Reform der Kohlepolitik als Beitrag zur Sicherung der Energieversorgung

Die Steinkohle hat seit Ende der fünfziger Jahre ihren Markt bei der Wärmeerzeugung der Industrie und der privaten Haushalte weitgehend an das Heizöl verloren. Um einen Mindestabsatz heimischer Steinkohle zu sichern, wurde der Kohlemarkt gespalten: Die Eisen- und Stahlindustrie sowie einige Abnehmer, die in bescheidenem Umfang über Importkontingente verfügen, können Steinkohle zum Weltmarktpreis einsetzen. Alle übrigen Abnehmer, darunter auch Teile der Elektrizitätswirtschaft, müssen dagegen einen fast doppelt so hohen Inlandspreis entrichten. Nach dem scharfen Anstieg der Preise für Erdöl liegt dessen Wärmepreis heute etwas höher als der für heimische Steinkohle. In größerem Umfang lohnt sich eine Substitution von ö l durch Kohle jedoch nur, wenn auf billigere Steinkohle zum Weltmarktpreis zurückgegriffen werden kann; denn große zusätzliche Mengen an heimischer Kohle können nur zu erheblich steigenden Kosten gefördert werden. Soll künftig im Zuge einer Politik des "weg vom ÜP verstärkt Steinkohle eingesetzt und der heimische Steinkohlenbergbau gleichzeitig aus versorgungspolitischen Gründen erhalten werden, so wäre es zweckmäßig, die Kohleeinfuhr völlig zu liberalisieren und das bisherige Stützungssystem vollständig durch ein System direkter Ausgleichszahlungen (Deficiency Payments) zu ersetzen. Ein System von Deficiency Payments für den gesamten Steinkohlenbergbau hätte den großen Vorteil, daß die Substitution von Ol durch Kohle nicht mehr durch Einfuhrhemmnisse und hohe Inlandspreise behindert und erschwert würde. Ober die Menge der insgesamt eingesetzten Kohle entschiede der niedrigere Weltmarktpreis. Der heimische Bergbau erhielte die Differenz zwischen den Förderkosten und dem Weltmarktpreis erstattet. Die fiskalischen Kosten, die bei der gegenwärtigen Fördermenge zusätzlich aufzubringen wären, liegen unter 1 Mrd. DM. In volkswirtschaftlicher Betrachtungsweise sind dies jedoch keine zusätzlichen Kosten, da bislang die inländischen Kohleabnehmer den gegenüber dem Weltmarktpreis höheren Binnenpreis für Steinkohle zahlen müssen. Das Mitte dieses Jahres vereinbarte "Kohlepaket" kann den energiewirtschaftlichen Erfordernissen nicht voll gerecht werden. Die vorgesehenen Importkontingente können das Potential für eine Substitution von Heizöl durch Steinkohle auf dem Wärmemarkt der Industrie und der Privathaushalte nur zu Bruchteilen ausschöpfen. Darüber hinaus besteht Anlaß zu der Sorge, daß die außenwirtschaftlichen Reglementierungen und die damit verbundenen Zuteilungskriterien eine volle Nutzung selbst dieser Einfuhrkontingente verhindern werden. Ohne eine umfassende Liberalisierung der Steinkohleneinfuhr und eine Umgestaltung des Stürzungssystems wird die Energiepolitik in der Bundesrepublik den Anteil des Erdöls an der Energieversorgung nicht in dem angestrebten Maß vermindern können

Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

We survey our recently proposed method for constructing biholomorphic invariants of quasihomogeneous isolated hypersurface singularities and, more generally, invariants of graded Artinian Gorenstein algebras. The method utilizes certain polynomials associated to such algebras, called nil-polynomials, and we compare them with two other classes of polynomials that have also been used to produce invariants.Comment: 13 page

Gravitational Waves: Just Plane Symmetry

We present some remarkable properties of the symmetry group for gravitational plane waves. Our main observation is that metrics with plane wave symmetry satisfy every system of generally covariant vacuum field equations except the Einstein equations. The proof uses the homothety admitted by metrics with plane wave symmetry and the scaling behavior of generally covariant field equations. We also discuss a mini-superspace description of spacetimes with plane wave symmetry.Comment: 10 pages, TeX, uses IOP style file

Killing Vector Fields in Three Dimensions: A Method to Solve Massive Gravity Field Equations

Killing vector fields in three dimensions play important role in the construction of the related spacetime geometry. In this work we show that when a three dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the ricci tensor. Using this property we give ways of solving the field equations of Topologically Massive Gravity (TMG) and New Massive Gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three dimensional symmetric tensors of the geometry, the ricci and einstein tensors, their covariant derivatives at all orders, their products of all orders are completely determined by the Killing vector field and the metric. Hence the corresponding three dimensional metrics are strong candidates of solving all higher derivative gravitational field equations in three dimensions.Comment: 25 pages, some changes made and some references added, to be published in Classical and Quantum Gravit

The Principle of Symmetric Criticality in General Relativity

We consider a version of Palais' Principle of Symmetric Criticality (PSC) that is applicable to the Lie symmetry reduction of Lagrangian field theories. PSC asserts that, given a group action, for any group-invariant Lagrangian the equations obtained by restriction of Euler-Lagrange equations to group-invariant fields are equivalent to the Euler-Lagrange equations of a canonically defined, symmetry-reduced Lagrangian. We investigate the validity of PSC for local gravitational theories built from a metric. It is shown that there are two independent conditions which must be satisfied for PSC to be valid. One of these conditions, obtained previously in the context of transverse symmetry group actions, provides a generalization of the well-known unimodularity condition that arises in spatially homogeneous cosmological models. The other condition seems to be new. The conditions that determine the validity of PSC are equivalent to pointwise conditions on the group action alone. These results are illustrated with a variety of examples from general relativity. It is straightforward to generalize all of our results to any relativistic field theory.Comment: 46 pages, Plain TeX, references added in revised versio

Twistor geometry of a pair of second order ODEs

We discuss the twistor correspondence between path geometries in three dimensions with vanishing Wilczynski invariants and anti-self-dual conformal structures of signature $(2, 2)$. We show how to reconstruct a system of ODEs with vanishing invariants for a given conformal structure, highlighting the Ricci-flat case in particular. Using this framework, we give a new derivation of the Wilczynski invariants for a system of ODEs whose solution space is endowed with a conformal structure. We explain how to reconstruct the conformal structure directly from the integral curves, and present new examples of systems of ODEs with point symmetry algebra of dimension four and greater which give rise to anti--self--dual structures with conformal symmetry algebra of the same dimension. Some of these examples are $(2, 2)$ analogues of plane wave space--times in General Relativity. Finally we discuss a variational principle for twistor curves arising from the Finsler structures with scalar flag curvature.Comment: Final version to appear in the Communications in Mathematical Physics. The procedure of recovering a system of torsion-fee ODEs from the heavenly equation has been clarified. The proof of Prop 7.1 has been expanded. Dedicated to Mike Eastwood on the occasion of his 60th birthda

Semiclassical States in Quantum Cosmology: Bianchi I Coherent States

We study coherent states for Bianchi type I cosmological models, as examples of semiclassical states for time-reparametrization invariant systems. This simple model allows us to study explicitly the relationship between exact semiclassical states in the kinematical Hilbert space and corresponding ones in the physical Hilbert space, which we construct here using the group averaging technique. We find that it is possible to construct good semiclassical physical states by such a procedure in this model; we also discuss the sense in which the original kinematical states may be a good approximation to the physical ones, and the situations in which this is the case. In addition, these models can be deparametrized in a natural way, and we study the effect of time evolution on an "intrinsic" coherent state in the reduced phase space, in order to estimate the time for this state to spread significantly.Comment: 21 pages, 1 figure; Version to be published in CQG; The discussion has been slightly reorganized, two references added, and some typos correcte

Significance Tests for Periodogram Peaks

We discuss methods currently in use for determining the significance of peaks in the periodograms of time series. We discuss some general methods for constructing significance tests, false alarm probability functions, and the role played in these by independent random variables and by empirical and theoretical cumulative distribution functions. We also discuss the concept of "independent frequencies" in periodogram analysis. We propose a practical method for estimating the significance of periodogram peaks, applicable to all time series irrespective of the spacing of the data. This method, based on Monte Carlo simulations, produces significance tests that are tailor-made for any given astronomical time series.Comment: 22 pages, 11 Encapsulated Postscript figures, AAS LaTeX v5.2 Submitted to Ap

Cosmology, cohomology, and compactification

Ashtekar and Samuel have shown that Bianchi cosmological models with compact spatial sections must be of Bianchi class A. Motivated by general results on the symmetry reduction of variational principles, we show how to extend the Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as defined, e.g., by Singer and Thurston. In particular, it is shown that any m-dimensional homogeneous space G/K admitting a G-invariant volume form will allow a compact discrete quotient only if the Lie algebra cohomology of G relative to K is non-vanishing at degree m.Comment: 6 pages, LaTe