1,340 research outputs found
PROCRUSTES: A computer algebra package for post-Newtonian calculations in General Relativity
We report on a package of routines for the computer algebra system Maple
which supports the explicit determination of the geometric quantities, field
equations, equations of motion, and conserved quantities of General Relativity
in the post-Newtonian approximation. The package structure is modular and
allows for an easy modification by the user. The set of routines can be used to
verify hand calculations or to generate the input for further numerical
investigations.Comment: 20 pages, 3 figures. The latest version of the package can be
obtained from http://www.thp.uni-koeln.de/~dp/procrustes.htm
Non-axisymmetric relativistic Bondi-Hoyle accretion onto a Kerr black hole
In our program of studying numerically the so-called Bondi-Hoyle accretion in
the fully relativistic regime, we present here first results concerning the
evolution of matter accreting supersonically onto a rotating (Kerr) black hole.
These computations generalize previous results where the non-rotating
(Schwarzschild) case was extensively considered. We parametrize our initial
data by the asymptotic conditions for the fluid and explore the dependence of
the solution on the angular momentum of the black hole. Towards quantifying the
robustness of our numerical results, we use two different geometrical
foliations of the black hole spacetime, the standard form of the Kerr metric in
Boyer-Lindquist coordinates as well as its Kerr-Schild form, which is free of
coordinate singularities at the black hole horizon. We demonstrate some
important advantages of using such horizon adapted coordinate systems.
Our numerical study indicates that regardless of the value of the black hole
spin the final accretion pattern is always stable, leading to constant
accretion rates of mass and momentum. The flow is characterized by a strong
tail shock, which, unlike the Schwarzschild case, is increasingly wrapped
around the central black hole as the hole angular momentum increases. The
rotation induced asymmetry in the pressure field implies that besides the well
known drag, the black hole will experience also a lift normal to the flow
direction. This situation exhibits some analogies with the Magnus effect of
classical fluid dynamics.Comment: 33 pages, 20 figures, submited to MNRA
A historical perspective on Modified Newtonian Dynamics
I review the history and development of Modified Newtonian Dynamics (MOND)
beginning with the phenomenological basis as it existed in the early 1980s. I
consider Milgrom's papers of 1983 introducing the idea and its consequences for
galaxies and galaxy groups, as well as the initial reactions, both negative and
positive. The early criticisms were primarily on matters of principle, such as
the absence of conservation laws and perceived cosmological problems; an
important step in addressing these issues was the development of the
Lagrangian-based non-relativistic theory of Bekenstein and Milgrom. This theory
led to the development of a tentative relativistic theory that formed the basis
for later multi-field theories of gravity. On an empirical level the predictive
success of the idea with respect to the phenomenology of galaxies presents
considerable challenges for cold dark matter. For MOND the essential challenge
remains the absence of a generally accepted theoretical underpinning of the
idea and, thus, cosmological predictions. I briefly review recent progress in
this direction. Finally I discuss the role and sociology of unconventional
ideas in astronomy in the presence of a strongly entrenched standard paradigm.Comment: 25 pages, 9 figures, previous uploaded file was out of date, Canadian
Journal of Physic
Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin
We derive a Hamiltonian for an extended spinning test body in a curved
background spacetime, to quadratic order in the spin, in terms of
three-dimensional position, momentum, and spin variables having canonical
Poisson brackets. This requires a careful analysis of how changes of the spin
supplementary condition are related to shifts of the body's representative
worldline and transformations of the body's multipole moments, and we employ
bitensor calculus for a precise framing of this analysis. We apply the result
to the case of the Kerr spacetime and thereby compute an explicit canonical
Hamiltonian for the test-body limit of the spinning two-body problem in general
relativity, valid for generic orbits and spin orientations, to quadratic order
in the test spin. This fully relativistic Hamiltonian is then expanded in
post-Newtonian orders and in powers of the Kerr spin parameter, allowing
comparisons with the test-mass limits of available post-Newtonian results. Both
the fully relativistic Hamiltonian and the results of its expansion can inform
the construction of waveform models, especially effective-one-body models, for
the analysis of gravitational waves from compact binaries.Comment: RevTeX, 25 pages, 2 figures. v2: Updated to match PRD version;
further references added; some changes in presentation and notation;
typographical errors corrected, most notably in Eqs. (7.51) and (7.58
Gravitational Waves from Gravitational Collapse
Gravitational wave emission from the gravitational collapse of massive stars
has been studied for more than three decades. Current state of the art
numerical investigations of collapse include those that use progenitors with
realistic angular momentum profiles, properly treat microphysics issues,
account for general relativity, and examine non--axisymmetric effects in three
dimensions. Such simulations predict that gravitational waves from various
phenomena associated with gravitational collapse could be detectable with
advanced ground--based and future space--based interferometric observatories.Comment: 68 pages including 13 figures; revised version accepted for
publication in Living Reviews in Relativity (http://www.livingreviews.org
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