17 research outputs found
The Vacuum Einstein Equations via Holonomy around Closed Loops on Characteristic Surfaces
We reformulate the standard local equations of general relativity for
asymptotically flat spacetimes in terms of two non-local quantities, the
holonomy around certain closed null loops on characteristic surfaces and
the light cone cut function , which describes the intersection of the future
null cones from arbitrary spacetime points, with future null infinity. We
obtain a set of differential equations for and equivalent to the vacuum
Einstein equations. By finding an algebraic relation between and this
set of equations is reduced to just two coupled equations: an
integro-differential equation for which yields the conformal structure of
the underlying spacetime and a linear differential equation for the ``vacuum''
conformal factor. These equations, which apply to all vacuum asymptotically
flat spacetimes, are however lengthy and complicated and we do not yet know of
any solution generating technique. They nevertheless are amenable to an
attractive perturbative scheme which has Minkowski space as a zeroth order
solution.Comment: 28 pages, RevTeX, 3 PostScript figure
Center of Mass and spin for isolated sources of gravitational radiation
We define the center of mass and spin of an isolated system in General
Relativity. The resulting relationships between these variables and the total
linear and angular momentum of the gravitational system are remarkably similar
to their Newtonian counterparts, though only variables at the null boundary of
an asymptotically flat spacetime are used for their definition. We also derive
equations of motion linking their time evolution to the emitted gravitational
radiation. The results are then compared to other approaches. In particular one
obtains unexpected similarities as well as some differences with results
obtained in the Post Newtonian literature . These equations of motion should be
useful when describing the radiation emitted by compact sources such as
coalescing binaries capable of producing gravitational kicks, supernovas, or
scattering of compact objects.Comment: 16 pages. Accepted for publication in Phys. Rev.
Astrophysical limits on quantum gravity motivated birefringence
We obtain observational upper bounds on a class of quantum gravity related
birefringence effects, by analyzing the presence of linear polarization in the
optical and ultraviolet spectrum of some distant sources. In the notation of
Gambini and Pullin we find .Comment: 4 pages, submitted to Phys. Rev. Let
Superselection Sectors in Asymptotic Quantization of Gravity
Using the continuity of the scalar (the mass aspect) at null
infinity through we show that the space of radiative solutions of general
relativity can be thought of a fibered space where the value of at
plays the role of the base space. We also show that the restriction of
the available symplectic form to each ``fiber'' is degenerate. By finding the
orbit manifold of this degenerate direction we obtain the reduced phase space
for the radiation data. This reduced phase space posses a global structure,
i.e., it does not distinguishes between future or past null infinity. Thus, it
can be used as the space of quantum gravitons. Moreover, a Hilbert space can be
constructed on each ``fiber'' if an appropriate definition of scalar product is
provided. Since there is no natural correspondence between the Hilbert spaces
of different foliations they define superselection sectors on the space of
asymptotic quantum states.Comment: 22 pages, revtex fil
Linearized Einstein theory via null surfaces
Recently there has been developed a reformulation of General Relativity -
referred to as {\it the null surface version of GR} - where instead of the
metric field as the basic variable of the theory, families of three-surfaces in
a four-manifold become basic. From these surfaces themselves, a conformal
metric, conformal to an Einstein metric, can be constructed. A choice of
conformal factor turns them into Einstein metrics. The surfaces are then
automatically characteristic surfaces of this metric. In the present paper we
explore the linearization of this {\it null surface theory} and compare it with
the standard linear GR. This allows a better understanding of many of the
subtle mathematical issues and sheds light on some of the obscure points of the
null surface theory. It furthermore permits a very simple solution generating
scheme for the linear theory and the beginning of a perturbation scheme for the
full theory.Comment: 22 page
Final velocity and radiated energy in numerical simulations of binary black holes
The evolution of global binary black holes variables such as energy or linear
momentum are mainly obtained by applying numerical methods near coalescence,
post-Newtonian (PN) expansions, or a combination of both. In this paper, we use
a fully relativistic formalism presented several years ago that only uses
global variables defined at null infinity together with the gravitational
radiation emitted by the source to obtain the time evolution of such variables
for binary black holes (BBH) systems. For that, we use the Rochester catalog
composed of 776 BBHs simulations. We compute the final velocity, radiated
energy, and intrinsic angular momentum predicted by the dynamical equations in
this formalism for nonspinning, aligned and antialigned spins, and several
different precessing configurations. We compare obtained values with reported
values in numerical simulations. As BBHs parameter space is still not
completely covered by numerical simulations, we fit phenomenological formulas
for practical applications to the radiated energy and final velocities
obtained. Also, we compare the fits with reported values. In conclusion, we see
that our formulae and correlations for the variables described in this work are
consistent with those found in the general literature.Comment: 12 pages, 16 figure
Smooth null hypersurfaces near the horizon in the presence of tails
We show that the power-law decay modes found in linear perturbations of
Schwarzschild black holes, generally called tails, do not produce caustics on a
naturally defined family of null surfaces in the neighborhood of i+ of a black
hole horizon
Conformal Einstein equations and Cartan conformal connection
Necessary and sufficient conditions for a space-time to be conformal to an
Einstein space-time are interpreted in terms of curvature restrictions for the
corresponding Cartan conformal connection
On low energy quantum gravity induced effects on the propagation of light
Present models describing the interaction of quantum Maxwell and
gravitational fields predict a breakdown of Lorentz invariance and a non
standard dispersion relation in the semiclassical approximation. Comparison
with observational data however, does not support their predictions. In this
work we introduce a different set of ab initio assumptions in the canonical
approach, namely that the homogeneous Maxwell equations are valid in the
semiclassical approximation, and find that the resulting field equations are
Lorentz invariant in the semiclassical limit. We also include a
phenomenological analysis of possible effects on the propagation of light, and
their dependence on energy, in a cosmological context.Comment: 12 page