955 research outputs found
The Einstein 3-form G_a and its equivalent 1-form L_a in Riemann-Cartan space
The definition of the Einstein 3-form G_a is motivated by means of the
contracted 2nd Bianchi identity. This definition involves at first the complete
curvature 2-form. The 1-form L_a is defined via G_a = L^b \wedge #(o_b \wedge
o_a). Here # denotes the Hodge-star, o_a the coframe, and \wedge the exterior
product. The L_a is equivalent to the Einstein 3-form and represents a certain
contraction of the curvature 2-form. A variational formula of Salgado on
quadratic invariants of the L_a 1-form is discussed, generalized, and put into
proper perspective.Comment: LaTeX, 13 Pages. To appear in Gen. Rel. Gra
Second order superintegrable systems in conformally flat spaces. IV. The classical 3D StÀckel transform and 3D classification theory
This article is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. In the first part of the article we study the StÀckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is StÀckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems
Universal Field Equations with Reparametrisation Invariance
New reparametrisation invariant field equations are constructed which
describe -brane models in a space of dimensions. These equations, like
the recently discovered scalar field equations in dimensions, are
universal, in the sense that they can be derived from an infinity of
inequivalent Lagrangians, but are nonetheless Lorentz (Euclidean) invariant.
Moreover, they admit a hierarchical structure, in which they can be derived by
a sequence of iterations from an arbitrary reparametrisation covariant
Lagrangian, homogeneous of weight one. None of the equations of motion which
appear in the hierarchy of iterations have derivatives of the fields higher
than the second. The new sequence of Universal equations is related to the
previous one by an inverse function transformation. The particular case of
, giving a new reparametrisation invariant string equation in 3 dimensions
is solved.Comment: 9page
Unimodular cosmology and the weight of energy
Some models are presented in which the strength of the gravitational coupling
of the potential energy relative to the same coupling for the kinetic energy
is, in a precise sense, adjustable. The gauge symmetry of these models consists
of those coordinate changes with unit jacobian.Comment: LaTeX, 23 pages, conclusions expanded. Two paragraphs and a new
reference adde
Chaplygin gas dominated anisotropic brane world cosmological models
We present exact solutions of the gravitational field equations in the
generalized Randall-Sundrum model for an anisotropic brane with Bianchi type I
geometry, with a generalized Chaplygin gas as matter source. The generalized
Chaplygin gas, which interpolates between a high density relativistic era and a
non-relativistic matter phase, is a popular dark energy candidate. For a
Bianchi type I space-time brane filled with a cosmological fluid obeying the
generalized Chaplygin equation of state the general solution of the
gravitational field equations can be expressed in an exact parametric form,
with the comoving volume taken as parameter. In the limiting cases of a stiff
cosmological fluid, with pressure equal to the energy density, and for a
pressureless fluid, the solution of the field equations can be expressed in an
exact analytical form. The evolution of the scalar field associated to the
Chaplygin fluid is also considered and the corresponding potential is obtained.
The behavior of the observationally important parameters like shear, anisotropy
and deceleration parameter is considered in detail.Comment: 13 pages, 6 figures, accepted for publication in PR
Geometric Properties of Static EMdL Horizons
We study non-degenerate and degenerate (extremal) Killing horizons of
arbitrary geometry and topology within the Einstein-Maxwell-dilaton model with
a Liouville potential (the EMdL model) in d-dimensional (d>=4) static
space-times. Using Israel's description of a static space-time, we construct
the EMdL equations and the space-time curvature invariants: the Ricci scalar,
the square of the Ricci tensor, and the Kretschmann scalar. Assuming that
space-time metric functions and the model fields are real analytic functions in
the vicinity of a space-time horizon, we study behavior of the space-time
metric and the fields near the horizon and derive relations between the
space-time curvature invariants calculated on the horizon and geometric
invariants of the horizon surface. The derived relations generalize the similar
relations known for horizons of static four and 5-dimensional vacuum and
4-dimensional electrovacuum space-times. Our analysis shows that all the
extremal horizon surfaces are Einstein spaces. We present necessary conditions
for existence of static extremal horizons within the EMdL model.Comment: 10 page
On extra forces from large extra dimensions
The motion of a classical test particle moving on a 4-dimensional brane
embedded in an -dimensional bulk is studied in which the brane is allowed to
fluctuate along the extra dimensions. It is shown that these fluctuations
produce three different forces acting on the particle, all stemming from the
effects of extra dimensions. Interpretations are then offered to describe the
origin of these forces and a relationship between the 4 and -dimensional
mass of the particle is obtained by introducing charges associated with large
extra dimensions.Comment: 9 pages, no figuer
Flat deformation of a spacetime admitting two Killing fields
It is shown that given an analytic Lorentzian metric on a 4-manifold, ,
which admits two Killing vector fields, then it exists a local deformation law
, where is a 2-dimensional projector, such that is
flat and admits the same Killing vectors. We also characterize the particular
case when the projector coincides with the quotient metric. We apply some
of our results to general stationary axisymmetric spacetime
The geometry of the Barbour-Bertotti theories II. The three body problem
We present a geometric approach to the three-body problem in the
non-relativistic context of the Barbour-Bertotti theories. The Riemannian
metric characterizing the dynamics is analyzed in detail in terms of the
relative separations. Consequences of a conformal symmetry are exploited and
the sectional curvatures of geometrically preferred surfaces are computed. The
geodesic motions are integrated. Line configurations, which lead to curvature
singularities for , are investigated. None of the independent scalars
formed from the metric and curvature tensor diverges there.Comment: 16 pages, 2 eps figures, to appear in Classical and Quantum Gravit
A Comment on Junction and Energy Conditions in Thin Shells
This comment contains a suggestion for a slight modification of Israel's
covariant formulation of junction conditions between two spacetimes, placing
both sides on equal footing with normals having uniquely defined orientations.
The signs of mass energy densities in thin shells at the junction depend not
only on the orientations of the normals and it is useful therefore to discuss
the sign separately. Calculations gain in clarity by not choosing the
orientations in advance. Simple examples illustrate our point and complete
previous classifications of spherical thin shells in spherically symmetric
spacetimes relevant to cosmology.Comment: (Tex file + PS file with a figure) Tex errors were correcte
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