arXiv subjects

Wolfgang Graf

Publications and source records attributed to Wolfgang Graf.

4 recordsLinked to original sources

arXiv2017

Existence and Stability of Circular Orbits in Time-Dependent Spherically Symmetric Spacetimes

For a general spherically four--dimensional metric the notion of "circularity" of a family of equatorial geodesic trajectories is defined in geometrical terms. The main object turns out to be the angular--momentum function $J$ obeying a consistency condition involving the mean extrinsic curvature of the submanifold containing the geodesics. The ana\-ly\-sis of linear stability is reduced to a simple dynamical system formally describing a damped harmonic oscillator. For static metrics the existence of such geodesics is given when $J^2 > 0$, and $(J^2)' > 0$ for stability. The formalism is then applied to the Schwarzschild--de Sitter solution, both in its static and in its time--dependent cosmological version, as well to the Kerr--de Sitter solution. In addition we present an approximate solution to a cosmological metric containing a massive source and solving the Einstein field equation for a massless scalar.

gr-qc↗

arXiv2007

Ricci Flow Gravity

A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gravity. In particular there is no adjustable coupling constant. For the solar system the effects of Ricci flow gravity cannot be distinguished from Einstein gravity and therefore it passes all classical tests. However for cosmology significant deviations from standard Einstein cosmology will appear.

gr-qc↗

arXiv2002

Geometric Dilaton Coupling and Smooth Charged Wormholes

A particular type of coupling of the dilaton field to the metric is shown to admit a simple geometric interpretation in terms of a volume element density independent from the metric. For dimension n = 4 two families of either magnetically or electrically charged static spherically symmetric solutions to the Maxwell-Einstein-Dilaton field equations are derived. Whereas the metrics of the "magnetic" spacetimes are smooth, geodesically complete and have the topology of a wormhole, the "electric" metrics behave similarly as the singular and geodesically incomplete classical Reissner-Nordstroem metrics. At the price of losing the simple geometric interpretation, a closely related "alternative" dilaton coupling can nevertheless be defined, admitting as solutions smooth "electric" metrics.

gr-qc↗

arXiv2001

Nonanalytic extensions of the extreme Reissner-Nordstroem metric in terms of weak solutions

A basic extension of the exterior part of the extreme Reissner-Nordstroem solution in terms of a continuous metric and gauge potential is constructed. This extension is not smooth at the null hypersurface given by the Cauchy-Killing horizon which separates isometric copies of the exterior metric. The Maxwell-Einstein system of equations is satisfied only in a weak sense. The manifold is topologically incomplete and the spherical symmetry is globally broken down to an axial symmetry. This behaviour can be attributed to the effect of a 'topological string', in the sense of a infinitesimally thin closed stringlike object 'sitting on the rim' of the black hole and holding it open by means of an accompanying impulsive gravitational wave. The resulting differentiable manifold and the corresponding horizons are not anymore simply connected, being 'pierced' by the strings.

gr-qc↗