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

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

Incompressible fluid inside an astrophysical black hole?

It is argued that under natural hypothesis the Fermions inside a black hole formed after the collapse of a neutron star could form a non compressible fluid (well before reaching the Planck scale) leading to some features of integer Quantum Hall Effect. The relations with black hole entropy are analyzed. Insights coming from Quantum Hall Effect are used to analyze the coupling with Einstein equations. Connections with some cosmological scenarios and with higher dimensional Quantum Hall Effect are shortly pointed out.Comment: 30 pages, 2 figures. Accepted for publication on Physical Review D: references added, typos corrected, test polishe

Quantum Effects in Black Hole Interiors

The Weyl curvature inside a black hole formed in a generic collapse grows, classically without bound, near to the inner horizon, due to partial absorption and blueshifting of the radiative tail of the collapse. Using a spherical model, we examine how this growth is modified by quantum effects of conformally coupled massless fields.Comment: 13 pages, 1 figure (not included), RevTe

Low energy effective gravitational equations on a Gauss-Bonnet brane

We present effective gravitational equations at low energies in a $Z_2$-symmetric braneworld with the Gauss-Bonnet term. Our derivation is based on the geometrical projection approach, and we solve iteratively the bulk geometry using the gradient expansion scheme. Although the original field equations are quite complicated due to the presence of the Gauss-Bonnet term, our final result clearly has the form of the Einstein equations plus correction terms, which is simple enough to handle. As an application, we consider homogeneous and isotropic cosmology on the brane. We also comment on the holographic interpretation of bulk gravity in the Gauss-Bonnet braneworld.Comment: 10 pages, v2: minor clarification

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

HCN versus HCO+ as dense molecular gas mass tracer in Luminous Infrared Galaxies

It has been recently argued that the HCN J=1--0 line emission may not be an unbiased tracer of dense molecular gas (\rm n\ga 10^4 cm^{-3}) in Luminous Infrared Galaxies (LIRGs: $\rm L_{FIR}> 10^{11} L_{\odot}$) and HCO$^+$ J=1--0 may constitute a better tracer instead (Graci\'a-Carpio et al. 2006), casting doubt into earlier claims supporting the former as a good tracer of such gas (Gao & Solomon 2004; Wu et al. 2006). In this paper new sensitive HCN J=4--3 observations of four such galaxies are presented, revealing a surprisingly wide excitation range for their dense gas phase that may render the J=1--0 transition from either species a poor proxy of its mass. Moreover the well-known sensitivity of the HCO$^+$ abundance on the ionization degree of the molecular gas (an important issue omitted from the ongoing discussion about the relative merits of HCN and HCO$^+$ as dense gas tracers) may severely reduce the HCO$^+$ abundance in the star-forming and highly turbulent molecular gas found in LIRGs, while HCN remains abundant. This may result to the decreasing HCO$^+$/HCN J=1--0 line ratio with increasing IR luminosity found in LIRGs, and casts doubts on the HCO$^+$ rather than the HCN as a good dense molecular gas tracer. Multi-transition observations of both molecules are needed to identify the best such tracer, its relation to ongoing star formation, and constrain what may be a considerable range of dense gas properties in such galaxies.Comment: 16 pages, 4 figures, Accepted for publication in the Astrophysical Journa

Unified Models of Inflation and Quintessence

We apply an extended version of the method developed in reference Int.J.Mod.Phys.D5(1996)71, to derive exact cosmological (flat) Friedmann-Robertson-Walker solutions in RS2 brane models with a perfect fluid of ordinary matter plus a scalar field fluid trapped on the brane. We found new exact solutions, that can serve to unify inflation and quintessence in a common theoretical framework.Comment: 8 pages, no figure