Black-Hole Solutions with Scalar Hair in Einstein-Scalar-Gauss-Bonnet Theories

In the context of the Einstein-scalar-Gauss-Bonnet theory, with a general coupling function between the scalar field and the quadratic Gauss-Bonnet term, we investigate the existence of regular black-hole solutions with scalar hair. Based on a previous theoretical analysis, that studied the evasion of the old and novel no-hair theorems, we consider a variety of forms for the coupling function (exponential, even and odd polynomial, inverse polynomial, and logarithmic) that, in conjunction with the profile of the scalar field, satisfy a basic constraint. Our numerical analysis then always leads to families of regular, asymptotically-flat black-hole solutions with non-trivial scalar hair. The solution for the scalar field and the profile of the corresponding energy-momentum tensor, depending on the value of the coupling constant, may exhibit a non-monotonic behaviour, an unusual feature that highlights the limitations of the existing no-hair theorems. We also determine and study in detail the scalar charge, horizon area and entropy of our solutions.Comment: PdfLatex file, 29 Pages, 18 figures, the analysis was extended to study the scalar charge, horizon area and entropy of our solutions, comments added, typos corrected, version to appear in Physical Review

A common origin of all the species of high-energy cosmic rays?

Cosmic ray nuclei, cosmic ray electrons with energy above a few GeV, and the diffuse gamma-ray background radiation (GBR) above a few MeV, presumed to be extragalactic, could all have their origin or residence in our galaxy and its halo. The mechanism accelerating hadrons and electrons is the same, the electron spectrum is modulated by inverse Compton scattering on starlight and on the microwave background radiation; the $\gamma$-rays are the resulting recoiling photons. The spectral indices of the cosmic-ray electrons and of the GBR, calculated on this simple basis, agree with observations. The angular dependence and the approximate magnitude of the GBR are also explained.Comment: Includes a discussion of the contribution of inverse Compton scattering of CR electrons by starlight in the halo to the gamma background radiation. One corrected typo. Additional references, and figures to compare predictions for the angular dependence of the gamma background radiation with data. Conclusions are unchange

The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius--Perron operator $U$ of the cusp map $F:[-1,1]\to[-1,1]$, $F(x)=1-2\sqrt{|x|}$ (which is an approximation of the Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in(0,1)$ the spectrum of $U$ in the Hardy space in the disk \{z\in\C:|z-q|<1+q\} is the union of the segment $[0,1]$ and some finite or countably infinite set of isolated eigenvalues of finite multiplicity.Comment: Submitted to JMP; The description of the spectrum in some Hardy spaces is adde