Comment on "Correlation between Compact Radio Lout Quasars and Ultrahigh Energy Cosmic Rays"

In a recent paper, Farrar and Biermann argue that there is a strong correlation between the direction of the five highest-energy cosmic-ray events and compact, radio-loud quasars. This Comment shows that this analysis contains several inconsistencies and errors so that the significance of any such correlation is certainly greatly overestimated and perhaps nonexistent.Comment: 2 pages, REVTE

RASS-SDSS Galaxy Cluster Survey. VI. The dependence of the cluster SFR on the cluster global properties

Using a subsample of 79 nearby clusters from the RASS-SDSS galaxy cluster catalogue of Popesso et al. (2005a), we perform a regression analysis between the cluster integrated star formation rate (Sigma_SFR) the cluster total stellar mass (M_star), the fractions of star forming (f_SF) and blue (f_b) galaxies and other cluster global properties, namely its richness (N_gal, i.e. the total number of cluster members within the cluster virial radius), velocity dispersion (sigma_v), virial mass (M_200), and X-ray luminosity (L_X). All cluster global quantities are corrected for projection effects before the analysis. Galaxy SFRs and stellar masses are taken from the catalog of Brinchmann et al. (2004), which is based on SDSS spectra. We only consider galaxies with M_r <= -20.25 in our analysis, and exclude AGNs. We find that both Sigma_SFR and M_star are correlated with all the cluster global quantities. A partial correlation analysis show that all the correlations are induced by the fundamental one between Sigma_SFR and N_gal, hence there is no evidence that the cluster properties affect the mean SFR or M_star per galaxy. The relations between Sigma_SFR and M_star, on one side, and both N_gal and M_200, on the other side, are linear, i.e. we see no evidence that different clusters have different SFR or different M_star per galaxy and per unit mass. The fraction f_SF does not depend on any cluster property considered, while f_b does depend on L_X. We note that a significant fraction of star-forming cluster galaxies are red (~25% of the whole cluster galaxy population). We conclude that the global cluster properties are unable to affect the SF properties of cluster galaxies, but the presence of the X-ray luminous intra-cluster medium can affect their colors, perhaps through the ram-pressure stripping mechanism.Comment: 14 pages, 12 figures, accepted for publication on A&A; corrected coefficient in Tab.

Hamiltonian Formulation of Two Body Problem in Wheeler-Feynman electrodynamics

A Hamiltonian formulation for the classical problem of electromagnetic interaction of two charged relativistic particles is found.Comment: 22 pages, 8 Uuencoded Postscript figure

Empirical constraints on vacuum decay in the stringy landscape

It is generally considered as self evident that the lifetime of our vacuum in the landscape of string theory cannot be much shorter than the current age of the universe. Here I show why this lower limit is invalid. A certain type of ``parallel universes'' is a necessary consequence of the string-landscape dynamics and might well allow us to ``survive'' vacuum decay. As a consequence our stringy vacuum's lifetime is empirically unconstrained and could be very short. Based on this counter-intuitive insight I propose a novel type of laboratory experiment that searches for an apparent violation of the quantum-mechanical Born rule by gravitational effects on vacuum decay. If the lifetime of our vacuum should turn out to be shorter than 6 x 10^{-13} seconds such an experiment is sufficiently sensitive to determine its value with state-of-the-art equipment.Comment: 13 pages, 2 figures, proposes a laboratory experimen

Kerr black holes in horizon-generating form

New coordinates are given which describe non-degenerate Kerr black holes in dual-null foliations based on the outer (or inner) horizons, generalizing the Kruskal form for Schwarzschild black holes. The construction involves an area radius for the transverse surfaces and a generalization of the Regge-Wheeler radial function, both functions of the original radial coordinate only.Comment: 4 revtex4 page

A Simple Family of Analytical Trumpet Slices of the Schwarzschild Spacetime

We describe a simple family of analytical coordinate systems for the Schwarzschild spacetime. The coordinates penetrate the horizon smoothly and are spatially isotropic. Spatial slices of constant coordinate time $t$ feature a trumpet geometry with an asymptotically cylindrical end inside the horizon at a prescribed areal radius $R_0$ (with $0<R_{0}\leq M$) that serves as the free parameter for the family. The slices also have an asymptotically flat end at spatial infinity. In the limit $R_{0}=0$ the spatial slices lose their trumpet geometry and become flat -- in this limit, our coordinates reduce to Painlev\'e-Gullstrand coordinates.Comment: 7 pages, 3 figure

SHORTCUT METHOD OF SOLUTION OF GEODESIC EQUATIONS FOR SCHWARZSCHILD BLACK HOLE

It is shown how the use of the Kerr-Schild coordinate system can greatly simplify the formulation of the geodesic equation of the Schwarzschild solution. An application of this formulation to the numerical computation of the aspect of a non-rotating black hole is presented. The generalization to the case of the Kerr solution is presented too.Comment: 11 pages, 2 PostScript figures (available as uuencoded compressed tar file), uses epsfig.tex). Accepted on February 1995 for publication in Classical and Quantum Gravit

The gravitational analogue to the hydrogen atom (A summer study at the borders of quantum mechanics and general relativity)

This article reports on a student summer project performed in 2006 at the University of Frankfurt. It is addressed to undergraduate students familiar with the basic principles of relativistic quantum mechanics and general relativity. The aim of the project was to study the Dirac equation in curved space time. To obtain the general relativistic Dirac equation we use the formulation of gravity as a gauge theory in the first part. After these general considerations we restrict the further discussion to the special case of the Schwarzschild metric. This setting corresponds to the hydrogen atom, with the electromagnetic field replaced by gravity. Although there is a singularity at the event horizon it turns out that a regular solution of the time independent Dirac equation exists. Finally the Dirac equation is solved numerically using suitable boundary conditions.Comment: 19 pages, 3 figure

Active gravitational mass and the invariant characterization of Reissner-Nordstrom spacetime

We analyse the concept of active gravitational mass for Reissner-Nordstrom spacetime in terms of scalar polynomial invariants and the Karlhede classification. We show that while the Kretschmann scalar does not produce the expected expression for the active gravitational mass, both scalar polynomial invariants formed from the Weyl tensor, and the Cartan scalars, do.Comment: 6 pages Latex, to appear in General Relativity and Gravitatio

Gravity of a static massless scalar field and a limiting Schwarzschild-like geometry

We study a set of static solutions of the Einstein equations in presence of a massless scalar field and establish their connection to the Kantowski-Sachs cosmological solutions based on some kind of duality transformations. The physical properties of the limiting case of an empty hyperbolic spacetime (pseudo-Schwarzschild geometry) are analyzed in some detail.Comment: 13 pages, 4 figure