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Making use of geometrical invariants in black hole collisions
We consider curvature invariants in the context of black hole collision
simulations. In particular, we propose a simple and elegant combination of the
Weyl invariants I and J, the {\sl speciality index} . In the context
of black hole perturbations provides a measure of the size of the
distortions from an ideal Kerr black hole spacetime. Explicit calculations in
well-known examples of axisymmetric black hole collisions demonstrate that this
quantity may serve as a useful tool for predicting in which cases perturbative
dynamics provide an accurate estimate of the radiation waveform and energy.
This makes particularly suited to studying the transition from
nonlinear to linear dynamics and for invariant interpretation of numerical
results.Comment: 4 pages, 3 eps figures, Revte
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
Dark Energy from structure: a status report
The effective evolution of an inhomogeneous universe model in any theory of
gravitation may be described in terms of spatially averaged variables. In
Einstein's theory, restricting attention to scalar variables, this evolution
can be modeled by solutions of a set of Friedmann equations for an effective
volume scale factor, with matter and backreaction source terms. The latter can
be represented by an effective scalar field (`morphon field') modeling Dark
Energy.
The present work provides an overview over the Dark Energy debate in
connection with the impact of inhomogeneities, and formulates strategies for a
comprehensive quantitative evaluation of backreaction effects both in
theoretical and observational cosmology. We recall the basic steps of a
description of backreaction effects in relativistic cosmology that lead to
refurnishing the standard cosmological equations, but also lay down a number of
challenges and unresolved issues in connection with their observational
interpretation.
The present status of this subject is intermediate: we have a good
qualitative understanding of backreaction effects pointing to a global
instability of the standard model of cosmology; exact solutions and
perturbative results modeling this instability lie in the right sector to
explain Dark Energy from inhomogeneities. It is fair to say that, even if
backreaction effects turn out to be less important than anticipated by some
researchers, the concordance high-precision cosmology, the architecture of
current N-body simulations, as well as standard perturbative approaches may all
fall short in correctly describing the Late Universe.Comment: Invited Review for a special Gen. Rel. Grav. issue on Dark Energy, 59
pages, 2 figures; matches published versio
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