Distorted cyclotron line profile in Cep X-4 as observed by NuSTAR

We present spectral analysis of NuSTAR and Swift observations of Cep X-4 during its outburst in 2014. We observed the source once during the peak of the outburst and once during the decay, finding good agreement in the spectral shape between the observations. We describe the continuum using a powerlaw with a Fermi-Dirac cutoff at high energies. Cep X-4 has a very strong cyclotron resonant scattering feature (CRSF) around 30 keV. A simple absorption-like line with a Gaussian optical depth or a pseudo-Lorentzian profile both fail to describe the shape of the CRSF accurately, leaving significant deviations at the red side of the line. We characterize this asymmetry with a second absorption feature around 19 keV. The line energy of the CRSF, which is not influenced by the addition of this feature, shows a small but significant positive luminosity dependence. With luminosities between (1-6)e36 erg/s, Cep X-4 is below the theoretical limit where such a correlation is expected. This behavior is similar to Vela X-1 and we discuss parallels between the two systems.Comment: 6 pages, 4 figure, accepted for publication in ApJ letter

The Tulczyjew triple for classical fields

The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of variational calculus, we construct the Tulczyjew triple for first-order Field Theory. The important feature of our approach is that we do not postulate {\it ad hoc} the ingredients of the theory, but obtain them as unavoidable consequences of the variational calculus. This picture of Field Theory is covariant and complete, containing not only the Lagrangian formalism and Euler-Lagrange equations but also the phase space, the phase dynamics and the Hamiltonian formalism. Since the configuration space turns out to be an affine bundle, we have to use affine geometry, in particular the notion of the affine duality. In our formulation, the two maps $\alpha$ and $\beta$ which constitute the Tulczyjew triple are morphisms of double structures of affine-vector bundles. We discuss also the Legendre transformation, i.e. the transition between the Lagrangian and the Hamiltonian formulation of the first-order field theor

A Renormalization Group Approach to Relativistic Cosmology

We discuss the averaging hypothesis tacitly assumed in standard cosmology. Our approach is implemented in a "3+1" formalism and invokes the coarse graining arguments, provided and supported by the real-space Renormalization Group (RG) methods. Block variables are introduced and the recursion relations written down explicitly enabling us to characterize the corresponding RG flow. To leading order, the RG flow is provided by the Ricci-Hamilton equations studied in connection with the geometry of three-manifolds. The properties of the Ricci-Hamilton flow make it possible to study a critical behaviour of cosmological models. This criticality is discussed and it is argued that it may be related to the formation of sheet-like structures in the universe. We provide an explicit expression for the renormalized Hubble constant and for the scale dependence of the matter distribution. It is shown that the Hubble constant is affected by non-trivial scale dependent shear terms, while the spatial anisotropy of the metric influences significantly the scale-dependence of the matter distribution.Comment: 57 pages, LaTeX, 15 pictures available on request from the Author

Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis

Anisotropic 'hairs' in string cosmology

In this letter we investigate whether the isotropy problem is naturally solved in inflationary cosmologies inspired by string theory, so called pre-big-bang cosmologies. We find that, in contrast to what happens in the more common 'potential inflation' models, initial anisotropies do not decay during pre-big-bang inflation.Comment: 4 pages, 1 figur

On multi-graviton and multi-gravitino gauge theories

This paper studies nonlinear deformations of the linear gauge theory of any number of spin-2 and spin-3/2 fields with general formal multiplication rules in place of standard Grassmann rules for manipulating the fields, in four spacetime dimensions. General possibilities for multiplication rules and coupling constants are simultaneously accommodated by regarding the set of fields equivalently as a single algebra-valued spin-2 field and single algebra-valued spin-3/2 field, where the underlying algebra is factorized into a field-coupling part and an internal multiplication part. The condition that there exist a gauge invariant Lagrangian (to within a divergence) for these algebra-valued fields is used to derive determining equations whose solutions give all allowed deformation terms, yielding nonlinear field equations and nonabelian gauge symmetries, together with all allowed formal multiplication rules as needed in the Lagrangian for demonstration of invariance under the gauge symmetries and for derivation of the field equations. In the case of spin-2 fields alone, the main result of this analysis is that all deformations (without any higher derivatives than appear in the linear theory) are equivalent to an algebra-valued Einstein gravity theory. By a systematic examination of factorizations of the algebra, a novel type of nonlinear gauge theory of two or more spin-2 fields is found, where the coupling for the fields is based on structure constants of an anticommutative, anti-associative algebra, and with formal multiplication rules that make the fields anticommuting (while products obey anti-associativity). Supersymmetric extensions of these results are obtained in the more general case when spin-3/2 fields are included.Comment: 33 pages (latex

Event horizons and apparent horizons in spherically symmetric geometries

Spherical configurations that are very massive must be surrounded by apparent horizons. These in turn, when placed outside a collapsing body, must propagate outward with a velocity equal to the velocity of radially outgoing photons. That proves, within the framework of (1+3) formalism and without resorting to the Birkhoff theorem, that apparent horizons coincide with event horizons.Comment: 5 pages, plainte

The Singularity Problem for Space-Times with Torsion

The problem of a rigorous theory of singularities in space-times with torsion is addressed. We define geodesics as curves whose tangent vector moves by parallel transport. This is different from what other authors have done, because their definition of geodesics only involves the Christoffel connection, though studying theories with torsion. We propose a preliminary definition of singularities which is based on timelike or null geodesic incompleteness, even though for theories with torsion the paths of particles are not geodesics. The study of the geodesic equation for cosmological models with torsion shows that the definition has a physical relevance. It can also be motivated, as done in the literature, remarking that the causal structure of a space-time with torsion does not get changed with respect to general relativity. We then prove how to extend Hawking's singularity theorem without causality assumptions to the space-time of the ECSK theory. This is achieved studying the generalized Raychaudhuri equation in the ECSK theory, the conditions for the existence of conjugate points and properties of maximal timelike geodesics. Hawking's theorem can be generalized, provided the torsion tensor obeys some conditions. Thus our result can also be interpreted as a no-singularity theorem if these additional conditions are not satisfied. In other words, it turns out that the occurrence of singularities in closed cosmological models based on the ECSK theory is less generic than in general relativity. Our work is to be compared with previous papers in the literature. There are some relevant differences, because we rely on a different definition of geodesics, we keep the field equations of the ECSK theory in their original form rather than casting them in a form similar to general relativity with a modified energy momentum tensor,Comment: 17 pages, plain-tex, published in Nuovo Cimento B, volume 105, pages 75-90, year 199

Ricci flow and black holes

Gradient flow in a potential energy (or Euclidean action) landscape provides a natural set of paths connecting different saddle points. We apply this method to General Relativity, where gradient flow is Ricci flow, and focus on the example of 4-dimensional Euclidean gravity with boundary S^1 x S^2, representing the canonical ensemble for gravity in a box. At high temperature the action has three saddle points: hot flat space and a large and small black hole. Adding a time direction, these also give static 5-dimensional Kaluza-Klein solutions, whose potential energy equals the 4-dimensional action. The small black hole has a Gross-Perry-Yaffe-type negative mode, and is therefore unstable under Ricci flow. We numerically simulate the two flows seeded by this mode, finding that they lead to the large black hole and to hot flat space respectively, in the latter case via a topology-changing singularity. In the context of string theory these flows are world-sheet renormalization group trajectories. We also use them to construct a novel free energy diagram for the canonical ensemble.Comment: 31 pages, 14 color figures. v2: Discussion of the metric on the space of metrics corrected and expanded, references adde

Time and "angular" dependent backgrounds from stationary axisymmetric solutions

Backgrounds depending on time and on "angular" variable, namely polarized and unpolarized $S^1 \times S^2$ Gowdy models, are generated as the sector inside the horizons of the manifold corresponding to axisymmetric solutions. As is known, an analytical continuation of ordinary $D$-branes, $iD$-branes allows one to find $S$-brane solutions. Simple models have been constructed by means of analytic continuation of the Schwarzchild and the Kerr metrics. The possibility of studying the $i$-Gowdy models obtained here is outlined with an eye toward seeing if they could represent some kind of generalized $S$-branes depending not only on time but also on an ``angular'' variable.Comment: 24 pages, 5 figures, corrected typos, references adde