Mirko Schäfer

PSEUDO-COMPLEX GENERAL RELATIVITY: SCHWARZSCHILD, REISSNER–NORDSTRÖM AND KERR SOLUTIONS

The pseudo-complex General Relativity (pc-GR) is further considered. A new projection method is proposed. It is shown that the pc-GR introduces automatically terms into the system which can be interpreted as dark energy. The modified pseudo-complex Schwarzschild solution is investigated. The dark energy part is treated as a liquid and possible solutions are discussed. As a consequence, the collapse of a large stellar mass into a singularity at r = 0 is avoided and no event-horizon is formed. Thus, black holes do not exist. The resulting object can be viewed as a gray star. It contains no singularity which emphasizes, again, that it is not a black hole. The corrections implied by a charged large mass object (Reissner–Nordstrom) and a rotating gray star (Kerr) are presented. For the latter, a special solution is presented. Finally, we will consider the orbital speed of a mass in a circular orbit and suggest a possible experimental verification.

Experimental Tests of Pseudo-Complex General Relativity

Based on a recently proposed extension to General Relativity (GR), called pseudo-complex General Relativity (pc-GR), we present a selection of several tests of GR near compact massive objects. The investigated phenomena are the redshift, the orbital frequency of a test particle and the innermost stable circular orbit (ISCO) around a massive object. We observe that the redshift and orbital frequency are in general lower in pc-GR compared to Einstein’s GR. Also the orbital frequency for prograde motion now exhibits a maximum, which is not present in GR. In addition the concept of an innermost stable circular orbit does not hold in pc-GR as it arises in GR. All modifications due to pc-GR correction terms appear only at small distances (mostly below three Schwarzschild radii) and thus can only be observed by measurements in regions of strong gravity. Those and more results have been published already in [1].

Ray-tracing in pseudo-complex General Relativity

Motivated by possible observations of the black hole candidate in the center of our galaxy (Gillessen et al., 2012; Eisenhauer et al., 2011), raytracing methods are applied to both standard General Relativity (GR) and a recently proposed extension, the pseudo-complex General Relativity (pc-GR). The correction terms due to the investigated pc-GR model lead to weaker gravitational eects and slower orbital motions close to massive objects. Thus, the accretion disk, surrounding a massive object, is brighter in pc-GR than in GR. Iron K emission line profiles are also calculated as those are a good observable for regions of strong gravity. Dierences between the two theories are pointed out.

Power flow tracing in a simplified highly renewable European electricity network

The increasing transmission capacity needs in a future energy system raise the question how associated costs should be allocated to the users of a strengthened power grid. In contrast to straightforward oversimplified methods, a flow tracing based approach provides a fair and consistent nodal usage and thus cost assignment of transmission investments. This technique follows the power flow through the network and assigns the link capacity usage to the respective sources or sinks using a diffusion-like process, thus taking into account the underlying network structure and injection pattern. As a showcase, we apply power flow tracing to a simplified model of the European electricity grid with a high share of renewable wind and solar power generation, based on long-term weather and load data with an hourly temporal resolution.

Power Flow Tracing in Complex Networks

The increasing share of decentralized renewable power generation represents a challenge to the current and future energy system. Providing a geographical smoothing effect, long-range power transmission plays a key role for the system integration of these fluctuating resources. However, the build-up and operation of the necessary network infrastructure incur costs which have to be allocated to the users of the system. Flow tracing techniques, which attribute the power flow on a transmission line to the geographical location of its generation and consumption, represent a valuable tool set to design fair usage and thus cost allocation schemes for transmission investments. In this article, we introduce a general formulation of the flow tracing method and apply it to a simplified model of a highly renewable European electricity system. We review a statistical usage measure which allows to integrate network usage information for longer time series, and illustrate this measure using an analytical test case.

Discrete symmetries of chaotic strings

Chaotic strings are particular classes of coupled map lattices that can serve as models for vacuum fluctuations in stochastically quantized field theories. In this article we look at two important properties of chaotic strings, namely (i) the behaviour under discrete symmetry transformations and (ii) the loss of ergodic behaviour in certain coupling regions. We show that several of the chaotic string dynamics can be transformed into each other by simple discrete coordinate transformations. We investigate how expectation values converge in the various coupling parameter regions and single out those stable zeros of the correlation function that correspond to ergodic states with well-defined convergence properties.

Flow tracing as a tool set for the analysis of networked large-scale renewable electricity systems

Abstract The method of flow tracing follows the power flow from net-generating sources through the network to the net-consuming sinks, which allows to assign the usage of the underlying transmission infrastructure to the system participants. This article presents a reformulation that is applicable to arbitrary compositions of inflow appearing naturally in models of large-scale electricity systems with a high share of renewable power generation. We propose an application which allows to associate power flows on the grid to specific regions or generation technologies, and emphasizes the capability of this technique to disentangle the spatio-temporal patterns of physical imports and exports occurring in such systems. The analytical potential of this method is showcased for a scenario based on the IEEE 118 bus network.

Flow-based nodal cost allocation in a heterogeneous highly renewable European electricity network

Abstract For a cost efficient design of a future renewable European electricity system, the placement of renewable generation capacity will seek to exploit locations with good resource quality, that is for instance onshore wind in countries bordering the North Sea and solar PV in South European countries. Regions with less favorable renewable generation conditions benefit from this remote capacity by importing the respective electricity as power flows through the transmission grid. The resulting intricate pattern of imports and exports represents a challenge for the analysis of system costs on the level of individual countries. Using a tracing technique, we introduce flow-based nodal levelized costs of electricity (LCOE) which allow to incorporate capital and operational costs associated with the usage of generation capacity located outside the respective country under consideration. This concept and a complementary allocation of transmission infrastructure costs is applied to a simplified model of an interconnected highly renewable European electricity system. We observe that cooperation between the European countries in a heterogeneous system layout does not only reduce the system-wide LCOE, but also the flow-based nodal LCOEs for every country individually.

Allocation of nodal costs in heterogeneous highly renewable European electricity networks

We consider a simplified model of a future European electricity network with a high share of renewable generation. In a cost optimal design of such a system, most of the renewable generation capacity is placed at locations with favorable weather conditions, that is for instance onshore wind in countries bordering the North Sea and solar PV in South European countries. Countries with less favorable renewable generation conditions benefit from this capacity by importing the respective electricity as power flows through the transmission grid. Using flow tracing techniques, we disentangle the emerging pattern of imports and exports and assign shares of the distributed generation capacity in the European system to the countries which actually make use of them. This procedure yields nodal levelized costs, which incorporate both internal and external generation costs associated with the electricity consumption in a country.

New Horizons in Fundamental Physics

We present the derivation of the Yang-Mills gauge theory based on the covariant Hamiltonian representation of Noether’s theorem. As the starting point, we re-formulate our previous presentation of the canonical Hamiltonian derivation of Noether’s theorem [1]. The formalism is then applied to derive the Yang-Mills gauge theory. The Noether currents of U(1) and SU(N) gauge theories are derived from the respective infinitesimal generating functions of the pertinent symmetry transformations which maintain the form of the Hamiltonian.This volume presents the state-of-the-art in selected topics across modern nuclear physics, covering fields of central importance to research and illustrating their connection to many different areas of physics. It describes recent progress in the study of superheavy and exotic nuclei, which is pushing our knowledge to ever heavier elements and neutron-richer isotopes. Extending nuclear physics to systems that are many times denser than even the core of an atomic nucleus, one enters the realm of the physics of neutron stars and possibly quark stars, a topic that is intensively investigated with many ground-based and outer-space research missions as well as numerous theoretical works. By colliding two nuclei at very high ultra-relativistic energies one can create a fireball of extremely hot matter, reminiscent of the universe very shortly after the big bang, leading to a phase of melted hadrons and free quarks and gluons, the so-called quark-gluon plasma. These studies tie up with effects of crucial importance in other fields. During the collision of heavy ions, electric fields of extreme strength are produced, potentially destabilizing the vacuum of the atomic physics system, subsequently leading to the decay of the vacuum state and the emission of positrons. In neutron stars the ultra-dense matter might support extremely high magnetic fields, far beyond anything that can be produced in the laboratory, significantly affecting the stellar properties. At very high densities general relativity predicts the stellar collapse to a black hole. However, a number of current theoretical activities, modifying Einstein’s theory, point to possible alternative scenarios, where this collapse might be avoided. These and related topics are addressed in this book in a series of highly readable chapters. In addition, the book includes fundamental analyses of the practicalities involved in transiting to an electricity supply mainly based on renewable energies, investigating this scenario less from an engineering and more from a physics point of view. While the topics comprise a large scope of activities, the contributions also show an extensive overlap in the methodology and in the analytical and numerical tools involved in tackling these diverse research fields that are the forefront of modern science.