23,346 research outputs found
On the mass of a Kerr-anti-de Sitter spacetime in D dimensions
We show how to compute the mass of a Kerr-anti-de Sitter spacetime with
respect to the anti-de Sitter background in any dimension, using a
superpotential which has been derived from standard Noether identities. The
calculation takes no account of the source of the curvature and confirms
results obtained for black holes via the first law of thermodynamics.Comment: minor changes; accepted by CQ
Superpotentials from variational derivatives rather than Lagrangians in relativistic theories of gravity
The prescription of Silva to derive superpotential equations from variational
derivatives rather than from Lagrangian densities is applied to theories of
gravity derived from Lovelock Lagrangians in the Palatini representation.
Spacetimes are without torsion and isolated sources of gravity are minimally
coupled. On a closed boundary of spacetime, the metric is given and the
connection coefficients are those of Christoffel. We derive equations for the
superpotentials in these conditions. The equations are easily integrated and we
give the general expression for all superpotentials associated with Lovelock
Lagrangians. We find, in particular, that in Einstein's theory, in any number
of dimensions, the superpotential, valid at spatial and at null infinity, is
that of Katz, Bicak and Lynden-Bell, the KBL superpotential. We also give
explicitly the superpotential for Gauss-Bonnet theories of gravity. Finally, we
find a simple expression for the superpotential of Einstein-Gauss-Bonnet
theories with an anti-de Sitter background: it is minus the KBL superpotential,
confirming, as it should, the calculation of the total mass-energy of spacetime
at spatial infinity by Deser and Tekin.Comment: Scheduled to appear in Class. Quantum Grav. August 200
Accurate determination of the Lagrangian bias for the dark matter halos
We use a new method, the cross power spectrum between the linear density
field and the halo number density field, to measure the Lagrangian bias for
dark matter halos. The method has several important advantages over the
conventional correlation function analysis. By applying this method to a set of
high-resolution simulations of 256^3 particles, we have accurately determined
the Lagrangian bias, over 4 magnitudes in halo mass, for four scale-free models
with the index n=-0.5, -1.0, -1.5 and -2.0 and three typical CDM models. Our
result for massive halos with ( is a characteristic non-linear
mass) is in very good agreement with the analytical formula of Mo & White for
the Lagrangian bias, but the analytical formula significantly underestimates
the Lagrangian clustering for the less massive halos $M < M_*. Our simulation
result however can be satisfactorily described, with an accuracy better than
15%, by the fitting formula of Jing for Eulerian bias under the assumption that
the Lagrangian clustering and the Eulerian clustering are related with a linear
mapping. It implies that it is the failure of the Press-Schechter theories for
describing the formation of small halos that leads to the inaccuracy of the Mo
& White formula for the Eulerian bias. The non-linear mapping between the
Lagrangian clustering and the Eulerian clustering, which was speculated as
another possible cause for the inaccuracy of the Mo & White formula, must at
most have a second-order effect. Our result indicates that the halo formation
model adopted by the Press-Schechter theories must be improved.Comment: Minor changes; accepted for publication in ApJ (Letters) ; 11 pages
with 2 figures include
Mass and angular momenta of Kerr anti-de Sitter spacetimes in Einstein-Gauss-Bonnet theory
We compute the mass and angular momenta of rotating anti-de Sitter spacetimes
in Einstein-Gauss-Bonnet theory of gravity using a superpotential derived from
standard Noether identities. The calculation relies on the fact that the
Einstein and Einstein-Gauss-Bonnet vacuum equations are the same when
linearized on maximally symmetric backgrounds and uses the recently discovered
D-dimensional Kerr-anti-de Sitter solutions to Einstein's equations
Gravitational energy
Observers at rest in a stationary spacetime flat at infinity can measure
small amounts of rest-mass+internal energies+kinetic energies+pressure energy
in a small volume of fluid attached to a local inertial frame. The sum of these
small amounts is the total "matter energy" for those observers. The total
mass-energy minus the matter energy is the binding gravitational energy.
Misner, Thorne and Wheeler evaluated the gravitational energy of a
spherically symmetric static spacetime. Here we show how to calculate
gravitational energy in any static and stationary spacetime for isolated
sources with a set of observers at rest.
The result of MTW is recovered and we find that electromagnetic and
gravitational 3-covariant energy densities in conformastatic spacetimes are of
opposite signs. Various examples suggest that gravitational energy is negative
in spacetimes with special symmetries or when the energy-momentum tensor
satisfies usual energy conditions.Comment: 12 pages. Accepted for publication in Class. Quantum Gra
High sensitivity phonon spectroscopy of Bose-Einstein condensates using matter-wave interference
We study low momentum excitations of a Bose-Einstein condensate using a novel
matter-wave interference technique. In time-of-flight expansion images we
observe strong matter-wave fringe patterns. The fringe contrast is a sensitive
spectroscopic probe of in-trap phonons and is explained by use of a Bogoliubov
excitation projection method applied to the rescaled order parameter of the
expanding condensate. Gross-Pitaevskii simulations agree with the experimental
data and confirm the validity of the theoretical interpretation. We show that
the high sensitivity of this detection scheme gives access to the quantized
quasiparticle regime.Comment: 5 pages, 5 figures, author list update
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