190 research outputs found
"Peeling property" for linearized gravity in null coordinates
A complete description of the linearized gravitational field on a flat
background is given in terms of gauge-independent quasilocal quantities. This
is an extension of the results from gr-qc/9801068. Asymptotic spherical
quasilocal parameterization of the Weyl field and its relation with Einstein
equations is presented. The field equations are equivalent to the wave
equation. A generalization for Schwarzschild background is developed and the
axial part of gravitational field is fully analyzed. In the case of axial
degree of freedom for linearized gravitational field the corresponding
generalization of the d'Alembert operator is a Regge-Wheeler equation. Finally,
the asymptotics at null infinity is investigated and strong peeling property
for axial waves is proved.Comment: 27 page
CYK Tensors, Maxwell Field and Conserved Quantities for Spin-2 Field
Starting from an important application of Conformal Yano--Killing tensors for
the existence of global charges in gravity, some new observations at \scri^+
are given. They allow to define asymptotic charges (at future null infinity) in
terms of the Weyl tensor together with their fluxes through \scri^+. It
occurs that some of them play a role of obstructions for the existence of
angular momentum.
Moreover, new relations between solutions of the Maxwell equations and the
spin-2 field are given. They are used in the construction of new conserved
quantities which are quadratic in terms of the Weyl tensor. The obtained
formulae are similar to the functionals obtained from the
Bel--Robinson tensor.Comment: 20 pages, LaTe
Energy and angular momentum of the weak gravitational waves on the Schwarzschild background -- quasilocal gauge-invariant formulation
It is shown that the axial and polar perturbations of the spherically
symmetric black hole can be described in a gauge-invariant way. The reduced
phase space describing gravitational waves outside of the horizon is described
by the gauge-invariant quantities. Both degrees of freedom fulfill generalized
scalar wave equation. For the axial degree of freedom the radial part of the
equation corresponds to the Regge-Wheeler result (Phys. Rev. 108, 1063-1069
(1957)) and for the polar one we get Zerilli result (Phys. Rev. D2, 2141-2160
(1970)), see also Chandrasekhar (The Mathematical Theory of Black
Holes,(Clarendon Press Oxford, 1983)), Moncrief (Annals of Physics 88, 323-342
(1974)) for both. An important ingredient of the analysis is the concept of
quasilocality which does duty for the separation of the angular variables in
the usual approach. Moreover, there is no need to represent perturbations by
normal modes (with time dependence ), we have fields in spacetime
and the Cauchy problem for them is well defined outside of the horizon. The
reduced symplectic structure explains the origin of the axial and polar
invariants. It allows to introduce an energy and angular momentum for the
gravitational waves which is invariant with respect to the gauge
transformations. Both generators represent quadratic approximation of the ADM
nonlinear formulae in terms of the perturbations of the Schwarzschild metric.
We also discuss the boundary-initial value problem for the linearized Einstein
equations on a Schwarzschild background outside of the horizon.Comment: 23 page
Asymptotic Conformal Yano--Killing Tensors for Schwarzschild Metric
The asymptotic conformal Yano--Killing tensor proposed in J. Jezierski, On
the relation between metric and spin-2 formulation of linearized Einstein
theory [GRG, in print (1994)] is analyzed for Schwarzschild metric and tensor
equations defining this object are given. The result shows that the
Schwarzschild metric (and other metrics which are asymptotically
``Schwarzschildean'' up to O(1/r^2) at spatial infinity) is among the metrics
fullfilling stronger asymptotic conditions and supertranslations ambiguities
disappear. It is also clear from the result that 14 asymptotic gravitational
charges are well defined on the ``Schwarzschildean'' background.Comment: 8 pages, latex, no figure
The Trautman-Bondi mass of hyperboloidal initial data sets
We give a definition of mass for conformally compactifiable initial data sets. The asymptotic conditions are compatible with existence of gravitational radiation, and the compactifications are allowed to be polyhomogeneous. We show that the resulting mass is a geometric invariant, and we prove positivity thereof in the case of a spherical conformal infinity. When R(g) - or, equivalently, the trace of the extrinsic curvature tensor - tends to a negative constant to order one at infinity, the definition is expressed purely in terms of three-dimensional or two-dimensional objects
Conformal Yano-Killing tensor for the Kerr metric and conserved quantities
Properties of (skew-symmetric) conformal Yano--Killing tensors are reviewed.
Explicit forms of three symmetric conformal Killing tensors in Kerr spacetime
are obtained from the Yano--Killing tensor. The relation between spin-2 fields
and solutions to the Maxwell equations is used in the construction of a new
conserved quantity which is quadratic in terms of the Weyl tensor. The formula
obtained is similar to the functional obtained from the Bel--Robinson tensor
and is examined in Kerr spacetime. A new interpretation of the conserved
quantity obtained is proposed.Comment: 29 page
Energy-minimizing two black holes initial data
An attempt to construct the ``ground state'' vacuum initial data for the
gravitational field surrounding two black holes is presented. The ground state
is defined as the gravitational initial data minimizing the ADM mass within the
class of data for which the masses of the holes and their distance are fixed.
To parameterize different geometric arrangements of the two holes (and,
therefore, their distance) we use an appropriately chosen scale factor. A
method for analyzing the variations of the ADM mass and the masses (areas) of
the horizons in terms of gravitational degrees of freedom is proposed. The
Misner initial data are analyzed in this context: it is shown that they do not
minimize the ADM mass.Comment: Minor corrections, 2 references adde
Spacetimes foliated by Killing horizons
It seems to be expected, that a horizon of a quasi-local type, like a Killing
or an isolated horizon, by analogy with a globally defined event horizon,
should be unique in some open neighborhood in the spacetime, provided the
vacuum Einstein or the Einstein-Maxwell equations are satisfied. The aim of our
paper is to verify whether that intuition is correct. If one can extend a so
called Kundt metric, in such a way that its null, shear-free surfaces have
spherical spacetime sections, the resulting spacetime is foliated by so called
non-expanding horizons. The obstacle is Kundt's constraint induced at the
surfaces by the Einstein or the Einstein-Maxwell equations, and the requirement
that a solution be globally defined on the sphere. We derived a transformation
(reflection) that creates a solution to Kundt's constraint out of data defining
an extremal isolated horizon. Using that transformation, we derived a class of
exact solutions to the Einstein or Einstein-Maxwell equations of very special
properties. Each spacetime we construct is foliated by a family of the Killing
horizons. Moreover, it admits another, transversal Killing horizon. The
intrinsic and extrinsic geometry of the transversal Killing horizon coincides
with the one defined on the event horizon of the extremal Kerr-Newman solution.
However, the Killing horizon in our example admits yet another Killing vector
tangent to and null at it. The geometries of the leaves are given by the
reflection.Comment: LaTeX 2e, 13 page
Trapped surfaces and the Penrose inequality in spherically symmetric geometries
We demonstrate that the Penrose inequality is valid for spherically symmetric
geometries even when the horizon is immersed in matter. The matter field need
not be at rest. The only restriction is that the source satisfies the weak
energy condition outside the horizon. No restrictions are placed on the matter
inside the horizon. The proof of the Penrose inequality gives a new necessary
condition for the formation of trapped surfaces. This formulation can also be
adapted to give a sufficient condition. We show that a modification of the
Penrose inequality proposed by Gibbons for charged black holes can be broken in
early stages of gravitational collapse. This investigation is based exclusively
on the initial data formulation of General Relativity.Comment: plain te
Construction and enlargement of traversable wormholes from Schwarzschild black holes
Analytic solutions are presented which describe the construction of a
traversable wormhole from a Schwarzschild black hole, and the enlargement of
such a wormhole, in Einstein gravity. The matter model is pure radiation which
may have negative energy density (phantom or ghost radiation) and the
idealization of impulsive radiation (infinitesimally thin null shells) is
employed.Comment: 22 pages, 7 figure
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