arXiv subjects

H. -J. Schmidt

Publications and source records attributed to H. -J. Schmidt.

77 records · Page 5Linked to original sources

arXiv1997

A new proof of Birkhoff's theorem

Assuming SO(3)-spherical symmetry, the 4-dimensional Einstein equation reduces to an equation conformally related to the field equation for 2-dimensional gravity following from the Lagrangian L = R^(1/3). Solutions for 2-dimensional gravity always possess a local isometry because the traceless part of its Ricci tensor identically vanishes. Combining both facts, we get a new proof of Birkhoff's theorem; contrary to other proofs, no coordinates must be introduced. The SO(m)-spherically symmetric solutions of the (m+1)-dimensional Einstein equation can be found by considering L = R^(1/m) in two dimensions. This yields several generalizations of Birkhoff's theorem in an arbitrary number of dimensions, and to an arbitrary signature of the metric.

gr-qc↗

arXiv1997

Classification of multidimensional inflationary models

We define under which circumstances two multi-warped product spacetimes can be considered equivalent and then we classify the spaces of constant curvature in the Euclidean and Lorentzian signature. For dimension D=2, we get essentially twelve representations, for D=3 exactly eighteen. More general, for every even D, 5D+2 cases exist, whereas for every odd D, 5D+3 cases exist. For every D, exactly one half of them has the Euclidean signature. Our definition is well suited for the discussion of multidimensional cosmological models, and our results give a simple algorithm to decide whether a given metric represents the inflationary de Sitter spacetime (in unusual coordinates) or not.

gr-qc↗

arXiv1997

Answer to question Nr. 55

We answer to question Nr. 55 [Are there pictorial examples that distinguish covariant and contravariant vectors ?] posed by D. Neuenschwander, Am. J. Phys. 65 (1), 11 (1997)

gr-qc↗

arXiv1995

Inhomogeneous Cosmological Models with Homogeneous Inner Hypersurface Geometry

Space-times which allow a slicing into homogeneous spatial hypersurfaces generalize the usual Bianchi models. One knows already that in these models the Bianchi type may change with time. Here we show which of the changes really appear. To this end we characterize the topological space whose points are the 3-dimensional oriented homogeneous Riemannian manifolds; locally isometric manifolds are considered as same.

gr-qc↗

arXiv1994

Stability Properties of the Starobinsky Cosmological Model

We discuss the instabilities appearing in the cosmological model with a quasi de Sitter phase following from a fourth-order gravity theory. Both the classical equation as well as the quantization in form of a Wheeler - De Witt equation are conformally related to the analogous model with Einstein's theory of gravity with a minimally coupled scalar field. Results are: 1. In the non-tachyonic case, classical fourth-order gravity is not more unstable than Einstein's theory itself. 2. The well-known classically valid conformal relation is also (at least for some typical cases) valid on the level of the corresponding Wheeler - De Witt equations, which turns out to be a non-trivial statement. (to appear in: Proc. Sem. Relativistic Astrophysics Potsdam 1994, Ed .: J. Mücket)

gr-qc↗