69 research outputs found
General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry
The Hamiltonian formulation of general relativity on a null surface is
established in the teleparallel geometry. No particular gauge conditons on the
tetrads are imposed, such as the time gauge condition. By means of a 3+1
decomposition the resulting Hamiltonian arises as a completely constrained
system. However, it is structurally different from the the standard
Arnowitt-Deser-Misner (ADM) type formulation. In this geometrical framework the
basic field quantities are tetrads that transform under the global SO(3,1) and
the torsion tensor.Comment: 15 pages, Latex, no figures, to appear in the Gen. Rel. Gra
Asymptotically Non-Static Kerr-deSitter Spacetime With No Event Horizon
We present our derivations for Kerr-deSitter metric in a proper comoving
coordinate system.It asymptotically approaches to the deSitter metric in
Robertson-walker form.This has been done by considring the stationary
axially-symmetric spacetime in which motion of particle is integrable.That is
the Hamilton-Jacobi and Klein-Gordon equations are separable.In this form it is
asymptotically consistent with comoving frame.Comment: Title changed,revised arguments,results unchanged
On the spectral shift and the time delay of light in a Rindler accelerated frame
We discuss two effects predicted by the general theory of relativity in the
context of Rindler accelerated observers: the gravitational spectral shift and
the time delay of light. We show that these effects also appear in a Rindler
frame in the absence of gravitational field, in accordance with the Einstein's
equivalence principle.Comment: 12 pages, 3 figure
Singularity in Gravitational Collapse of Plane Symmetric Charged Vaidya Spacetime
We study the final outcome of gravitational collapse resulting from the plane
symmetric charged Vaidya spacetime. Using the field equations, we show that the
weak energy condition is always satisfied by collapsing fluid. It is found that
the singularity formed is naked. The strength of singularity is also
investigated by using Nolan's method. This turns out to be a strong curvature
singularity in Tipler's sense and hence provides a counter example to the
cosmic censorship hypothesis.Comment: 8 pages, accepted for publication in Mod. Phys. Lett
Linearized solutions of the Einstein equations within a Bondi-Sachs framework, and implications for boundary conditions in numerical simulations
We linearize the Einstein equations when the metric is Bondi-Sachs, when the
background is Schwarzschild or Minkowski, and when there is a matter source in
the form of a thin shell whose density varies with time and angular position.
By performing an eigenfunction decomposition, we reduce the problem to a system
of linear ordinary differential equations which we are able to solve. The
solutions are relevant to the characteristic formulation of numerical
relativity: (a) as exact solutions against which computations of gravitational
radiation can be compared; and (b) in formulating boundary conditions on the
Schwarzschild horizon.Comment: Revised following referee comment
Quasi-Spherical Light Cones of the Kerr Geometry
Quasi-spherical light cones are lightlike hypersurfaces of the Kerr geometry
that are asymptotic to Minkowski light cones at infinity. We develop the
equations of these surfaces and examine their properties. In particular, we
show that they are free of caustics for all positive values of the Kerr radial
coordinate r. Useful applications include the propagation of high-frequency
waves, the definition of Kruskal-like coordinates for a spinning black hole and
the characteristic initial-value problem.Comment: LaTeX, 14 pages, 2 figure
Non-linear instability of Kerr-type Cauchy horizons
Using the general solution to the Einstein equations on intersecting null
surfaces developed by Hayward, we investigate the non-linear instability of the
Cauchy horizon inside a realistic black hole. Making a minimal assumption about
the free gravitational data allows us to solve the field equations along a null
surface crossing the Cauchy Horizon. As in the spherical case, the results
indicate that a diverging influx of gravitational energy, in concert with an
outflux across the CH, is responsible for the singularity. The spacetime is
asymptotically Petrov type N, the same algebraic type as a gravitational shock
wave. Implications for the continuation of spacetime through the singularity
are briefly discussed.Comment: 11 pages RevTeX, two postscript figures included using epsf.st
Quasi-local first law of black-hole dynamics
A property well known as the first law of black hole is a relation among
infinitesimal variations of parameters of stationary black holes. We consider a
dynamical version of the first law, which may be called the first law of black
hole dynamics. The first law of black hole dynamics is derived without assuming
any symmetry or any asymptotic conditions. In the derivation, a definition of
dynamical surface gravity is proposed. In spherical symmetry it reduces to that
defined recently by one of the authors (SAH).Comment: Latex, 8 pages; version to appear in Class. Quantum Gra
Finding Principal Null Direction for Numerical Relativists
We present a new method for finding principal null directions (PNDs). Because
our method assumes as input the intrinsic metric and extrinsic curvature of a
spacelike hypersurface, it should be particularly useful to numerical
relativists. We illustrate our method by finding the PNDs of the
Kastor-Traschen spacetimes, which contain arbitrarily many black holes in
a de Sitter back-ground.Comment: 10 pages, LaTeX style, WU-AP/38/93. Figures are available (hard
copies) upon requests [[email protected] (H.Shinkai)
Responses of the Brans-Dicke field due to gravitational collapses
We study responses of the Brans-Dicke field due to gravitational collapses of
scalar field pulses using numerical simulations. Double-null formalism is
employed to implement the numerical simulations. If we supply a scalar field
pulse, it will asymptotically form a black hole via dynamical interactions of
the Brans-Dicke field. Hence, we can observe the responses of the Brans-Dicke
field by two different regions. First, we observe the late time behaviors after
the gravitational collapse, which include formations of a singularity and an
apparent horizon. Second, we observe the fully dynamical behaviors during the
gravitational collapse and view the energy-momentum tensor components. For the
late time behaviors, if the Brans-Dicke coupling is greater (or smaller) than
-1.5, the Brans-Dicke field decreases (or increases) during the gravitational
collapse. Since the Brans-Dicke field should be relaxed to the asymptotic value
with the elapse of time, the final apparent horizon becomes time-like (or
space-like). For the dynamical behaviors, we observed the energy-momentum
tensors around ~ -1.5. If the Brans-Dicke coupling is greater than
-1.5, the component can be negative at the outside of the black hole.
This can allow an instantaneous inflating region during the gravitational
collapse. If the Brans-Dicke coupling is less than -1.5, the oscillation of the
component allows the apparent horizon to shrink. This allows a
combination that violates weak cosmic censorship. Finally, we discuss the
implications of the violation of the null energy condition and weak cosmic
censorship.Comment: 28 pages, 14 figure
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