Soccer: is scoring goals a predictable Poissonian process?

The non-scientific event of a soccer match is analysed on a strictly scientific level. The analysis is based on the recently introduced concept of a team fitness (Eur. Phys. J. B 67, 445, 2009) and requires the use of finite-size scaling. A uniquely defined function is derived which quantitatively predicts the expected average outcome of a soccer match in terms of the fitness of both teams. It is checked whether temporary fitness fluctuations of a team hamper the predictability of a soccer match. To a very good approximation scoring goals during a match can be characterized as independent Poissonian processes with pre-determined expectation values. Minor correlations give rise to an increase of the number of draws. The non-Poissonian overall goal distribution is just a consequence of the fitness distribution among different teams. The limits of predictability of soccer matches are quantified. Our model-free classification of the underlying ingredients determining the outcome of soccer matches can be generalized to different types of sports events

Non-BPS D8-branes and Dynamic Domain Walls in Massive IIA Supergravities

We study the D8-branes of the Romans massive IIA supergravity theory using the coupled supergravity and worldvolume actions. D8 branes can be regarded as domain walls with the jump in the extrinsic curvature at the brane given by the Israel matching conditions. We examine the restrictions that these conditions place on extreme and non-extreme solutions and find that they rule out some of the supersymmetric solutions given by Bergshoeff {\em et al}. We consider what happens when the dilaton varies on the worldvolume of the brane, which implies that the brane is no longer static. We obtain a family of D8-brane solutions parametrized by a non-extremality term on each side of the brane and the asymptotic values of the 10-form field. The non-extremality parameters can be related to the velocity of the brane. We also study 8-brane solutions of a massive IIA supergravity theory introduced by Howe, Lambert and West. This theory also admits a 10-form formulation, but the 10-form is not a R-R sector field and so these 8-branes are not D-branes.Comment: 23 pages REVTeX, 2 .eps figures. This paper completely replaces and extends an earlier paper (hep-th/9712112) by Chamblin and Perr

A Bestiary of Higher Dimensional Taub-NUT-AdS Spacetimes

We present a menagerie of solutions to the vacuum Einstein equations in six, eight and ten dimensions. These solutions describe spacetimes which are either locally asymptotically adS or locally asymptotically flat, and which have non-trivial topology. We discuss the global structure of these solutions, and their relevance within the context of M-theory.Comment: 11 pages, LaTex(v4: Comments and references added

Abelian Higgs Hair for a Static Charged Black String

We study the problem of vortex solutions in the background of an electrically charged black string. We show numerically that the Abelian Higgs field equations in the background of a four-dimensional black string have vortex solutions. These solutions which have axial symmetry, show that the black string can support the Abelian Higgs field as hair. This situation holds also in the case of the extremal black string. We also consider the self-gravity of the Abelian Higgs field and show that the effect of the vortex is to induce a deficit angle in the metric under consideration.Comment: REVTEX4, 12 pages, 6 figures, The version to be appeared in Phys. Rev.

Radion Potential and Brane Dynamics

We examine the cosmology of the Randall-Sundrum model in a dynamic setting where scalar fields are present in the bulk as well as the branes. This generates a mechanism similar to that of Goldberger-Wise for radion stabilization and the recovery of late-cosmology features in the branes. Due to the induced radion dynamics, the inflating branes roll towards the minimum of the radion potential, thereby exiting inflation and reheating the Universe. In the slow roll part of the potential, the 'TeV' branes have maximum inflation rate and energy as their coupling to the radion and bulk modes have minimum suppresion. Hence, when rolling down the steep end of the potential towards the stable point, the radion field (which appears as the inflaton of the effective 4D theory in the branes) decays very fast, reheats the Universe .This process results decayin a decrease of brane's canonical vacuum energy $\Lambda_4$. However, at the minimum of the potential $\Lambda_4$ is small but not neccessarily zero and the fine-tuning issue remains .Density perturbation constraints introduce an upper bound when the radion stabilizies. Due to the large radion mass and strong suppression to the bulk modes, moduli problems and bulk reheating do not occur. The reheat temperature and a sufficient number of e-folding constraints for the brane-universe are also satisfied. The model therefore recovers the radiation dominated FRW universe.Comment: 16 pages, 3 figures,extraneous sentences removed, 2 footnotes added, some typos correcte

Thick domain wall universes

We investigate the spacetime of a thick gravitating domain wall for a general potential $V(\Phi)$. Using general analytical arguments we show that all nontrivial solutions fall into two categories: those interpretable as an isolated domain wall with a cosmological event horizon, and those which are pure false vacuum de Sitter solutions. Although this latter solution is always unstable to the field rolling coherently to its true vacuum, we show that there is an additional instability to wall formation if the scalar field does not couple too strongly to gravity. Using the $\lambda \Phi^4$ and sine-Gordon models as illustrative examples, we investigate the phase space of the gravitating domain wall in detail numerically, following the solutions from weak to strong gravity. We find excellent agreement with the analytic work. Then, we analyse the domain wall in the presence of a cosmological constant finding again the two kinds of solutions, wall and de Sitter, even in the presence of a negative cosmological constant.Comment: 20 pages revtex, epsfig, references added, some conclusions altere

On the Thermodynamic Geometry and Critical Phenomena of AdS Black Holes

In this paper, we study various aspects of the equilibrium thermodynamic state space geometry of AdS black holes. We first examine the Reissner-Nordstrom-AdS (RN-AdS) and the Kerr-AdS black holes. In this context, the state space scalar curvature of these black holes is analysed in various regions of their thermodynamic parameter space. This provides important new insights into the structure and significance of the scalar curvature. We further investigate critical phenomena, and the behaviour of the scalar curvature near criticality, for KN-AdS black holes in two mixed ensembles, introduced and elucidated in our earlier work arXiv:1002.2538 [hep-th]. The critical exponents are identical to those in the RN-AdS and Kerr-AdS cases in the canonical ensemble. This suggests an universality in the scaling behaviour near critical points of AdS black holes. Our results further highlight qualitative differences in the thermodynamic state space geometry for electric charge and angular momentum fluctuations of these.Comment: 1 + 37 Pages, LaTeX, includes 31 figures. A figure and a clarification added

Relativistic Stars in Randall-Sundrum Gravity

The non-linear behaviour of Randall-Sundrum gravity with one brane is examined. Due to the non-compact extra dimension, the perturbation spectrum has no mass gap, and the long wavelength effective theory is only understood perturbatively. The full 5-dimensional Einstein equations are solved numerically for static, spherically symmetric matter localized on the brane, yielding regular geometries in the bulk with axial symmetry. An elliptic relaxation method is used, allowing both the brane and asymptotic radiation boundary conditions to be simultaneously imposed. The same data that specifies stars in 4-dimensional gravity, uniquely constructs a 5-dimensional solution. The algorithm performs best for small stars (radius less than the AdS length) yielding highly non-linear solutions. An upper mass limit is observed for these small stars, and the geometry shows no global pathologies. The geometric perturbation is shown to remain localized near the brane at high densities, the confinement interestingly increasing for both small and large stars as the upper mass limit is approached. Furthermore, the static spatial sections are found to be approximately conformal to those of AdS. We show that the intrinsic geometry of large stars, with radius several times the AdS length, is described by 4-dimensional General Relativity far past the perturbative regime. This indicates that the non-linear long wavelength effective action remains local, even though the perturbation spectrum has no mass gap. The implication is that Randall-Sundrum gravity, with localized brane matter, reproduces relativistic astrophysical solutions, such as neutron stars and massive black holes, consistent with observation.Comment: 57 pages, 26 (colour) figures; minor typos corrected, references added and introduction condense

Gravitational and electromagnetic fields near an anti-de Sitter-like infinity

We analyze asymptotic structure of general gravitational and electromagnetic fields near an anti-de Sitter-like conformal infinity. Dependence of the radiative component of the fields on a null direction along which the infinity is approached is obtained. The directional pattern of outgoing and ingoing radiation, which supplements standard peeling property, is determined by the algebraic (Petrov) type of the fields and also by orientation of principal null directions with respect to the timelike infinity. The dependence on the orientation is a new feature if compared to spacelike infinity.Comment: 4 pages, 2 figure