Lanczos potentials and a definition of gravitational entropy for perturbed FLRW space-times

We give a prescription for constructing a Lanczos potential for a cosmological model which is a purely gravitational perturbation of a Friedman-Lemaitre-Robertson-Walker space-time. For the radiation equation of state, we find the Lanczos potential explicitly via Fourier transforms. As an application, we follow up a suggestion of Penrose and propose a definition of gravitational entropy for these cosmologies. With this definition, the gravitational entropy initially is finite if and only if the initial Weyl tensor is finite.Comment: 16 pages, submitted for publication in Classical and Quantum Gravit

Comment on ``Strength and genericity of singularities in Tolman-Bondi-de Sitter collapse'' and a note on central singularities

It has been claimed that the Lemaitre-Tolman-Bondi-de Sitter solution always admits future-pointing radial time-like geodesics emerging from the shell-focussing singularity, regardless of the nature of the (regular) initial data. This is despite the fact that some data rule out the emergence of future pointing radial null geodesics. We correct this claim and show that in general in spherical symmetry, the absence of radial null geodesics emerging from a central singularity is sufficient to prove that the singularity is censored.Comment: 3 pages, revtex4, submitted to Phys. Lett.

Formation of Higher-dimensional Topological Black Holes

We study higher dimensional gravitational collapse to topological black holes in two steps. Firstly, we construct some (n+2)-dimensional collapsing space-times, which include generalised Lemaitre-Tolman-Bondi-like solutions, and we prove that these can be matched to static $\Lambda$-vacuum exterior space-times. We then investigate the global properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. Secondly, we consider as interiors classes of 5-dimensional collapsing solutions built on Riemannian Bianchi IX spatial metrics matched to radiating exteriors given by the Bizon-Chmaj-Schmidt metric. In some cases, the data at the boundary for the exterior can be chosen to be close to the data for the Schwarzschild solution.Comment: 16 pages, 3 figures; v2: typos corrected, matches final published versio

Spectral analysis of the high-energy IceCube neutrinos

A full energy and flavor-dependent analysis of the three-year high-energy IceCube neutrino events is presented. By means of multidimensional fits, we derive the current preferred values of the high-energy neutrino flavor ratios, the normalization and spectral index of the astrophysical fluxes, and the expected atmospheric background events, including a prompt component. A crucial assumption resides on the choice of the energy interval used for the analyses, which significantly biases the results. When restricting ourselves to the ~30 TeV - 3 PeV energy range, which contains all the observed IceCube events, we find that the inclusion of the spectral information improves the fit to the canonical flavor composition at Earth, (1:1:1), with respect to a single-energy bin analysis. Increasing both the minimum and the maximum deposited energies has dramatic effects on the reconstructed flavor ratios as well as on the spectral index. Imposing a higher threshold of 60 TeV yields a slightly harder spectrum by allowing a larger muon neutrino component, since above this energy most atmospheric tracklike events are effectively removed. Extending the high-energy cutoff to fully cover the Glashow resonance region leads to a softer spectrum and a preference for tau neutrino dominance, as none of the expected electron antineutrino induced showers have been observed so far. The lack of showers at energies above 2 PeV may point to a broken power-law neutrino spectrum. Future data may confirm or falsify whether or not the recently discovered high-energy neutrino fluxes and the long-standing detected cosmic rays have a common origin.Comment: 33 pages, 13 figures. v3: one extra figure (fig. 13), some references updated and some formulae moved to the Appendix. It matches version published in PR