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

Critical Fluctuations at RHIC

On the basis of universal scaling properties, we claim that in Au+Au collisions at RHIC, the QCD critical point is within reach. The signal turns out to be an extended plateau of net baryons in rapidity with approximate height of the net-baryon rapidity density approximately 15 and a strong intermittency pattern with index s_2=1/6 in rapidity fluctuations. A window also exists, to reach the critical point at the SPS, especially in Si+Si collisions at maximal energy.Comment: 8 pages, 3 figure

Critical Opalescence in Baryonic QCD Matter

We show that critical opalescence, a clear signature of second-order phase transition in conventional matter, manifests itself as critical intermittency in QCD matter produced in experiments with nuclei. This behaviour is revealed in transverse momentum spectra as a pattern of power laws in factorial moments, to all orders, associated with baryon production. This phenomenon together with a similar effect in the isoscalar sector of pions (sigma mode) provide us with a set of observables associated with the search for the QCD critical point in experiments with nuclei at high energies.Comment: 7 pages, 1 figur

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

Criticality, Fractality and Intermittency in Strong Interactions

Assuming a second-order phase transition for the hadronization process, we attempt to associate intermittency patterns in high-energy hadronic collisions to fractal structures in configuration space and corresponding intermittency indices to the isothermal critical exponent at the transition temperature. In this approach, the most general multidimensional intermittency pattern, associated to a second-order phase transition of the strongly interacting system, is determined, and its relevance to present and future experiments is discussed.Comment: 15 pages + 2 figures (available on request), CERN-TH.6990/93, UA/NPPS-5-9