5,364 research outputs found
The Maxwell Lagrangian in purely affine gravity
The purely affine Lagrangian for linear electrodynamics, that has the form of
the Maxwell Lagrangian in which the metric tensor is replaced by the
symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of
homothetic curvature, is dynamically equivalent to the Einstein-Maxwell
equations in the metric-affine and metric formulation. We show that this
equivalence is related to the invariance of the Maxwell Lagrangian under
conformal transformations of the metric tensor. We also apply to a purely
affine Lagrangian the Legendre transformation with respect to the tensor of
homothetic curvature to show that the corresponding Legendre term and the new
Hamiltonian density are related to the Maxwell-Palatini Lagrangian for the
electromagnetic field. Therefore the purely affine picture, in addition to
generating the gravitational Lagrangian that is linear in the curvature,
justifies why the electromagnetic Lagrangian is quadratic in the
electromagnetic field.Comment: 9 pages; published versio
Cosmological Constant and Noncommutative Spacetime
We show that the cosmological constant appears as a Lagrange multiplier if
nature is described by a canonical noncommutative spacetime. It is thus an
arbitrary parameter unrelated to the action and thus to vacuum fluctuations.
The noncommutative algebra restricts general coordinate transformations to
four-volume preserving noncommutative coordinate transformations. The
noncommutative gravitational action is thus an unimodular noncommutative
gravity. We show that spacetime noncommutativity provides a very natural
justification to an unimodular gravity solution to the cosmological problem. We
obtain the right order of magnitude for the critical energy density of the
universe if we assume that the scale for spacetime noncommutativity is the
Planck scale.Comment: 7 page
Dynamics of Einstein - de Haas Effect: Application to Magnetic Cantilever
Local time-dependent theory of Einstein - de Haas effect is developed. We
begin with microscopicinteractions and derive dynamical equations that couple
elastic deformations with internal twists due to spins. The theory is applied
to the description of the motion of a magnetic cantilever caused by the
oscillation of the domain wall. Theoretical results are compared with a recent
experiment on Einstein - de Haas effect in a microcantilever.Comment: 7 PR pages, 5 figures, submitted to PR
Two-dimensional gravity with a dynamical aether
We investigate the two-dimensional behavior of gravity coupled to a dynamical
unit timelike vector field, i.e. "Einstein-aether theory". The classical
solutions of this theory in two dimensions depend on one coupling constant.
When this coupling is positive the only solutions are (i) flat spacetime with
constant aether, (ii) de Sitter or anti-de Sitter spacetimes with a uniformly
accelerated unit vector invariant under a two-dimensional subgroup of SO(2,1)
generated by a boost and a null rotation, and (iii) a non-constant curvature
spacetime that has no Killing symmetries and contains singularities. In this
case the sign of the curvature is determined by whether the coupling is less or
greater than one. When instead the coupling is negative only solutions (i) and
(iii) are present. This classical study of the behavior of Einstein-aether
theory in 1+1 dimensions may provide a starting point for further
investigations into semiclassical and fully quantum toy models of quantum
gravity with a dynamical preferred frame.Comment: 11 pages, 4 figure
Comment on "Bell's Theorem without Inequalities and without Probabilities for Two Observers"
In this Comment we show that Cabello's argument [Phys. Rev. Lett. 86, 1911
(2001)] which proves the nonlocal feature of any classical model of quantum
mechanics based on Einstein-Podolsky-Rosen (EPR) criterion of elements of
reality, must involve at least four distant observers rather than the two
employed by the author. Moreover we raise a remark on the necessity of
performing a real experiment confirming Cabello's argument.Comment: 1 page, REVTex4 fil
A Possible Origin of Dark Energy
We discuss the possibility that the existence of dark energy may be due to
the presence of a spin zero field , either elementary or composite. In
the presence of other matter field, the transformation
constant can generate a negative pressure, like the cosmological constant. In
this picture, our universe can be thought as a very large bag, similar to the
much smaller MIT bag model for a single nucleon.Comment: 4 pages, no figure, typos correcte
Action Principle for the Generalized Harmonic Formulation of General Relativity
An action principle for the generalized harmonic formulation of general
relativity is presented. The action is a functional of the spacetime metric and
the gauge source vector. An action principle for the Z4 formulation of general
relativity has been proposed recently by Bona, Bona--Casas and Palenzuela
(BBP). The relationship between the generalized harmonic action and the BBP
action is discussed in detail.Comment: This version is contains more thorough presentations and discussions
of the key results. To be published in PRD. (8 pages, no figures
Reply to "Can gravitational dynamics be obtained by diffeomorphism invariance of action?"
In a previous work we showed that, in a suitable setting, one can use
diffeomorphism invariance in order to derive gravitational field equations from
boundary terms of the gravitational action. Standing by our results we reply
here to a recent comment questioning their validity.Comment: Accepted for publication in PR
Post-Newtonian Approximation in Maxwell-Like Form
The equations of the linearized first post-Newtonian approximation to general
relativity are often written in "gravitoelectromagnetic" Maxwell-like form,
since that facilitates physical intuition. Damour, Soffel and Xu (DSX) (as a
side issue in their complex but elegant papers on relativistic celestial
mechanics) have expressed the first post-Newtonian approximation, including all
nonlinearities, in Maxwell-like form. This paper summarizes that DSX
Maxwell-like formalism (which is not easily extracted from their celestial
mechanics papers), and then extends it to include the post-Newtonian
(Landau-Lifshitz-based) gravitational momentum density, momentum flux (i.e.
gravitational stress tensor) and law of momentum conservation in Maxwell-like
form. The authors and their colleagues have found these Maxwell-like momentum
tools useful for developing physical intuition into numerical-relativity
simulations of compact binaries with spin.Comment: v4: Revised for resubmission to Phys Rev D, 6 pages. v3: Reformulated
in terms of DSX papers. Submitted to Phys Rev D, 6 pages. v2: Added
references. Changed definitions & convention
Mass as a Relativistic Quantum Observable
A field state containing photons propagating in different directions has a
non vanishing mass which is a quantum observable. We interpret the shift of
this mass under transformations to accelerated frames as defining space-time
observables canonically conjugated to energy-momentum observables. Shifts of
quantum observables differ from the predictions of classical relativity theory
in the presence of a non vanishing spin. In particular, quantum redshift of
energy-momentum is affected by spin. Shifts of position and energy-momentum
observables however obey simple universal rules derived from invariance of
canonical commutators.Comment: 5 pages, revised versio
- âŠ