2,417 research outputs found
Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries
A general recipe to define, via Noether theorem, the Hamiltonian in any
natural field theory is suggested. It is based on a Regge-Teitelboim-like
approach applied to the variation of Noether conserved quantities. The
Hamiltonian for General Relativity in presence of non-orthogonal boundaries is
analysed and the energy is defined as the on-shell value of the Hamiltonian.
The role played by boundary conditions in the formalism is outlined and the
quasilocal internal energy is defined by imposing metric Dirichlet boundary
conditions. A (conditioned) agreement with previous definitions is proved. A
correspondence with Brown-York original formulation of the first principle of
black hole thermodynamics is finally established.Comment: 29 pages with 1 figur
The Universality of Einstein Equations
It is shown that for a wide class of analytic Lagrangians which depend only
on the scalar curvature of a metric and a connection, the application of the
so--called ``Palatini formalism'', i.e., treating the metric and the connection
as independent variables, leads to ``universal'' equations. If the dimension
of space--time is greater than two these universal equations are Einstein
equations for a generic Lagrangian and are suitably replaced by other universal
equations at bifurcation points. We show that bifurcations take place in
particular for conformally invariant Lagrangians and prove
that their solutions are conformally equivalent to solutions of Einstein
equations. For 2--dimensional space--time we find instead that the universal
equation is always the equation of constant scalar curvature; the connection in
this case is a Weyl connection, containing the Levi--Civita connection of the
metric and an additional vectorfield ensuing from conformal invariance. As an
example, we investigate in detail some polynomial Lagrangians and discuss their
bifurcations.Comment: 15 pages, LaTeX, (Extended Version), TO-JLL-P1/9
Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part I: the General Setting
The BTZ stationary black hole solution is considered and its mass and angular
momentum are calculated by means of Noether theorem. In particular, relative
conserved quantities with respect to a suitably fixed background are discussed.
Entropy is then computed in a geometric and macroscopic framework, so that it
satisfies the first principle of thermodynamics. In order to compare this more
general framework to the prescription by Wald et al. we construct the maximal
extension of the BTZ horizon by means of Kruskal-like coordinates. A discussion
about the different features of the two methods for computing entropy is
finally developed.Comment: PlainTEX, 16 pages. Revised version 1.
A Web-Based Distributed Virtual Educational Laboratory
Evolution and cost of measurement equipment, continuous training, and distance learning make it difficult to provide a complete set of updated workbenches to every student. For a preliminary familiarization and experimentation with instrumentation and measurement procedures, the use of virtual equipment is often considered more than sufficient from the didactic point of view, while the hands-on approach with real instrumentation and measurement systems still remains necessary to complete and refine the student's practical expertise. Creation and distribution of workbenches in networked computer laboratories therefore becomes attractive and convenient. This paper describes specification and design of a geographically distributed system based on commercially standard components
Expansion-induced contribution to the precession of binary orbits
We point out the existence of new effects of global spacetime expansion on
local binary systems. In addition to a possible change of orbital size, there
is a contribution to the precession of elliptic orbits, to be added to the
well-known general relativistic effect in static spacetimes, and the
eccentricity can change. Our model calculations are done using geodesics in a
McVittie metric, representing a localized system in an asymptotically
Robertson-Walker spacetime; we give a few numerical estimates for that case,
and indicate ways in which the model should be improved.Comment: revtex, 7 pages, no figures; revised for publication in Classical and
Quantum Gravity, with minor changes in response to referees' comment
Saturation excess runoff numerical simulation
Saturation excess runoff is a relevant process which needs additional experimental
and modeling efforts. This work is focused on its numerical modeling. The final objective
is the successive interpretation of ongoing experimental monitoring results in
two watersheds in different areas of Italy where the saturation excess runoff formation
mechanism seems to be important. The numerical solution of the two-dimensional
Richards\u2019 equation allows the evaluation of the sensitivity to the various influent parameters
: rainfall intensity, soil properties, depth and initial water content, slope and
hillslope length.
Also the subsurface flow is simulated at the same time, allowing the evaluation of the
different characteristic times and dominances of the two processes, namely subsurface
and surface runoff. Only steady runoff intensities are considered for the sake of simplifying
the results interpretation, but unsteady ones can be easily implemented. The
same holds for soil layering
The Hawking temperature of expanding cosmological black holes
In the context of a debate on the correct expression of the Hawking
temperature of an expanding cosmological black hole, we show that the correct
expression in terms of the Hawking-Hayward quasi-local energy m of the hole is
T=1/(8\pi m(t)). This expression holds for comoving black holes and agrees with
a recent proposal by Saida, Harada, and Maeda.Comment: 5 latex pages, to appear in Phys. Rev. D. Some references adde
Conserved Quantities from the Equations of Motion (with applications to natural and gauge natural theories of gravitation)
We present an alternative field theoretical approach to the definition of
conserved quantities, based directly on the field equations content of a
Lagrangian theory (in the standard framework of the Calculus of Variations in
jet bundles). The contraction of the Euler-Lagrange equations with Lie
derivatives of the dynamical fields allows one to derive a variational
Lagrangian for any given set of Lagrangian equations. A two steps algorithmical
procedure can be thence applied to the variational Lagrangian in order to
produce a general expression for the variation of all quantities which are
(covariantly) conserved along the given dynamics. As a concrete example we test
this new formalism on Einstein's equations: well known and widely accepted
formulae for the variation of the Hamiltonian and the variation of Energy for
General Relativity are recovered. We also consider the Einstein-Cartan
(Sciama-Kibble) theory in tetrad formalism and as a by-product we gain some new
insight on the Kosmann lift in gauge natural theories, which arises when trying
to restore naturality in a gauge natural variational Lagrangian.Comment: Latex file, 31 page
On the universality of the Carter and McLenaghan formula
It is shown that the formula of the isometry generators of the spinor
representation given by Carter and McLenaghan is universal in the sense that
this holds for any representation either in local frames or even in natural
ones. The point-dependent spin matrices in natural frames are introduced for
any tensor representation deriving the covariant form of the isometry
generators in these frames.Comment: 7 pages, no figure
Universal field equations for metric-affine theories of gravity
We show that almost all metric--affine theories of gravity yield Einstein
equations with a non--null cosmological constant . Under certain
circumstances and for any dimension, it is also possible to incorporate a Weyl
vector field and therefore the presence of an anisotropy. The viability
of these field equations is discussed in view of recent astrophysical
observations.Comment: 13 pages. This is a copy of the published paper. We are posting it
here because of the increasing interest in f(R) theories of gravit
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