A cluster expansion approach to renormalization group transformations

The renormalization group (RG) approach is largely responsible for the considerable success which has been achieved in developing a quantitative theory of phase transitions. This work treats the rigorous definition of the RG map for classical Ising-type lattice systems in the infinite volume limit at high temperature. A cluster expansion is used to justify the existence of the partial derivatives of the renormalized interaction with respect to the original interaction. This expansion is derived from the formal expressions, but it is itself well-defined and convergent. Suppose in addition that the original interaction is finite-range and translation-invariant. We will show that the matrix of partial derivatives in this case displays an approximate band property. This in turn gives an upper bound for the RG linearization.Comment: 13 page

Higher-Dimensional Bulk Wormholes and their Manifestations in Brane Worlds

There is nothing to prevent a higher-dimensional anti-de Sitter bulk spacetime from containing various other branes in addition to hosting our universe, presumed to be a positive-tension 3-brane. In particular, it could contain closed, microscopic branes that form the boundary surfaces of void bubbles and thus violate the null energy condition in the bulk. The possible existence of such micro branes can be investigated by considering the properties of the ground state of a pseudo-Wheeler-DeWitt equation describing brane quantum dynamics in minisuperspace. If they exist, a concentration of these micro branes could act as a fluid of exotic matter able to support macroscopic wormholes connecting otherwise distant regions of the bulk. Were the brane constituting our universe to expand into a region of the bulk containing such higher-dimensional macroscopic wormholes, they would likely manifest themselves in our brane as wormholes of normal dimensionality, whose spontaneous appearance and general dynamics would seem inexplicably peculiar. This encounter could also result in the formation of baby universes of a particular type.Comment: 21 pages, 1 figur

Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory

We develop a Hamiltonian formalism of brane-world gravity, which singles out two preferred, mutually orthogonal directions. One is a unit twist-free field of spatial vectors with integral lines intersecting perpendicularly the brane. The other is a temporal vector field with respect to which we perform the Arnowitt-Deser-Misner decomposition of the Einstein-Hilbert Lagrangian. The gravitational variables arise from the projections of the spatial metric and their canonically conjugated momenta as tensorial, vectorial and scalar quantities defined on the family of hypersurfaces containing the brane. They represent the gravitons, a gravi-photon and a gravi-scalar, respectively. From the action we derive the canonical evolution equations and the constraints for these gravitational degrees of freedom both on the brane and outside it. By integrating across the brane, the dynamics also generates the tensorial and scalar projection of the Lanczos equation. The vectorial projection of the Lanczos equation arises in a similar way from the diffeomorphism constraint. Both the graviton and the gravi-scalar are continuous across the brane, however the momentum of the gravi-vector has a jump, related to the energy transport (heat flow) on the brane.Comment: 13 page

Thermodynamic of Distorted Reissner-Nordstr\"om Black Holes in Five-dimensions

In this paper, we study mechanics and thermodynamics of distorted, five-dimensional, electrically charged (non-extremal) black holes on the example of a static and "axisymmetric" black hole distorted by external, electrically neutral matter. Such a black hole is represented by the derived here solution of the Einstein-Maxwell equations which admits an $\mathbb{R}^1\times U(1)\times U(1)$ isometry group. We study the properties of this distorted black hole.Comment: 7 pages, submitted for the proceedings of the First Karl Schwarzschild Meeting (Frankfurt, 2013

Deep VLT infrared observations of X-ray Dim Isolated Neutron Stars

X-ray observations have unveiled the existence of a family of radio-quiet Isolated Neutron Stars whose X-ray emission is purely thermal, hence dubbed X-ray Dim Isolated Neutron Stars (XDINSs). While optical observations have allowed to relate the thermal emission to the neutron star cooling and to build the neutron star surface thermal map, IR observations are critical to pinpoint a spectral turnover produced by a so far unseen magnetospheric component, or by the presence of a fallback disk. The detection of such a turnover can provide further evidence of a link between this class of isolated neutron stars and the magnetars, which show a distinctive spectral flattening in the IR. Here we present the deepest IR observations ever of five XDINSs, which we use to constrain a spectral turnover in the IR and the presence of a fallback disk. The data are obtained using the ISAAC instrument at the VLT. For none of our targets it was possible to identify the IR counterpart down to limiting magnitudes H = 21.5 - 22.9. Although these limits are the deepest ever obtained for neutron stars of this class, they are not deep enough to rule out the existence and the nature of a possible spectral flattening in the IR. We also derive, by using disk models, the upper limits on the mass inflow rate in a fallback disk. We find the existence of a putative fallback disk consistent (although not confirmed) with our observations.Comment: 6 pages, 2 figures, accepted by A&A on 26-06-200

Gravitational collapse and evolution of holographic black holes

Gravitational collapse is analyzed in the Brane-World by arguing that regularity of five-dimensional geodesics require that stars on the brane have an atmosphere. For the simple case of a spherically symmetric cloud of non-dissipating dust, conditions are found for which the collapsing star evaporates and approaches the Hawking behavior as the (apparent) horizon is being formed. The effective energy of the star vanishes at a finite radius and the star afterwards re-expands and "anti-evaporates". Israel junction conditions across the brane (holographically related to the matter trace anomaly) and the projection of the Weyl tensor on the brane (holographically interpreted as the quantum back-reaction on the brane metric) contribute to the total energy as, respectively, an "anti-evaporation" and an "evaporation" term.Comment: 6 pages; Talk given at QG05, Cala Gonone (Italy), September 200

Junction conditions in General Relativity with spin sources

The junction conditions for General Relativity in the presence of domain walls with intrinsic spin are derived in three and higher dimensions. A stress tensor and a spin current can be defined just by requiring the existence of a well defined volume element instead of an induced metric, so as to allow for generic torsion sources. In general, when the torsion is localized on the domain wall, it is necessary to relax the continuity of the tangential components of the vielbein. In fact it is found that the spin current is proportional to the jump in the vielbein and the stress-energy tensor is proportional to the jump in the spin connection. The consistency of the junction conditions implies a constraint between the direction of flow of energy and the orientation of the spin. As an application, we derive the circularly symmetric solutions for both the rotating string with tension and the spinning dust string in three dimensions. The rotating string with tension generates a rotating truncated cone outside and a flat space-time with inevitable frame dragging inside. In the case of a string made of spinning dust, in opposition to the previous case no frame dragging is present inside, so that in this sense, the dragging effect can be "shielded" by considering spinning instead of rotating sources. Both solutions are consistently lifted as cylinders in the four-dimensional case.Comment: 24 pages, no figures, CECS style. References added and misprints corrected. Published Versio

Inflation from IIB Superstrings with Fluxes

We study the conditions needed to have an early epoch of inflationary expansion with a potential coming from IIB superstring theory with fluxes involving two moduli fields. The phenomenology of this potential is different from the usual hybrid inflation scenario and we analize the possibility that the system of field equations undergo a period of inflation in three different regimes with the dynamics modified by a Randall-Sundrum II term in the Friedmann equation. We find that the system can produce inflation and due to the modification of the dynamics, a period of accelerated contraction can follow or preceed this inflationary stage depending on the sign of one of the parameters of the potential. We discuss on the viability of this model in a cosmological context.Comment: 10 pages, 6 figure

The irradiated ISM of ULIRGs

The nuclei of ULIRGs harbor massive young stars, an accreting central black hole, or both. Results are presented for molecular gas that is exposed to X-rays (1-100 keV, XDRs) and far-ultraviolet radiation (6-13.6 eV, PDRs). Attention is paid to species like HCO+, HCN, HNC, OH, H2O and CO. Line ratios of HCN/HCO+ and HNC/HCN discriminate between PDRs and XDRs. Very high J (>10) CO lines, observable with HIFI/Herschel, discriminate very well between XDRs and PDRs. In XDRs, it is easy to produce large abundances of warm (T>100 K) H2O and OH. In PDRs, only OH is produced similarly well.Comment: 5 pages, 6 figures, to appear in: IAU Symposium 242 Astrophysical Masers and their Environment

[CII] 158μ\mum and [NII] 205μ\mum emission from IC 342 - Disentangling the emission from ionized and photo-dissociated regions

Aims: We investigate how much of the [CII] emission in the nucleus of the nearby spiral galaxy IC 342 is contributed by PDRs and by the ionized gas. We examine the spatial variations of starburst/PDR activity and study the correlation of the [CII] line with the [NII] 205{\textmu}m emission line coming exclusively from the HII regions. Methods: We present small maps of [CII] and [NII] lines recently observed with the GREAT receiver on board SOFIA. In particular we present a super-resolution method to derive how unresolved, kinematically correlated structures in the beam contribute to the observed line shapes. Results: We find that the emission coming from the ionized gas shows a kinematic component in addition to the general Doppler signature of the molecular gas. We interpret this as the signature of two bi-polar lobes of ionized gas expanding out of the galactic plane. We then show how this requires an adaptation of our understanding of the geometrical structure of the nucleus of IC~342. Examining the starburst activity we find ratios $I([CII])/I(^{12}\mathrm{CO} (1-0))$ between 400 and 1800 in energy units. Applying predictions from numerical models of HII and PDR regions to derive the contribution from the ionized phase to the total [CII] emission we find that 35-90% of the observed [CII] intensity stems from the ionized gas if both phases contribute. Averaged over the central few hundred parsec we find for the [CII] contribution a HII-to-PDR ratio of 70:30. Conclusions: The ionized gas in the center of IC 342 contributes more strongly to the overall [CII] emission than is commonly observed on larger scales and than is predicted. Kinematic analysis shows that the majority of the [CII] emission is related to the strong but embedded star formation in the nuclear molecular ring and only marginally emitted from the expanding bi-polar lobes of ionized gas.Comment: 20 pages spectra available online: http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/ submitted to and accepted by A&