On the nonexistence of conformally flat slices in the Kerr and other stationary spacetimes

It is proved that a stationary solutions to the vacuum Einstein field equations with non-vanishing angular momentum have no Cauchy slice that is maximal, conformally flat, and non-boosted. The proof is based on results coming from a certain type of asymptotic expansions near null and spatial infinity --which also show that the developments of Bowen-York type of data cannot have a development admitting a smooth null infinity--, and from the fact that stationary solutions do admit a smooth null infinity

On smoothness-asymmetric null infinities

We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past and a future null infinity of different smoothness. For simplicity, the analysis is restricted to the class of conformally flat, axially symmetric initial data sets. It is shown how the free parameters in the second fundamental form of the data can be used to satisfy certain obstructions to the smoothness of null infinity. The resulting initial data sets could be interpreted as those of some sort of (non-linearly) distorted Schwarzschild black hole. Its developments would be so that they admit a peeling future null infinity, but at the same time have a polyhomogeneous (non-peeling) past null infinity.Comment: 13 pages, 1 figur

Inflectional loci of scrolls

Let $X\subset \mathbb P^N$ be a scroll over a smooth curve $C$ and let \L=\mathcal O_{\mathbb P^N}(1)|_X denote the hyperplane bundle. The special geometry of $X$ implies that some sheaves related to the principal part bundles of \L are locally free. The inflectional loci of $X$ can be expressed in terms of these sheaves, leading to explicit formulas for the cohomology classes of the loci. The formulas imply that the only uninflected scrolls are the balanced rational normal scrolls.Comment: 9 pages, improved version. Accepted in Mathematische Zeitschrif

Baryogenesis through Collapsing String Loops in Gauged Baryon and Lepton Models

A scenario for the generation of the baryon asymmetry in the early Universe is proposed in which cosmic string loops, predicted by theories where the baryon and/or lepton numbers are gauged symmetries, collapse during the friction dominated period of string evolution. This provides a mechanism for the departure from thermal equilibrium necessary to have a nonvanishing baryon asymmetry. Examples of models are given where this idea can be implemented. In particular, the model with the gauge symmetry $SU(3)_{c}\otimes SU(2)_{L}\otimes U(1)_{Y}\otimes U(1)_{B} \otimes U(1)_{L}$ has the interesting feature where sphaleron processes do not violate the baryon and lepton numbers so that no wash out of any initial baryon asymmetry occurs at the electroweak scale.Comment: 21 pages, LaTeX, PURD-TH-93-09, SISSA 87/93/

Estimation of Gap Acceptance Parameters for HCM 2010 Roundabout Capacity Model Applications

This paper deals with the field data observation and successive application of estimation procedures in order to estimate follow-up headway and critical headway at roundabouts. Average follow-up and average critical headway are two critical parameters in the new roundabout capacity model presented in the 2010 edition of the Highway Capacity Manual (HCM). The HCM 2010 capacity model was developed as an exponential regression model with parameter estimates based on gap acceptance theory. Gap acceptance models are strongly affected by driver behaviour and local habits. Follow-up headways can be field measured, while critical headway cannot be obtained directly. The paper mainly aims to check if general suggested values are well-suited also for Italy or not. There have been numerous techniques developed for estimating critical headway. In order to perform a better check of a sample of experimentally observed values, three different procedures are chosen and applied. The first is a quite popular mathematical method based on maximum likelihood technique. The second is a statistical method based on the median of the observed sample distribution. The third is a graphical method known as Raff’s method. All these three methods require information about the accepted headway and the largest rejected headway for each driver. Therefore a sample of field data was recorded by digital camera and processed following the instructions suggested by NCHRP. The sample data of critical headway and follow-up headway are gathered in seven selected roundabouts located in Northern Tuscany (Italy). Our first obtained results indicate that the average critical headway is significantly lower than the values recommended by some international references. However, the average follow-up headway is only higher than that recommended for the State of California and it is lower than that recommended by all other international references. Finally, conclusions drawn along with insights for further research developments are suggested

Polyhomogeneity and zero-rest-mass fields with applications to Newman-Penrose constants

A discussion of polyhomogeneity (asymptotic expansions in terms of $1/r$ and $\ln r$) for zero-rest-mass fields and gravity and its relation with the Newman-Penrose (NP) constants is given. It is shown that for spin-$s$ zero-rest-mass fields propagating on Minkowski spacetime, the logarithmic terms in the asymptotic expansion appear naturally if the field does not obey the ``Peeling theorem''. The terms that give rise to the slower fall-off admit a natural interpretation in terms of advanced field. The connection between such fields and the NP constants is also discussed. The case when the background spacetime is curved and polyhomogeneous (in general) is considered. The free fields have to be polyhomogeneous, but the logarithmic terms due to the connection appear at higher powers of $1/r$. In the case of gravity, it is shown that it is possible to define a new auxiliary field, regular at null infinity, and containing some relevant information on the asymptotic behaviour of the spacetime. This auxiliary zero-rest-mass field ``evaluated at future infinity ($i^+$)'' yields the logarithmic NP constants.Comment: 19 page

Dynamical decompactification from brane gases in eleven-dimensional supergravity

Brane gas cosmology provides a dynamical decompactification mechanism that could account for the number of spacetime dimensions we observe today. In this work we discuss this scenario taking into account the full bosonic sector of eleven-dimensional supergravity. We find new cosmological solutions that can dynamically explain the existence of three large spatial dimensions characterised by an universal asymptotic scaling behaviour and a large number of initially unwrapped dimensions. This type of solutions enlarge the possible initial conditions of the Universe in the Hagedorn phase and consequently can potentially increase the probability of dynamical decompactification from anisotropically wrapped backgrounds.Comment: 8 figures, JHEP3 styl

CP violation in supersymmetric model with non-degenerate A-terms

We study the CP phases of the soft supersymmetry breaking terms in string-inspired models with non-universal trilinear couplings. We show that such non-universality plays an important role on all CP violating processes. In particular these new supersymmetric sources of CP violation may significantly contribute to the observed CP phenomena in kaon physics while respecting the severe bound on the electric dipole moment of the neutron.Comment: 14 pages, Late