Flat deformation of a spacetime admitting two Killing fields

It is shown that given an analytic Lorentzian metric on a 4-manifold, $g$, which admits two Killing vector fields, then it exists a local deformation law $\eta = a g + b H$, where $H$ is a 2-dimensional projector, such that $\eta$ is flat and admits the same Killing vectors. We also characterize the particular case when the projector $H$ coincides with the quotient metric. We apply some of our results to general stationary axisymmetric spacetime

Comment on "Canonical formalism for Lagrangians with nonlocality of finite extent"

We show by some counterexamples that Lagrangian sysytems with nonlocality of finite extent are not necessarily unstable.Comment: 8 pages, 1 figure Submitted to Phys. Rev.

Flat deformation theorem and symmetries in spacetime

The \emph{flat deformation theorem} states that given a semi-Riemannian analytic metric $g$ on a manifold, locally there always exists a two-form $F$, a scalar function $c$, and an arbitrarily prescribed scalar constraint depending on the point $x$ of the manifold and on $F$ and $c$, say $\Psi (c, F, x)=0$, such that the \emph{deformed metric} $\eta = cg -\epsilon F^2$ is semi-Riemannian and flat. In this paper we first show that the above result implies that every (Lorentzian analytic) metric $g$ may be written in the \emph{extended Kerr-Schild form}, namely $\eta_{ab} := a g_{ab} - 2 b k_{(a} l_{b)}$ where $\eta$ is flat and $k_a, l_a$ are two null covectors such that $k_a l^a= -1$; next we show how the symmetries of $g$ are connected to those of $\eta$, more precisely; we show that if the original metric $g$ admits a Conformal Killing vector (including Killing vectors and homotheties), then the deformation may be carried out in a way such that the flat deformed metric $\eta$ `inherits' that symmetry.Comment: 30 pages, 0 figure

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A translocation motif in relaxase TrwC specifically affects recruitment by its conjugative type IV secretion system

Type IV secretion system (T4SS) substrates are recruited through a translocation signal that is poorly defined for conjugative relaxases. The relaxase TrwC of plasmid R388 is translocated by its cognate conjugative T4SS, and it can also be translocated by the VirB/D4 T4SS of Bartonella henselae, causing DNA transfer to human cells. In this work, we constructed a series of TrwC variants and assayed them for DNA transfer to bacteria and human cells to compare recruitment requirements by both T4SSs. Comparison with other reported relaxase translocation signals allowed us to determine two putative translocation sequence (TS) motifs, TS1 and TS2. Mutations affecting TS1 drastically affected conjugation frequencies, while mutations affecting either motif had only a mild effect on DNA transfer rates through the VirB/D4 T4SS of B. henselae. These results indicate that a single substrate can be recruited by two different T4SSs through different signals. The C terminus affected DNA transfer rates through both T4SSs tested, but no specific sequence requirement was detected. The addition of a Bartonella intracellular delivery (BID) domain, the translocation signal for the Bartonella VirB/D4 T4SS, increased DNA transfer up to 4% of infected human cells, providing an excellent tool for DNA delivery to specific cell types. We show that the R388 coupling protein TrwB is also required for this high-efficiency TrwC-BID translocation. Other elements apart from the coupling protein may also be involved in substrate recognition by T4SSs

On the degrees of freedom of a semi-Riemannian metric

A semi-Riemannian metric in a n-manifold has n(n-1)/2 degrees of freedom, i.e. as many as the number of components of a differential 2-form. We prove that any semi-Riemannian metric can be obtained as a deformation of a constant curvature metric, this deformation being parametrized by a 2-for

Arnowitt-Deser-Misner representation and Hamiltonian analysis of covariant renormalizable gravity

We study the recently proposed Covariant Renormalizable Gravity (CRG), which aims to provide a generally covariant ultraviolet completion of general relativity. We obtain a space-time decomposed form --- an Arnowitt-Deser-Misner (ADM) representation --- of the CRG action. The action is found to contain time derivatives of the gravitational fields up to fourth order. Some ways to reduce the order of these time derivatives are considered. The resulting action is analyzed using the Hamiltonian formalism, which was originally adapted for constrained theories by Dirac. It is shown that the theory has a consistent set of constraints. It is, however, found that the theory exhibits four propagating physical degrees of freedom. This is one degree of freedom more than in Ho\v{r}ava-Lifshitz (HL) gravity and two more propagating modes than in general relativity. One extra physical degree of freedom has its origin in the higher order nature of the CRG action. The other extra propagating mode is a consequence of a projectability condition similarly as in HL gravity. Some additional gauge symmetry may need to be introduced in order to get rid of the extra gravitational degrees of freedom.Comment: 21 pages, LaTeX. A correction inserted to Hamiltonian formalism in Sec.

Stochastic to deterministic crossover of fractal dimension for a Langevin equation

Using algorithms of Higuchi and of Grassberger and Procaccia, we study numerically how fractal dimensions cross over from finite-dimensional Brownian noise at short time scales to finite values of deterministic chaos at longer time scales for data generated from a Langevin equation that has a strange attractor in the limit of zero noise. Our results suggest that the crossover occurs at such short time scales that there is little chance of finite-dimensional Brownian noise being incorrectly identified as deterministic chaos.Comment: 12 pages including 3 figures, RevTex and epsf. To appear Phys. Rev. E, April, 199

Advanced radiation measurement techniques in diagnostic radiology and molecular imaging.

This paper reports some technological advances recently achieved in the fields of micro-CT and small animal PET instrumentation. It highlights a balance between image-quality improvement and dose reduction. Most of the recent accomplishments in these fields are due to the use of novel imaging sensors such as CMOS-based X-ray detectors and silicon photomultipliers (SiPM). Some of the research projects carried out at the University of Pisa for the development of such advanced radiation imaging technology are also described

On the motion of a classical charged particle

We show that the Lorentz-Dirac equation is not an unavoidable consequence of energy-momentum conservation for a point charge. What follows solely from conservation laws is a less restrictive equation already obtained by Honig and Szamosi. The latter is not properly an equation of motion because, as it contains an extra scalar variable, it does not determine the future evolution of the charge. We show that a supplementary constitutive relation can be added so that the motion is determined and free from the troubles that are customary in Lorentz-Dirac equation, i. e. preacceleration and runaways