2,525 research outputs found
Infinite slabs and other weird plane symmetric space-times with constant positive density
We present the exact solution of Einstein's equation corresponding to a
static and plane symmetric distribution of matter with constant positive
density located below . This solution depends essentially on two
constants: the density and a parameter . We show that this
space-time finishes down below at an inner singularity at finite depth. We
match this solution to the vacuum one and compute the external gravitational
field in terms of slab's parameters. Depending on the value of , these
slabs can be attractive, repulsive or neutral. In the first case, the
space-time also finishes up above at another singularity. In the other cases,
they turn out to be semi-infinite and asymptotically flat when .
We also find solutions consisting of joining an attractive slab and a
repulsive one, and two neutral ones. We also discuss how to assemble a
"gravitational capacitor" by inserting a slice of vacuum between two such
slabs.Comment: 8 page
The electromagnetic energy-momentum tensor
We clarify the relation between canonical and metric energy-momentum tensors.
In particular, we show that a natural definition arises from Noether's Theorem
which directly leads to a symmetric and gauge invariant tensor for
electromagnetic field theories on an arbitrary space-time of any dimension
On gauge invariant regularization of fermion currents
We compare Schwinger and complex powers methods to construct regularized
fermion currents. We show that although both of them are gauge invariant they
not always yield the same result.Comment: 10 pages, 1 figur
An alternative well-posedness property and static spacetimes with naked singularities
In the first part of this paper, we show that the Cauchy problem for wave
propagation in some static spacetimes presenting a singular time-like boundary
is well posed, if we only demand the waves to have finite energy, although no
boundary condition is required. This feature does not come from essential
self-adjointness, which is false in these cases, but from a different
phenomenon that we call the alternative well-posedness property, whose origin
is due to the degeneracy of the metric components near the boundary.
Beyond these examples, in the second part, we characterize the type of
degeneracy which leads to this phenomenon.Comment: 34 pages, 3 figures. Accepted for publication in Class. Quantum Gra
On the energy-momentum tensor
We clarify the relation among canonical, metric and Belinfante's
energy-momentum tensors for general tensor field theories. For any tensor field
T, we define a new tensor field \til {\bm T}, in terms of which the
Belinfante tensor is readily computed. We show that the latter is the one that
arises naturally from Noether Theorem for an arbitrary spacetime and it
coincides on-shell with the metric one.Comment: 11 pages, 1 figur
Determinants of Dirac operators with local boundary conditions
We study functional determinants for Dirac operators on manifolds with
boundary. We give, for local boundary conditions, an explicit formula relating
these determinants to the corresponding Green functions. We finally apply this
result to the case of a bidimensional disk under bag-like conditions.Comment: standard LaTeX, 24 pages. To appear in Jour. Math. Phy
On the Initial Singularity Problem in Two Dimensional Quantum Cosmology
The problem of how to put interactions in two-dimensional quantum gravity in
the strong coupling regime is studied. It shows that the most general
interaction consistent with this symmetry is a Liouville term that contain two
parameters satisfying the algebraic relation in order to assure the closure of the diffeomorphism algebra. The model is
classically soluble and it contains as general solution the temporal
singularity. The theory is quantized and we show that the propagation amplitude
fall tozero in . This result shows that the classical singularities
are smoothed by quantum effects and the bing-bang concept could be considered
as a classical extrapolation instead of a physical concept.Comment: 9pp, Revtex 3.0. New references added. To appear in Phys. Rev.
On the global version of Euler-Lagrange equations
The introduction of a covariant derivative on the velocity phase space is
needed for a global expression of Euler-Lagrange equations. The aim of this
paper is to show how its torsion tensor turns out to be involved in such a
version.Comment: 5 pages, 1 figur
Symmetry types of hyperelliptic Riemann surfaces
Let be a compact hyperelliptic Riemann surface which admits anti-analytic involutions (also called symmetries or real structures). For instance, a complex projective plane curve of genus two, defined by an equation with real coefficients, gives rise to such a surface, and complex conjugation is such a symmetry. In this memoir, the real structures of are classified up to isomorphism (i.e., up to conjugation). This is done as follows: the number of connected components of the set of fixed points of together with the connectedness or disconnectedness of the complementary set in classifies topologically; they determine the species of , which only depends on the conjugacy class of (however, different conjugacy classes may have identical species). On these grounds, for a given genus , the authors first give a list of all full groups of analytic and anti-analytic automorphisms of genus compact hyperelliptic Riemann surfaces. For every such group , the authors compute polynomial equations for a surface having as full group and then find the number of conjugacy classes containing symmetries; they also compute a representative in every such class. Finally, they compute the species corresponding to such classes. This memoir is an exhaustive piece of work, going through a case-by-case analysis. The problem for general compact Riemann surfaces dates back to 1893, when {\it F. Klein} [Math. Ann. 42, 1--29 (1893)] first studied it. For zero genus, it is easy. For genus one, that is, for elliptic surfaces, it was solved by {\it N. Alling} ["Real elliptic curves" (1981)]. Partial results for hyperelliptic surfaces of genus two were obtained by {\it E. Bujalance} and {\it D. Singerman} [Proc. Lond. Math. Soc. 51, 501--519 (1985)]
Empty singularities in higher-dimensional Gravity
We study the exact solution of Einstein's field equations consisting of a
()-dimensional static and hyperplane symmetric thick slice of matter, with
constant and positive energy density and thickness , surrounded by
two different vacua. We explicitly write down the pressure and the external
gravitational fields in terms of and , the pressure is positive and
bounded, presenting a maximum at an asymmetrical position. And if
is small enough, the dominant energy condition is satisfied
all over the spacetime. We find that this solution presents many interesting
features. In particular, it has an empty singular boundary in one of the vacua.Comment: 13 page
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