistic stars and to current 3D codes that provide pieces of a
binary black hole spacetime. Cauchy codes have now been successful at
simulating all aspects of the binary black hole problem inside an artificially
constructed outer boundary. A prime application of characteristic evolution is
to extend such simulations to null infinity where the waveform from the binary
inspiral and merger can be unambiguously computed. This has now been
accomplished by Cauchy-characteristic extraction, where data for the
characteristic evolution is supplied by Cauchy data on an extraction worldtube
inside the artificial outer boundary. The ultimate application of
characteristic evolution is to eliminate the role of this outer boundary by
constructing a global solution via Cauchy-characteristic matching. Progress in
this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note:
updated version of arXiv:gr-qc/050809
The motion of point particles in curved spacetime
This review is concerned with the motion of a point scalar charge, a point
electric charge, and a point mass in a specified background spacetime. In each
of the three cases the particle produces a field that behaves as outgoing
radiation in the wave zone, and therefore removes energy from the particle. In
the near zone the field acts on the particle and gives rise to a self-force
that prevents the particle from moving on a geodesic of the background
spacetime. The field's action on the particle is difficult to calculate because
of its singular nature: the field diverges at the position of the particle. But
it is possible to isolate the field's singular part and show that it exerts no
force on the particle -- its only effect is to contribute to the particle's
inertia. What remains after subtraction is a smooth field that is fully
responsible for the self-force. Because this field satisfies a homogeneous wave
equation, it can be thought of as a free (radiative) field that interacts with
the particle; it is this interaction that gives rise to the self-force. The
mathematical tools required to derive the equations of motion of a point scalar
charge, a point electric charge, and a point mass in a specified background
spacetime are developed here from scratch. The review begins with a discussion
of the basic theory of bitensors (part I). It then applies the theory to the
construction of convenient coordinate systems to chart a neighbourhood of the
particle's word line (part II). It continues with a thorough discussion of
Green's functions in curved spacetime (part III). The review concludes with a
detailed derivation of each of the three equations of motion (part IV).Comment: LaTeX2e, 116 pages, 10 figures. This is the final version, as it will
appear in Living Reviews in Relativit
Spin and quadrupole contributions to the motion of astrophysical binaries
Compact objects in general relativity approximately move along geodesics of
spacetime. It is shown that the corrections to geodesic motion due to spin
(dipole), quadrupole, and higher multipoles can be modeled by an extension of
the point mass action. The quadrupole contributions are discussed in detail for
astrophysical objects like neutron stars or black holes. Implications for
binaries are analyzed for a small mass ratio situation. There quadrupole
effects can encode information about the internal structure of the compact
object, e.g., in principle they allow a distinction between black holes and
neutron stars, and also different equations of state for the latter.
Furthermore, a connection between the relativistic oscillation modes of the
object and a dynamical quadrupole evolution is established.Comment: 43 pages. Proceedings of the 524. WE-Heraeus-Seminar "Equations of
Motion in Relativistic Gravity". v2: fixed reference. v3: corrected typos in
eqs. (1), (57), (85
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