5,276 research outputs found
Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions
The Lanczos-Lovelock models of gravity constitute the most general theories
of gravity in D dimensions which satisfy (a) the principle of of equivalence,
(b) the principle of general co-variance, and (c) have field equations
involving derivatives of the metric tensor only up to second order. The mth
order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature
tensor. The field equations resulting from it become trivial in the critical
dimension and the action itself can be written as the integral of an
exterior derivative of an expression involving the vierbeins, in the
differential form language. While these results are well known, there is some
controversy in the literature as to whether the Lanczos-Lovelock Lagrangian
itself can be expressed as a total divergence of quantities built only from the
metric and its derivatives (without using the vierbeins) in . We settle
this issue by showing that this is indeed possible and provide an algorithm for
its construction. In particular, we demonstrate that, in two dimensions, for a doublet of functions which
depends only on the metric and its first derivatives. We explicitly construct
families of such R^j -s in two dimensions. We also address related questions
regarding the Gauss-Bonnet Lagrangian in . Finally, we demonstrate the
relation between the Chern-Simons form and the mth order Lanczos-Lovelock
Lagrangian.Comment: 15 pages, no figure
Charged Rotating BTZ Black Hole and Thermodynamic Behavior of Field Equations at its Horizon
In this paper, we study different cases of the charged rotating BTZ black
hole with reference to their horizons. For the existence of these cases
conditions on mass, charge and angular momentum of the black hole are obtained.
It is also shown that the Einstein field equations for the charged rotating BTZ
black hole at the horizon can be expressed as first law of thermodynamics,
.Comment: 12 pages, 3 figure
Combining general relativity and quantum theory: points of conflict and contact
The issues related to bringing together the principles of general relativity
and quantum theory are discussed. After briefly summarising the points of
conflict between the two formalisms I focus on four specific themes in which
some contact has been established in the past between GR and quantum field
theory: (i) The role of planck length in the microstructure of spacetime (ii)
The role of quantum effects in cosmology and origin of the universe (iii) The
thermodynamics of spacetimes with horizons and especially the concept of
entropy related to spacetime geometry (iv) The problem of the cosmological
constant.Comment: Invited Talk at "The Early Universe and Cosmological Observations: a
Critical Review", UCT, Cape Town, 23-25 July,2001; to appear in
Class.Quan.Gra
Transference of Transport Anisotropy to Composite Fermions
When interacting two-dimensional electrons are placed in a large
perpendicular magnetic field, to minimize their energy, they capture an even
number of flux quanta and create new particles called composite fermions (CFs).
These complex electron-flux-bound states offer an elegant explanation for the
fractional quantum Hall effect. Furthermore, thanks to the flux attachment, the
effective field vanishes at a half-filled Landau level and CFs exhibit
Fermi-liquid-like properties, similar to their zero-field electron
counterparts. However, being solely influenced by interactions, CFs should
possess no memory whatever of the electron parameters. Here we address a
fundamental question: Does an anisotropy of the electron effective mass and
Fermi surface (FS) survive composite fermionization? We measure the resistance
of CFs in AlAs quantum wells where electrons occupy an elliptical FS with large
eccentricity and anisotropic effective mass. Similar to their electron
counterparts, CFs also exhibit anisotropic transport, suggesting an anisotropy
of CF effective mass and FS.Comment: 5 pages, 5 figure
Contrast between spin and valley degrees of freedom
We measure the renormalized effective mass (m*) of interacting
two-dimensional electrons confined to an AlAs quantum well while we control
their distribution between two spin and two valley subbands. We observe a
marked contrast between the spin and valley degrees of freedom: When electrons
occupy two spin subbands, m* strongly depends on the valley occupation, but not
vice versa. Combining our m* data with the measured spin and valley
susceptibilities, we find that the renormalized effective Lande g-factor
strongly depends on valley occupation, but the renormalized conduction-band
deformation potential is nearly independent of the spin occupation.Comment: 4+ pages, 2 figure
Self-similar collapse and the structure of dark matter halos: A fluid approach
We explore the dynamical restrictions on the structure of dark matter halos
through a study of cosmological self-similar gravitational collapse solutions.
A fluid approach to the collisionless dynamics of dark matter is developed and
the resulting closed set of moment equations are solved numerically including
the effect of halo velocity dispersions (both radial and tangential), for a
range of spherically averaged initial density profiles. Our results highlight
the importance of tangential velocity dispersions to obtain density profiles
shallower than in the core regions, and for retaining a memory of the
initial density profile, in self-similar collapse. For an isotropic core
velocity dispersion only a partial memory of the initial density profile is
retained. If tangential velocity dispersions in the core are constrained to be
less than the radial dispersion, a cuspy core density profile shallower than
cannot obtain, in self-similar collapse.Comment: 25 pages, 7 figures, submitted to Ap
Cosmological production of H_2 before the formation of the first galaxies
Previous calculations of the pregalactic chemistry have found that a small
amount of H_2, x[H_2]=n[H_2]/n[H] = 2.6e-6, is produced catalytically through
the H^-, H_2^+, and HeH^+ mechanisms. We revisit this standard calculation
taking into account the effects of the nonthermal radiation background produced
by cosmic hydrogen recombination, which is particularly effective at destroying
H^- via photodetachment. We also take into consideration the non-equilibrium
level populations of H_2^+, which occur since transitions among the
rotational-vibrational levels are slow compared to photodissociation. The new
calculation predicts a final H_2 abundance of x[H_2] = 6e-7 for the standard
cosmology. This production is due almost entirely to the H^- mechanism, with ~1
per cent coming from HeH^+ and ~0.004 per cent from H_2^+. We evaluate the
heating of the diffuse pregalactic gas from the chemical reactions that produce
H_2 and from rotational transitions in H_2, and find them to be negligible.Comment: 13 pages, 5 figures, MNRAS submitte
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