The extended Conformal Einstein field equations with matter: the Einstein-Maxwell field

A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the presence of matter it is possible to construct a conformal gauge which allows to know \emph{a priori} the location of the conformal boundary. In vacuum this gauge reduces to the so-called conformal Gaussian gauge. These ideas are applied to obtain: (i) a new proof of the stability of Einstein-Maxwell de Sitter-like spacetimes; (ii) a proof of the semi-global stability of purely radiative Einstein-Maxwell spacetimes.Comment: 29 page

Does asymptotic simplicity allow for radiation near spatial infinity?

A representation of spatial infinity based in the properties of conformal geodesics is used to obtain asymptotic expansions of the gravitational field near the region where null infinity touches spatial infinity. These expansions show that generic time symmetric initial data with an analytic conformal metric at spatial infinity will give rise to developments with a certain type of logarithmic singularities at the points where null infinity and spatial infinity meet. These logarithmic singularities produce a non-smooth null infinity. The sources of the logarithmic singularities are traced back down to the initial data. It is shown that is the parts of the initial data responsible for the non-regular behaviour of the solutions are not present, then the initial data is static to a certain order. On the basis of these results it is conjectured that the only time symmetric data sets with developments having a smooth null infinity are those which are static in a neighbourhood of infinity. This conjecture generalises a previous conjecture regarding time symmetric, conformally flat data. The relation of these conjectures to Penrose's proposal for the description of the asymptotic gravitational field of isolated bodies is discussed.Comment: 22 pages, 4 figures. Typos and grammatical mistakes corrected. Version to appear in Comm. Math. Phy

A conformal approach for the analysis of the non-linear stability of pure radiation cosmologies

The conformal Einstein equations for a tracefree (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like tracefree (radiation) perfect fluid Friedman-Lema\^{\i}tre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete.Comment: 21 page

Asymptotic simplicity and static data

The present article considers time symmetric initial data sets for the vacuum Einstein field equations which in a neighbourhood of infinity have the same massless part as that of some static initial data set. It is shown that the solutions to the regular finite initial value problem at spatial infinity for this class of initial data sets extend smoothly through the critical sets where null infinity touches spatial infinity if and only if the initial data sets coincide with static data in a neighbourhood of infinity. This result highlights the special role played by static data among the class of initial data sets for the Einstein field equations whose development gives rise to a spacetime with a smooth conformal compactification at null infinity.Comment: 25 page

A welfare analysis of the electricity transmission regulatory regime in Germany

We analyze the current regulatory regime for electricity transmission in Germany, which combines network planning with both cost-plus and revenue-cap regulations. After reviewing international experiences on transmission investment, we first make a qualitative assessment of the overall German regime. The German TSOs have in general incentives to overinvest and inefficiently inflate costs. We further develop two models to analyze the transmission planning process. In the first model there is no trade-off between transmission expansion and generation dispatch. This is a modeling set-up similar to the one actually used in the German transmission planning (Netzentwicklungsplan). A second model alternatively allows for such a trade-off, and thus represents an optimal way of transmission network planning. Simulations with the two models are carried out and compared so as to illustrate the amount of excessive transmission capacity investment and welfare losses associated with the current regime

Making the best of mixed-field orientation of polar molecules: A recipe for achieving adiabatic dynamics in an electrostatic field combined with laser pulses

We have experimentally and theoretically investigated the mixed-field orientation of rotational-state-selected OCS molecules and we achieve strong degrees of alignment and orientation. The applied moderately intense nanosecond laser pulses are long enough to adiabatically align molecules. However, in combination with a weak dc electric field, the same laser pulses result in nonadiabatic dynamics in the mixed-field orientation. These observations are fully explained by calculations employing, both, adiabatic and non-adiabatic time-dependent models.Comment: 5 pages, 4 figure

A rigidity property of asymptotically simple spacetimes arising from conformally flat data

Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through the critical sets where null infinity touches spatial infinity if and only if the initial data coincides with Schwarzschild data near infinity.Comment: 37 page

Tradable Permits

Tradable Permits – a Market-Based Allocation System for the Environment. Tradable Permits and Other Environmental Policy Instruments – Killing one Bird with two Stones. Tradable Permits – Ten Key Design Issues. Tradable Permits with Imperfect Monitoring. Emissions Trading with Greenhouse Gases in the European Union.Umweltzertifikat, Umweltökonomik, Immissionsschutz, Umweltpolitik, Klimaschutz, EU-Umweltpolitik, Wirtschaftspolitische Wirkungsanalyse, EU-Staaten, Vereinigte Staaten, Environmental economics, Emission control, Environmental policy, Climate protection, EU environmental policy, Economic policy analysis, EU countries, United States

On smoothness-asymmetric null infinities

We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past and a future null infinity of different smoothness. For simplicity, the analysis is restricted to the class of conformally flat, axially symmetric initial data sets. It is shown how the free parameters in the second fundamental form of the data can be used to satisfy certain obstructions to the smoothness of null infinity. The resulting initial data sets could be interpreted as those of some sort of (non-linearly) distorted Schwarzschild black hole. Its developments would be so that they admit a peeling future null infinity, but at the same time have a polyhomogeneous (non-peeling) past null infinity.Comment: 13 pages, 1 figur

Time asymmetric spacetimes near null and spatial infinity. I. Expansions of developments of conformally flat data

The Conformal Einstein equations and the representation of spatial infinity as a cylinder introduced by Friedrich are used to analyse the behaviour of the gravitational field near null and spatial infinity for the development of data which are asymptotically Euclidean, conformally flat and time asymmetric. Our analysis allows for initial data whose second fundamental form is more general than the one given by the standard Bowen-York Ansatz. The Conformal Einstein equations imply upon evaluation on the cylinder at spatial infinity a hierarchy of transport equations which can be used to calculate in a recursive way asymptotic expansions for the gravitational field. It is found that the the solutions to these transport equations develop logarithmic divergences at certain critical sets where null infinity meets spatial infinity. Associated to these, there is a series of quantities expressible in terms of the initial data (obstructions), which if zero, preclude the appearance of some of the logarithmic divergences. The obstructions are, in general, time asymmetric. That is, the obstructions at the intersection of future null infinity with spatial infinity are different, and do not generically imply those obtained at the intersection of past null infinity with spatial infinity. The latter allows for the possibility of having spacetimes where future and past null infinity have different degrees of smoothness. Finally, it is shown that if both sets of obstructions vanish up to a certain order, then the initial data has to be asymptotically Schwarzschildean to some degree.Comment: 32 pages. First part of a series of 2 papers. Typos correcte