401 research outputs found
The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - II: Dirac versus Bergmann observables and the Objectivity of Space-Time
(abridged)The achievements of the present work include: a) A clarification of
the multiple definition given by Bergmann of the concept of {\it (Bergmann)
observable. This clarification leads to the proposal of a {\it main conjecture}
asserting the existence of i) special Dirac's observables which are also
Bergmann's observables, ii) gauge variables that are coordinate independent
(namely they behave like the tetradic scalar fields of the Newman-Penrose
formalism). b) The analysis of the so-called {\it Hole} phenomenology in strict
connection with the Hamiltonian treatment of the initial value problem in
metric gravity for the class of Christoudoulou -Klainermann space-times, in
which the temporal evolution is ruled by the {\it weak} ADM energy. It is
crucial the re-interpretation of {\it active} diffeomorphisms as {\it passive
and metric-dependent} dynamical symmetries of Einstein's equations, a
re-interpretation which enables to disclose their (nearly unknown) connection
to gauge transformations on-shell; this is expounded in the first paper
(gr-qc/0403081). The use of the Bergmann-Komar {\it intrinsic
pseudo-coordinates} allows to construct a {\it physical atlas} of 4-coordinate
systems for the 4-dimensional {\it mathematical} manifold, in terms of the
highly non-local degrees of freedom of the gravitational field (its four
independent {\it Dirac observables}), and to realize the {\it physical
individuation} of the points of space-time as {\it point-events} as a
gauge-fixing problem, also associating a non-commutative structure to each
4-coordinate system.Comment: 41 pages, Revtex
Symmetries, Horizons, and Black Hole Entropy
Black holes behave as thermodynamic systems, and a central task of any
quantum theory of gravity is to explain these thermal properties. A statistical
mechanical description of black hole entropy once seemed remote, but today we
suffer an embarrassment of riches: despite counting very different states, many
inequivalent approaches to quantum gravity obtain identical results. Such
``universality'' may reflect an underlying two-dimensional conformal symmetry
near the horizon, which can be powerful enough to control the thermal
characteristics independent of other details of the theory. This picture
suggests an elegant description of the relevant degrees of freedom as
Goldstone-boson-like excitations arising from symmetry breaking by the
conformal anomaly.Comment: 6 pages; first prize essay, 2007 Gravity Research Foundation essay
contes
GPS observables in general relativity
I present a complete set of gauge invariant observables, in the context of
general relativity coupled with a minimal amount of realistic matter (four
particles). These observables have a straightforward and realistic physical
interpretation. In fact, the technology to measure them is realized by the
Global Positioning System: they are defined by the physical reference system
determined by GPS readings. The components of the metric tensor in this
physical reference system are gauge invariant quantities and, remarkably, their
evolution equations are local.Comment: 6 pages, 1 figure, references adde
Reparameterization invariants for anisotropic Bianchi I cosmology with a massless scalar source
Intrinsic time-dependent invariants are constructed for classical, flat,
homogeneous, anisotropic cosmology with a massless scalar material source.
Invariance under the time reparameterization-induced canonical symmetry group
is displayed explicitly.Comment: 28 pages, to appear in General Relativity and Gravitation.
Substantial revisions: added foundational overview section 2, chose new
intrinsic time variable, worked with dimensionless variables, added appendix
with comparison and criticism of other approache
Energy Distribution in f(R) Gravity
The well-known energy problem is discussed in f(R) theory of gravity. We use
the generalized Landau-Lifshitz energy-momentum complex in the framework of
metric f(R) gravity to evaluate the energy density of plane symmetric solutions
for some general f(R) models. In particular, this quantity is found for some
popular choices of f(R) models. The constant scalar curvature condition and the
stability condition for these models are also discussed. Further, we
investigate the energy distribution of cosmic string spacetime.Comment: 15 pages, accepted for publication in Gen. Relativ. & Gra
On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection
In the framework of the Einstein-Palatini formalism, even though the
projective transformation connecting the arbitrary connection with the Levi
Civita connection has been floating in the literature for a long time and
perhaps the result was implicitly known in the affine gravity community, yet as
far as we know Julia and Silva were the first to realise its gauge character.
We rederive this result by using the Rosenfeld-Dirac-Bergmann approach to
constrained Hamiltonian systems and do a comprehensive self contained analysis
establishing the equivalence of the Einstein-Palatini and the metric
formulations without having to impose the gauge choice that the connection is
symmetric. We also make contact with the the Einstein-Cartan theory when the
matter Lagrangian has fermions.Comment: 18 pages. Slight change in the title and wording of some sections to
emphasize the main results. References added. Matches published versio
Gravitational and electroweak unification by replacing diffeomorphisms with larger group
The covariance group for general relativity, the diffeomorphisms, is replaced
by a group of coordinate transformations which contains the diffeomorphisms as
a proper subgroup. The larger group is defined by the assumption that all
observers will agree whether any given quantity is conserved. Alternatively,
and equivalently, it is defined by the assumption that all observers will agree
that the general relativistic wave equation describes the propagation of light.
Thus, the group replacement is analogous to the replacement of the Lorentz
group by the diffeomorphisms that led Einstein from special relativity to
general relativity, and is also consistent with the assumption of constant
light velocity that led him to special relativity. The enlarged covariance
group leads to a non-commutative geometry based not on a manifold, but on a
nonlocal space in which paths, rather than points, are the most primitive
invariant entities. This yields a theory which unifies the gravitational and
electroweak interactions. The theory contains no adjustable parameters, such as
those that are chosen arbitrarily in the standard model.Comment: 28 pages
Kinetic Inflation in Stringy and Other Cosmologies
An inflationary epoch driven by the kinetic energy density in a dynamical
Planck mass is studied. In the conformally related Einstein frame it is easiest
to see the demands of successful inflation cannot be satisfied by kinetic
inflation alone. Viewed in the original Jordan-Brans-Dicke frame, the obstacle
is manifest as a kind of graceful exit problem and/or a kind of flatness
problem. These arguments indicate the weakness of only the simplest
formulation. {}From them can be gleaned directions toward successful kinetic
inflation.Comment: 26 pages, LaTeX, CITA-94-2
Role of Brans-Dicke Theory with or without self-interacting potential in cosmic acceleration
In this work we have studied the possibility of obtaining cosmic acceleration
in Brans-Dicke theory with varying or constant (Brans- Dicke
parameter) and with or without self-interacting potential, the background fluid
being barotropic fluid or Generalized Chaplygin Gas. Here we take the power law
form of the scale factor and the scalar field. We show that accelerated
expansion can also be achieved for high values of for closed Universe.Comment: 12 Latex pages, 20 figures, RevTex styl
Entropy and Nonlinear Nonequilibrium Thermodynamic Relation for Heat Conducting Steady States
Among various possible routes to extend entropy and thermodynamics to
nonequilibrium steady states (NESS), we take the one which is guided by
operational thermodynamics and the Clausius relation. In our previous study, we
derived the extended Clausius relation for NESS, where the heat in the original
relation is replaced by its "renormalized" counterpart called the excess heat,
and the Gibbs-Shannon expression for the entropy by a new symmetrized
Gibbs-Shannon-like expression. Here we concentrate on Markov processes
describing heat conducting systems, and develop a new method for deriving
thermodynamic relations. We first present a new simpler derivation of the
extended Clausius relation, and clarify its close relation with the linear
response theory. We then derive a new improved extended Clausius relation with
a "nonlinear nonequilibrium" contribution which is written as a correlation
between work and heat. We argue that the "nonlinear nonequilibrium"
contribution is unavoidable, and is determined uniquely once we accept the
(very natural) definition of the excess heat. Moreover it turns out that to
operationally determine the difference in the nonequilibrium entropy to the
second order in the temperature difference, one may only use the previous
Clausius relation without a nonlinear term or must use the new relation,
depending on the operation (i.e., the path in the parameter space). This
peculiar "twist" may be a clue to a better understanding of thermodynamics and
statistical mechanics of NESS.Comment: 31 pages, 4 figure
- …