6,542 research outputs found
Series Solutions of Polarized Gowdy Universes
Einstein\u27s field equations are a system of ten partial differential equations. For a special class of spacetimes known as Gowdy spacetimes, the number of equations is reduced due to additional structure of two dimensional isometry groups with mutually orthogonal Killing vectors. In this thesis, we focus on a particular model of Gowdy spacetimes known as the polarized T3 model, and provide an explicit solution to Einstein\u27s equations
The Hamiltonian formulation of General Relativity: myths and reality
A conventional wisdom often perpetuated in the literature states that: (i) a
3+1 decomposition of space-time into space and time is synonymous with the
canonical treatment and this decomposition is essential for any Hamiltonian
formulation of General Relativity (GR); (ii) the canonical treatment
unavoidably breaks the symmetry between space and time in GR and the resulting
algebra of constraints is not the algebra of four-dimensional diffeomorphism;
(iii) according to some authors this algebra allows one to derive only spatial
diffeomorphism or, according to others, a specific field-dependent and
non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac
[Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in
"Gravitation: An Introduction to Current Research" (1962) 227] of the canonical
structure of GR are equivalent. We provide some general reasons why these
statements should be questioned. Points (i-iii) have been shown to be incorrect
in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly
re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that
points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation
of GR. We also demonstrate that ADM and Dirac formulations are related by a
transformation of phase-space variables from the metric to lapse
and shift functions and the three-metric , which is not canonical. This
proves that point (iv) is incorrect. Points (i-iii) are mere consequences of
using a non-canonical change of variables and are not an intrinsic property of
either the Hamilton-Dirac approach to constrained systems or Einstein's theory
itself.Comment: References are added and updated, Introduction is extended,
Subsection 3.5 is added, 83 pages; corresponds to the published versio
Doubletons and 5D Higher Spin Gauge Theory
We use Grassmann even spinor oscillators to construct a bosonic higher spin
extension hs(2,2) of the five-dimensional anti-de Sitter algebra SU(2,2), and
show that the gauging of hs(2,2) gives rise to a spectrum S of physical
massless fields with spin s=0,2,4,... that is a UIR of hs(2,2). In addition to
a master gauge field which contains the massless s=2,4,.. fields, we construct
a scalar master field containing the massless s=0 field, the generalized Weyl
tensors and their derivatives. We give the appropriate linearized constraint on
this master scalar field, which together with a linearized curvature constraint
produces the correct linearized field equations. A crucial step in the
construction of the theory is the identification of a central generator K which
is eliminated by means of a coset construction. Its charge vanishes in the
spectrum S, which is the symmetric product of two spin zero doubletons. We
expect our results to pave the way for constructing an interacting theory whose
curvature expansion is dual to a CFT based on higher spin currents formed out
of free doubletons in the large N limit. Thus, extending a recent proposal of
Sundborg (hep-th/0103247), we conjecture that the hs(2,2) gauge theory
describes a truncation of the bosonic massless sector of tensionless
Type IIB string theory on AdS_5 x S^5 for large N. This implies AdS/CFT
correspondence in a parameter regime where both boundary and bulk theories are
perturbative.Comment: 31 pages, late
Eleven-Dimensional Supergravity in Light-Cone Superspace
We show that Supergravity in eleven dimensions can be described in terms of a
constrained superfield on the light-cone, without the use of auxiliary fields.
We build its action to first order in the gravitational coupling constant
\kappa, by "oxidizing" (N=8,d=4) Supergravity. This is simply achieved, as for
N=4 Yang-Mills, by extending the transverse derivatives into superspace. The
eleven-dimensional SuperPoincare algebra is constructed and a fourth order
interaction is conjectured.Comment: 18 page
How Were the Hilbert--Einstein Equations Discovered?
The pathways along which A. Einstein and D. Hilbert independently came to the
gravitational field equations are traced. Some of the papers that assert a
point of view on the history of the derivation of the gravitational field
equations ``that radically differs from the standard point of view'' are
critically analyzed. It is shown that the conclusions drawn in these papers are
completely groundless.Comment: 40 pages, misprints remove
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