Static spherically symmetric Einstein-Vlasov shells made up of particles with a discrete set of values of their angular momentum

In this paper we study static spherically symmetric Einstein-Vlasov shells, made up of equal mass particles, where the angular momentum L of particles takes values only on a discrete finite set. We consider first the case where there is only one value of L, and prove their existence by constructing explicit examples. Shells with either hollow or black hole interiors have finite thickness. Of particular interest is the thin shell limit of these systems and we study its properties using both numerical and analytic arguments to compare with known results. The general case of a set of values of L is also considered and the particular case where L takes only two values is analyzed, and compared with the corresponding thin shell limit already given in the literature, finding good agreement in all cases.Comment: Comments: 16 pages, 5 figures. Section on thin shell limit revised. References adde

The quantitative measure and statistical distribution of fame

Fame and celebrity play an ever-increasing role in our culture. However, despite the cultural and economic importance of fame and its gradations, there exists no consensus method for quantifying the fame of an individual, or of comparing that of two individuals. We argue that, even if fame is difficult to measure with precision, one may develop useful metrics for fame that correlate well with intuition and that remain reasonably stable over time. Using datasets of recently deceased individuals who were highly renowned, we have evaluated several internet-based methods for quantifying fame. We find that some widely-used internet-derived metrics, such as search engine results, correlate poorly with human subject judgments of fame. However other metrics exist that agree well with human judgments and appear to offer workable, easily accessible measures of fame. Using such a metric we perform a preliminary investigation of the statistical distribution of fame, which has some of the power law character seen in other natural and social phenomena such as landslides and market crashes. In order to demonstrate how such findings can generate quantitative insight into celebrity culture, we assess some folk ideas regarding the frequency distribution and apparent clustering of celebrity deaths.Comment: 17 pages, 6 figure

The effect of radiative gravitational modes on the dynamics of a cylindrical shell of counter rotating particles

In this paper we consider some aspects of the relativistic dynamics of a cylindrical shell of counter rotating particles. In some sense these are the simplest systems with a physically acceptable matter content that display in a well defined sense an interaction with the radiative modes of the gravitational field. These systems have been analyzed previously, but in most cases resorting to approximations, or considering a particular form for the initial value data. Here we show that there exists a family of solutions where the space time inside the shell is flat and the equation of motion of the shell decouples completely from the gravitational modes. The motion of the shell is governed by an equation of the same form as that of a particle in a time independent one dimensional potential. We find that under appropriate initial conditions one can have collapsing, bounded periodic, and unbounded motions. We analyze and solve also the linearized equations that describe the dynamics of the system near a stable static solutions, keeping a regular interior. The surprising result here is that the motion of the shell is completely determined by the configuration of the radiative modes of the gravitational field. In particular, there are oscillating solutions for any chosen period, in contrast with the "approximately Newtonian plus small radiative corrections" motion expectation. We comment on the physical meaning of these results and provide some explicit examples. We also discuss the relation of our results to the initial value problem for the linearized dynamics of the shell

Chemical signatures of planets: beyond solar-twins

Elemental abundance studies of solar twin stars suggest that the solar chemical composition contains signatures of the formation of terrestrial planets in the solar system, namely small but significant depletions of the refractory elements. To test this hypothesis, we study stars which, compared to solar twins, have less massive convective envelopes (therefore increasing the amplitude of the predicted effect) or are, arguably, more likely to host planets (thus increasing the frequency of signature detections). We measure relative atmospheric parameters and elemental abundances of a late-F type dwarf sample (52 stars) and a sample of metal-rich solar analogs (59 stars). We detect refractory-element depletions with amplitudes up to about 0.15 dex. The distribution of depletion amplitudes for stars known to host gas giant planets is not different from that of the rest of stars. The maximum amplitude of depletion increases with effective temperature from 5650 K to 5950 K, while it appears to be constant for warmer stars (up to 6300 K). The depletions observed in solar twin stars have a maximum amplitude that is very similar to that seen here for both of our samples. Gas giant planet formation alone cannot explain the observed distributions of refractory-element depletions, leaving the formation of rocky material as a more likely explanation of our observations. More rocky material is necessary to explain the data of solar twins than metal-rich stars, and less for warm stars. However, the sizes of the stars' convective envelopes at the time of planet formation could be regulating these amplitudes. Our results could be explained if disk lifetimes were shorter in more massive stars, as independent observations indeed seem to suggest.Comment: Astronomy and Astrophysics, in press. Full tables available in the source downloa