For a spatially flat Friedmann model with line element ds 2 = a 2 [da 2 /B(a) − dx 2 − dy 2 − dz 2 ], the 00-component of the Einstein field equation reads 8πGT 00 = 3/a 2 containing no derivative. For a nonlinear Lagrangian L(R), we obtain a second– order differential equation for B instead of the expected fourth-order equation. We discuss this equation for the curvature-saturated model propos...

The Einstein equation is derived from the proportionality of entropy and horizon area together with the fundamental relation δQ = TdS connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with δQ and T interpreted as the energy flux and Unruh temperature seen by an accelerated observer...

Causal structure, inertial path structure and compatibility with quantum mechanics demand no full Lorentz metric, but only an integrable Weyl geometry for space time (Ehlers/Pirani/Schild 1972, Audretsch e.a. 1984). A proposal of (Tann 1998, Drechsler/Tann 1999) for a minimal coupling of the Hilbert-Einstein action to a scale covariant scalar vacuum field φ (weight −1) plus (among others) a Kle...

We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational eld with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new eld equation generalizing the notion of Killing spinors. The solutions of this spinor eld equation are called weak Killing spinors (WK-spinors). They are special solutions of the Einstein-Di...

In the framework of the Gross-Pitaevskii mean field approach, it is shown that the supersonic flow of a Bose-Einstein condensate can support a new type of pattern--an oblique dark soliton. The corresponding exact solution of the Gross-Pitaevskii equation is obtained. It is demonstrated by numerical simulations that oblique solitons can be generated by an obstacle inserted into the flow.

In this paper the Einstein-Vlasov system of self-consistent field equations is used to construct a cosmological model. A solution is found for a homogeneous isotropic space-time with positive curvature (R × S 3 topology). For the Universe consisting of massless particles the equation for R(t) is solved analytically.

We argue that Einstein gravity coupled to a Born-Infeld theory provides an attractive candidate to represent dark matter and dark energy. For cosmological models, the BornInfeld field has an equation of state which interpolates between matter, ω = 0 (small times), and a cosmological constant ω = −1 (large times). On galactic scales, the BornInfeld theory predicts asymptotically flat rotation cu...

In a space-time M with Killing vector field ξa which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of ξa gives a 3-dimension space S. An action of the fields on S is proposed which gives the same fields equations as those reduced from the vacuum Einstein equation on M . PACS number(s): 04.20.Fy, 04.20.Cv