126 research outputs found
Quasi-local contribution to the scalar self-force: Geodesic Motion
We consider a scalar charge travelling in a curved background spacetime. We
calculate the quasi-local contribution to the scalar self-force experienced by
such a particle following a geodesic in a general spacetime. We also show that
if we assume a massless field and a vacuum background spacetime, the expression
for the self-force simplifies significantly. We consider some specific cases
whose gravitational analog are of immediate physical interest for the
calculation of radiation reaction corrected orbits of binary black hole
systems. These systems are expected to be detectable by the LISA space based
gravitational wave observatory. We also investigate how alternate techniques
may be employed in some specific cases and use these as a check on our own
results.Comment: Final Phys. Rev. D version. 24 pages, revtex4. Minor typos correcte
Bianchi type I universe with viscous fluid: A qualitative analysis
The nature of cosmological solutions for a homogeneous, anisotropic Universe
given by a Bianchi type-I (BI) model in the presence of a Cosmological constant
is investigated by taking into account dissipative process due to
viscosity. The system in question is thoroughly studied both analytically and
numerically. It is shown the viscosity, as well as the term exhibit
essential influence on the character of the solutions. In particular a negative
gives rise to an ever-expanding Universe, whereas, a suitable choice
of initial conditions plus a positive can result in a
singularity-free oscillatory mode of expansion. For some special cases it is
possible to obtain oscillations in the exponential mode of expansion of the BI
model even with a negative , where oscillations arise by virtue of
viscosity.Comment: RevTex, 16 pages, 32 figure
Stress-Energy Tensor for the Massless Spin 1/2 Field in Static Black Hole Spacetimes
The stress-energy tensor for the massless spin 1/2 field is numerically
computed outside and on the event horizons of both charged and uncharged static
non-rotating black holes, corresponding to the Schwarzschild,
Reissner-Nordstrom and extreme Reissner-Nordstr\"om solutions of Einstein's
equations. The field is assumed to be in a thermal state at the black hole
temperature. Comparison is made between the numerical results and previous
analytic approximations for the stress-energy tensor in these spacetimes. For
the Schwarzschild (charge zero) solution, it is shown that the stress-energy
differs even in sign from the analytic approximation. For the
Reissner-Nordstrom and extreme Reissner-Nordstrom solutions, divergences
predicted by the analytic approximations are shown not to exist.Comment: 5 pages, 4 figures, additional discussio
Conditions for nonexistence of static or stationary, Einstein-Maxwell, non-inheriting black-holes
We consider asymptotically-flat, static and stationary solutions of the
Einstein equations representing Einstein-Maxwell space-times in which the
Maxwell field is not constant along the Killing vector defining stationarity,
so that the symmetry of the space-time is not inherited by the electromagnetic
field. We find that static degenerate black hole solutions are not possible
and, subject to stronger assumptions, nor are static, non-degenerate or
stationary black holes. We describe the possibilities if the stronger
assumptions are relaxed.Comment: 19 pages, to appear in GER
The cosmology of the Fab-Four
We have recently proposed a novel self tuning mechanism to alleviate the famous cosmological constant problem, based on the general scalar tensor theory proposed by Horndeski. The self-tuning model ends up consisting of four geometric terms in the action, with each term containing a free potential function of the scalar field; the four together being labeled as the Fab-Four. In this paper we begin the important task of deriving the cosmology associated with the Fab-Four Lagrangian. Performing a phase plane analysis of the system we are able to obtain a number of fixed points for the system, with some remarkable new solutions emerging from the trade-off between the various potentials. As well as obtaining inflationary solutions we also find conventional radiation/matter-like solutions, but in regimes where the energy density is dominated by a cosmological constant, and where we do not have any explicit forms of radiation or matter. Stability conditions for matter solutions are obtained and we show how it is possible for there to exist an extended period of `matter domination' opening up the possibility that we can generate cosmological structures, and recover a consistent cosmology even in the presence of a large cosmological constant
Rigid motion revisited: rigid quasilocal frames
We introduce the notion of a rigid quasilocal frame (RQF) as a geometrically
natural way to define a "system" in general relativity. An RQF is defined as a
two-parameter family of timelike worldlines comprising the worldtube boundary
of the history of a finite spatial volume, with the rigidity conditions that
the congruence of worldlines is expansion-free (constant size) and shear-free
(constant shape). This definition of a system is anticipated to yield simple,
exact geometrical insights into the problem of motion in general relativity. It
begins by answering the questions what is in motion (a rigid two-dimensional
system boundary), and what motions of this rigid boundary are possible. Nearly
a century ago Herglotz and Noether showed that a three-parameter family of
timelike worldlines in Minkowski space satisfying Born's 1909 rigidity
conditions has only three degrees of freedom instead of the six we are familiar
with from Newtonian mechanics. We argue that in fact we can implement Born's
notion of rigid motion in both flat spacetime (this paper) and arbitrary curved
spacetimes containing sources (subsequent papers) - with precisely the expected
three translational and three rotational degrees of freedom - provided the
system is defined quasilocally as the two-dimensional set of points comprising
the boundary of a finite spatial volume, rather than the three-dimensional set
of points within the volume.Comment: 10 pages (two column), 24 pages (preprint), 1 figur
Quasilocal Conservation Laws: Why We Need Them
We argue that conservation laws based on the local matter-only
stress-energy-momentum tensor (characterized by energy and momentum per unit
volume) cannot adequately explain a wide variety of even very simple physical
phenomena because they fail to properly account for gravitational effects. We
construct a general quasi}local conservation law based on the Brown and York
total (matter plus gravity) stress-energy-momentum tensor (characterized by
energy and momentum per unit area), and argue that it does properly account for
gravitational effects. As a simple example of the explanatory power of this
quasilocal approach, consider that, when we accelerate toward a freely-floating
massive object, the kinetic energy of that object increases (relative to our
frame). But how, exactly, does the object acquire this increasing kinetic
energy? Using the energy form of our quasilocal conservation law, we can see
precisely the actual mechanism by which the kinetic energy increases: It is due
to a bona fide gravitational energy flux that is exactly analogous to the
electromagnetic Poynting flux, and involves the general relativistic effect of
frame dragging caused by the object's motion relative to us.Comment: 20 pages, 1 figur
Semiclassical charged black holes with a quantized massive scalar field
Semiclassical perturbations to the Reissner-Nordstrom metric caused by the
presence of a quantized massive scalar field with arbitrary curvature coupling
are found to first order in \epsilon = \hbar/M^2. The DeWitt-Schwinger
approximation is used to determine the vacuum stress-energy tensor of the
massive scalar field. When the semiclassical perturbation are taken into
account, we find extreme black holes will have a charge-to-mass ratio that
exceeds unity, as measured at infinity. The effects of the perturbations on the
black hole temperature (surface gravity) are studied in detail, with particular
emphasis on near extreme ``bare'' states that might become precisely zero
temperature ``dressed'' semiclassical black hole states. We find that for
minimally or conformally coupled scalar fields there are no zero temperature
solutions among the perturbed black holes.Comment: 19 pages; 1 figure; ReVTe
Event Horizons in Numerical Relativity I: Methods and Tests
This is the first paper in a series on event horizons in numerical
relativity. In this paper we present methods for obtaining the location of an
event horizon in a numerically generated spacetime. The location of an event
horizon is determined based on two key ideas: (1) integrating backward in time,
and (2) integrating the whole horizon surface. The accuracy and efficiency of
the methods are examined with various sample spacetimes, including both
analytic (Schwarzschild and Kerr) and numerically generated black holes. The
numerically evolved spacetimes contain highly distorted black holes, rotating
black holes, and colliding black holes. In all cases studied, our methods can
find event horizons to within a very small fraction of a grid zone.Comment: 22 pages, LaTeX with RevTeX 3.0 macros, 20 uuencoded gz-compressed
postscript figures. Also available at http://jean-luc.ncsa.uiuc.edu/Papers/
Submitted to Physical Review
New Coordinate Systems for Axisymmetric Black Hole Collisions
We describe a numerical grid generating procedure to construct new classes of
orthogonal coordinate systems that are specially adapted to binary black hole
spacetimes. The new coordinates offer an alternative approach to the
conventional \v{C}ade\v{z} coordinates, in addition to providing a potentially
more stable and flexible platform to extend previous calculations of binary
black hole collisions.Comment: 3 pages, 5 postscript figures, LaTeX, uses mprocl.sty (available at
http://shemesh.fiz.huji.ac.il/MG8/submission.html) To appear in the
proceedings of the Marcel Grossmann 8 (Jerusalem, 1997
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