120807507
Solutions of the linearized Bach‐Einstein equation in the static spherically symmetric case
The Bach-Einstein equation linearized around Minkowski space-time is completely solved. The set of solutions depends on three parameters; a two-parameter subset of it becomes asymptotically flat. In that region the gravitational potential is of the type φ = -m/r + e exp (-r/l) m and e being small parameters. 
 
 
 
Because of the different asymptotic behaviour of both terms, it became necessary to linearize also around the Schwarzschild solution φ = -m/r. The linearized equation resulting in this case is discussed using qualitative methods. The result is that for m ≤ 2l the asymptotic behaviour is φ = -m/r + er−m/l exp (-r/l) u, and for m ≧ 2l φ = -m/r + er−2 exp (-r/l) u, where u is some bounded function; m is arbitray and e again small. Further, the relation between the solution of the linearized and the full equation is discussed. 
 
 
 
Fur eine Linearisierung um den Minkowskiraum wird die im Titel angegebene Gleichung vollstandig gelost. Es handelt sich dabei um eine 3-parametrige Loungsmenge, wobei eine 2-parametrige Teilmenge zu asymptotisch flachen Losungen fuhrt. Dabei ergibt sich ein Gravitationspotential der Gestalt φ = -m/r + e exp (-r/l). 
 
 
 
Wegen des unterschiedlichen asymptotischen Verhaltens der beiden Summanden macht sich auch eine Linearisierung um die Schwarzschild-Losung (φ = -m/r) erforderlich. Die zugehorige Gleichung wird mittels qualitativer Methoden diskutiert mit dem Ergebnis, das das asymptotische Verhalten bei m < 2l φ = -m/r + er-m/l exp (-r/l) u und bei < φ = -m/r + er−2 exp (-r/l) u ist; hierbei ist u eine gewisse beschrankte Funktion. Schlieslich wird die Beziehung zwischen Loungen der linearisierten und der voll standigen Gleichung diskutiert.
14074913
4D wormhole with signature change in the presence of extra dimensions
A regular vacuum solution in 5D gravity on the principal bundle with the U(1) structural group is proposed as a 4D wormhole. This solution has two null hypersurfaces where an interchange of the sign of some 5D metric components happens. For a 4D observer living on the base of this principal bundle this is a wormhole with two asymptotically flat Lorentzian (Euclidean) spacetimes connected by a Euclidean (Lorentzian) throat. The 4D Lorentzian observer sees these two null hypersurfaces as electric charges.
15961894
Comparing selfinteracting scalar fields and R + R**3 cosmological models
We generalize the well-known analogies between m2φ2 and R + R2 theories to include the selfinteraction λφ4-term for the scalar field. It turns out to be the R + R3 Lagrangian which gives an appropiate model for it. Considering a spatially flat Friedman cosmological model, common and different properties of these models are discussed, e. g., by linearizing around a ground state the masses of the resp. spin 0-parts concide. Finally, we prove a general conformal equivalence theorem between a Lagrangian L = L(R), L′L″ ≠ 0, and a minimally coupled scalar field in a general potential.
15300220
Exact Cosmological Solutions of Nonlinear F(R)-Gravity
We report on the cited papers refs. 1 - 18 from the following points of view: What do we exactly know about solutions when no exact solution (in the sense of "solution in closed form") is available? In which sense do these solutions possess a singularity? In which cases do conformal relations and/or dimensional reductions simplify the deduction? Furthermore, we outline some open questions worth of being studied in future research.
123288737
On Static Asymptotically Flat Solutions of Fourth Order Gravitational Field Equations
It is shown that each non-flat regular static asymptotically flat solution of the gravitational field equation following from the Lagrangian 
 
 
 
 
 
 
has in a certain sense positive energy. Further, for a set of parameters including the BACH-EINSTEIN theory 
 
 
 
 
 
 
some results concerning the full nonlinear behaviour of the solutions of the field equation will be given. 
 
 
 
Uber statisch asymptotisch flache Losungen von Gravitationsfeldgleichungen vierter Ordnung 
 
 
 
Es wird gezeigt, das jede nicht-flache regulare statische asymptotisch flache Losung der Gravitationsfeldgleichung, die aus einem Lagrangeausdruck 
 
 
 
 
 
 
folgt, in einem gewissen Sinne positive Energie hat. Ferner wird fur eine bestimmte Parametermenge, die die BACH-EINSTEIN-Theorie 
 
 
 
 
 
 
enthalt, einiges uber das volle nichtlineare Verhalten der Losungen der Feldgleichung mitgeteilt.
17350104
Inhomogeneous Cosmological Models with Flat Slices Generated from the EINSTEIN‐DE SITTER Universe
A family of cosmological models in considered which in a certain synchronized system of reference possess flat slices t = const. They are generated from the EINSTEIN-DE SITTER universe by a suitable transformation. Under physically reasonable presumptions these transformed models fulfil certain energy conditions. 
 
 
 
Es wird eine Familie kosmologischer Modelle betrachtet, die in einemi gewissen synchronisierten Bezugssystem flache Schichten t = const. besitzen. Sie werden mittels einer geeigneten Transformation aus dem EINSTEIN-DE SITTER-Universum erzeugt. Diese transformierten Modelle erfullen unter physikalisch sinnvollen Voraussetzungen gewisse Energie bedingungen.
31917251
On an algorithm solving two-level programming problems with nonunique lower level solutions
In the paper, an algorithm is presented for solving two-level programming problems. This algorithm combines a direction finding problem with a regularization of the lower level problem. The upper level objective function is included in the regularzation to yield uniqueness of the follower's solution set. This is possible if the problem functions are convex and the upper level objective function has a positive definite Hessian. The computation of a direction of descent and of the step size is discussed in more detail. Afterwards the convergence proof is given.Last but not least some remarks and examples describing the difficulty of the inclusion of upper-level constraints also depending on the variables of the lower level are added.
117822141
Axiomatic Characterization of Physical Geometry
Operations with rigid bodies.- Regions and transport mappings.- The Helmhotz-Lie problem.- Characterization of Euclidean geometry.
122589785
Models for Constrained Motion and d'Alembert's Principle
A theorem of Arnol'd and Gallavotti states that by a suitable potential of increasing rigidity a mechanical system with conservative forces can be constrained to a hypersurface of the configuration space and its motion approaches a solution of the reduced Lagrangian equation. In this paper the theorem will be generalized to time- and velocity-dependent forces including time-dependent constraints and proved with the aid of the method of averaging. This technique also allows us to identify the constraint force as the averaged negative gradient of the constraint potential.