1,320 research outputs found
Universality of Einstein Equations for the Ricci Squared Lagrangians
It has been recently shown that, in the first order (Palatini) formalism,
there is universality of Einstein equations and Komar energy-momentum complex,
in the sense that for a generic nonlinear Lagrangian depending only on the
scalar curvature of a metric and a torsionless connection one always gets
Einstein equations and Komar's expression for the energy-momentum complex. In
this paper a similar analysis (also in the framework of the first order
formalism) is performed for all nonlinear Lagrangians depending on the
(symmetrized) Ricci square invariant. The main result is that the universality
of Einstein equations and Komar energy-momentum complex also extends to this
case (modulo a conformal transformation of the metric).Comment: 21 pages, Late
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
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
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
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.
Handheld-Impedance-Measurement System with seven-decade capability and potentiostatic function
This paper describes design and test of a new impedance-measurement system for nonlinear devices that exhibits a seven-decade range and works down to a frequency of 0.01 Hz. The system is specifically designed for electrochemical measurements, but the proposed architecture can be employed in many other fields where flexible signal generation and analysis are required. The system employs an unconventional signal generator based on two pulsewidth modulation (PWM) oscillators and an autocalibration system that allows uncertainties of less than 3% to be obtained over a range of 1 kΩ to 100 GΩ. A synchronous demodulation processing allows the noise superimposed to the low-amplitude input signals to be made negligibl
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
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
Gravitation, electromagnetism and cosmological constant in purely affine gravity
The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field,
that has the form of the Maxwell Lagrangian with the metric tensor replaced by
the symmetrized Ricci tensor, is dynamically equivalent to the metric
Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric
tensor is not well-defined. This feature indicates that, for the
Ferraris-Kijowski model to be physical, there must exist a background field
that depends on the Ricci tensor. The simplest possibility, supported by recent
astronomical observations, is the cosmological constant, generated in the
purely affine formulation of gravity by the Eddington Lagrangian. In this paper
we combine the electromagnetic field and the cosmological constant in the
purely affine formulation. We show that the sum of the two affine (Eddington
and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of
the analogous (CDM and Einstein-Maxwell) Lagrangians in the
metric-affine/metric formulation. We also show that such a construction is
valid, like the affine Einstein-Born-Infeld formulation, only for weak
electromagnetic fields, on the order of the magnetic field in outer space of
the Solar System. Therefore the purely affine formulation that combines
gravity, electromagnetism and cosmological constant cannot be a simple sum of
affine terms corresponding separately to these fields. A quite complicated form
of the affine equivalent of the metric Einstein-Maxwell- Lagrangian
suggests that Nature can be described by a simpler affine Lagrangian, leading
to modifications of the Einstein-Maxwell-CDM theory for
electromagnetic fields that contribute to the spacetime curvature on the same
order as the cosmological constant.Comment: 17 pages, extended and combined with gr-qc/0612193; published versio
The dynamical equivalence of modified gravity revisited
We revisit the dynamical equivalence between different representations of
vacuum modified gravity models in view of Legendre transformations. The
equivalence is discussed for both bulk and boundary space, by including in our
analysis the relevant Gibbons-Hawking terms. In the f(R) case, the Legendre
transformed action coincides with the usual Einstein frame one. We then
re-express the R+f(G) action, where G is the Gauss-Bonnet term, as a second
order theory with a new set of field variables, four tensor fields and one
scalar and study its dynamics. For completeness, we also calculate the
conformal transformation of the full Jordan frame R+f(G) action. All the
appropriate Gibbons-Hawking terms are calculated explicitly.Comment: 17 pages; v3: Revised version. New comments added in Sections 3 & 5.
New results added in Section 6. Version to appear in Class. Quantum Gravit
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