Conformal symmetry transformations and nonlinear Maxwell equations

We make use of the conformal compactification of Minkowski spacetime $M^{\#}$ to explore a way of describing general, nonlinear Maxwell fields with conformal symmetry. We distinguish the inverse Minkowski spacetime $[M^{\#}]^{-1}$ obtained via conformal inversion, so as to discuss a doubled compactified spacetime on which Maxwell fields may be defined. Identifying $M^{\#}$ with the projective light cone in $(4+2)$-dimensional spacetime, we write two independent conformal-invariant functionals of the $6$-dimensional Maxwellian field strength tensors -- one bilinear, the other trilinear in the field strengths -- which are to enter general nonlinear constitutive equations. We also make some remarks regarding the dimensional reduction procedure as we consider its generalization from linear to general nonlinear theories.Comment: 12 pages, Based on a talk by the first author at the International Conference in Mathematics in honor of Prof. M. Norbert Hounkonnou (October 29-30, 2016, Cotonou, Benin). To be published in the Proceedings, Springer 201

Evidence for an active fault below the northwestern Alpine foreland of Switzerland

This study is devoted to the analysis of a prominent concentration of earthquakes whose epicenters delineate an active 20-30 km long N—S trending tectonic feature near the town of Fribourg, in the Molasse Basin of western Switzerland. This feature coincides with the possible southward continuation of the NNE—SSW trending Rhine Graben located approximately 80 km further north. In addition these epicenters are located in the vicinity of the Fribourg Syncline and the Alterswil Culmination, whose structural axes are oriented N—S in this area, instead of being aligned with the predominant regional NE—SW structural trend. Most of the earthquakes belong to one of three series of events that occurred over a time span of 2-4 months in 1987, 1995 and 1999. They include four events with magnitudes between 3 and 4 and one with a magnitude of 4.3. Focal depths, constrained by modelling sPMP-PMP traveltime differences with synthetic seismograms, are around 2 km, which places these events in the sedimentary cover. Fault plane solutions correspond to almost pure strike-slip mechanisms with nearly N—S and E—W oriented nodal planes. High-precision relative locations of individual events within the different earthquake clusters as well as of the relative locations of the clusters to each other show that these earthquakes are associated with left lateral motion along a N—S trending fault system. Deep reaching large scale flower structures in the Mesozoic and Tertiary overburden are observed on interpreted seismic profiles, close to the hypocenters. The unusual N—S trend of the Fribourg Syncline can be attributed to movements along these faults during Oligocene and Miocene times. Also magnetic data support the assumption of a N—S striking fault system in the Fribourg area, possibly related to a Permo-Carboniferous trough. Though the direct link between the fault traces in the overburden and the active fault system at depth could not be established in this study, their similar deformational style and their vicinity suggest that they are related. The total length of the inferred fault carries the potential of a magnitude 6 earthquake and thus constitutes a significant source of seismic hazar

Building blocks of a black hole

What is the nature of the energy spectrum of a black hole ? The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As stressed long ago by by Mukhanov, such eigenvalues must be exponentially degenerate with respect to the area quantum number if one is to understand black hole entropy as reflecting degeneracy of the observable states. Here we construct the black hole states by means of a pair of "creation operators" subject to a particular simple algebra, a slight generalization of that for the harmonic oscillator. We then prove rigorously that the n-th area eigenvalue is exactly 2 raised to the n-fold degenerate. Thus black hole entropy qua logarithm of the number of states for fixed horizon area comes out proportional to that area.Comment: PhysRevTeX, 14 page

Symmetry based determination of space-time functions in nonequilibrium growth processes

We study the space-time correlation and response functions in nonequilibrium growth processes described by linear stochastic Langevin equations. Exploiting exclusively the existence of space and time dependent symmetries of the noiseless part of these equations, we derive expressions for the universal scaling functions of two-time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion. The usefulness of the space-time functions is illustrated through the investigation of two atomistic growth models, the Family model and the restricted Family model, which are shown to belong to a unique universality class in 1+1 and in 2+1 space dimensions. This corrects earlier studies which claimed that in 2+1 dimensions the two models belong to different universality classes.Comment: 18 pages, three figures included, submitted to Phys. Rev.

The Blackbody Radiation Spectrum Follows from Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell's equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero-temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics.Comment: 21 page

A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole

We consider a Hamiltonian quantum theory of spherically symmetric, asymptotically flat electrovacuum spacetimes. The physical phase space of such spacetimes is spanned by the mass and the charge parameters $M$ and $Q$ of the Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical momenta. In this four-dimensional phase space, we perform a canonical transformation such that the resulting configuration variables describe the dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner. The classical Hamiltonian written in terms of these variables and their conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian operator, and an eigenvalue equation for the ADM mass of the hole, from the point of view of a distant observer at rest, is obtained. Our eigenvalue equation implies that the ADM mass and the electric charge spectra of the hole are discrete, and the mass spectrum is bounded below. Moreover, the spectrum of the quantity $M^2-Q^2$ is strictly positive when an appropriate self-adjoint extension is chosen. The WKB analysis yields the result that the large eigenvalues of the quantity $\sqrt{M^2-Q^2}$ are of the form $\sqrt{2n}$, where $n$ is an integer. It turns out that this result is closely related to Bekenstein's proposal on the discrete horizon area spectrum of black holes.Comment: 37 pages, Plain TeX, no figure

Central charges and boundary fields for two dimensional dilatonic black holes

In this paper we first show that within the Hamiltonian description of general relativity, the central charge of a near horizon asymptotic symmetry group is zero, and therefore that the entropy of the system cannot be estimated using Cardy's formula. This is done by mapping a static black hole to a two dimensional space. We explain how such a charge can only appear to a static observer who chooses to stay permanently outside the black hole. Then an alternative argument is given for the presence of a universal central charge. Finally we suggest an effective quantum theory on the horizon that is compatible with the thermodynamics behaviour of the black hole.Comment: 16 pages, no figures, LaTex 2e, references adde

S3 guidelines for intensive care in cardiac surgery patients: hemodynamic monitoring and cardiocirculary system

Hemodynamic monitoring and adequate volume-therapy, as well as the treatment with positive inotropic drugs and vasopressors are the basic principles of the postoperative intensive care treatment of patient after cardiothoracic surgery. The goal of these S3 guidelines is to evaluate the recommendations in regard to evidence based medicine and to define therapy goals for monitoring and therapy. In context with the clinical situation the evaluation of the different hemodynamic parameters allows the development of a therapeutic concept and the definition of goal criteria to evaluate the effect of treatment

Conformal linear gravity in de Sitter space II

From the group theoretical point of view, it is proved that the theory of linear conformal gravity should be written in terms of a tensor field of rank-3 and mixed symmetry [Binegar, et al, Phys. Rev. D 27, (1983) 2249]. We obtained such a field equation in de Sitter space [Takook, et al, J. Math. Phys. 51, (2010) 032503]. In this paper, a proper solution to this equation is obtained as a product of a generalized polarization tensor and a massless scalar field and then the conformally invariant two-point function is calculated. This two-point function is de Sitter invariant and free of any pathological large-distance behavior.Comment: 16 pages, no figure, published versio

Area spectrum of the Schwarzschild black hole

We consider a Hamiltonian theory of spherically symmetric vacuum Einstein gravity under Kruskal-like boundary conditions in variables associated with the Einstein-Rosen wormhole throat. The configuration variable in the reduced classical theory is the radius of the throat, in a foliation that is frozen at the left hand side infinity but asymptotically Minkowski at the right hand side infinity, and such that the proper time at the throat agrees with the right hand side Minkowski time. The classical Hamiltonian is numerically equal to the Schwarzschild mass. Within a class of Hamiltonian quantizations, we show that the spectrum of the Hamiltonian operator is discrete and bounded below, and can be made positive definite. The large eigenvalues behave asymptotically as~$\sqrt{2k}$, where $k$ is an integer. The resulting area spectrum agrees with that proposed by Bekenstein and others. Analogous results hold in the presence of a negative cosmological constant and electric charge. The classical input that led to the quantum results is discussed.Comment: 30 pages, REVTeX v3.0. (Minor additions, several added references.