TY - JOUR A1 - Dzhunushaliev, Vladimir A1 - Rurenko, O. A1 - Schmidt, Hans-Jürgen T1 - Spherically symmetric solutions in multidimensional gravity with the SU(2) gauge group as the extra dimensions Y1 - 2002 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - Stability and Hamiltonian formulation of higher derivative theories T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 04 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Stability and Hamiltonian formulation of higher derivative theories Y1 - 1994 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Kasper, Uwe A1 - Kluske, Sabine A1 - Rainer, Martin A1 - Reuter, Stefan T1 - Stability properties of the Starobinsky cosmological model Y1 - 1995 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - The classical solutions of two-dimensional gravity Y1 - 1999 ER - TY - BOOK A1 - Battaglia Mayer, Alexandra A1 - Schmidt, Hans-Jürgen T1 - The de Sitter space-time as attractor solution in eighth order gravity T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1993 VL - 1993, 05 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Rainer, Martin T1 - The natural classification of real lie algebras Y1 - 1995 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - The square of the Weyl tensor can be negative N2 - We show that the square of the Weyl tensor can be negative by giving an example Y1 - 2003 UR - http://arXiv.org/abs/gr-qc/0302078 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - The tetralogy of Birkhoff theorems JF - General relativity and gravitation N2 - We classify the existent Birkhoff-type theorems into four classes: first, in field theory, the theorem states the absence of helicity 0- and spin 0-parts of the gravitational field. Second, in relativistic astrophysics, it is the statement that the gravitational far-field of a spherically symmetric star carries, apart from its mass, no information about the star; therefore, a radially oscillating star has a static gravitational far-field. Third, in mathematical physics, Birkhoff's theorem reads: up to singular exceptions of measure zero, the spherically symmetric solutions of Einstein's vacuum field equation with can be expressed by the Schwarzschild metric; for , it is the Schwarzschild-de Sitter metric instead. Fourth, in differential geometry, any statement of the type: every member of a family of pseudo-Riemannian space-times has more isometries than expected from the original metric ansatz, carries the name Birkhoff-type theorem. Within the fourth of these classes we present some new results with further values of dimension and signature of the related spaces; including them are some counterexamples: families of space-times where no Birkhoff-type theorem is valid. These counterexamples further confirm the conjecture, that the Birkhoff-type theorems have their origin in the property, that the two eigenvalues of the Ricci tensor of 2-D pseudo-Riemannian spaces always coincide, a property not having an analogy in higher dimensions. Hence, Birkhoff-type theorems exist only for those physical situations which are reducible to 2-D. KW - Birkhoff theorem KW - Einstein space KW - Isometry group Y1 - 2013 U6 - https://doi.org/10.1007/s10714-012-1478-5 SN - 0001-7701 VL - 45 IS - 2 SP - 395 EP - 410 PB - Springer CY - New York ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - The tetralogy of Birkhoff theorems N2 - We classify the existent Birkhoff-type theorems into four classes: First, in field theory, the theorem states the absence of helicity 0- and spin 0-parts of the gravitational field. Second, in relativistic astrophysics, it is the statement that the gravitational far-field of a spherically symmetric star carries, apart from its mass, no information about the star; therefore, a radially oscillating star has a static gravitational far-field. Third, in mathematical physics, Birkhoff's theorem reads: up to singular exceptions of measure zero, the spherically symmetric solutions of Einstein's vacuum field equation with Lambda = 0 can be expressed by the Schwarzschild metric; for Lambda unequal 0, it is the Schwarzschild-de Sitter metric instead. Fourth, in differential geometry, any statement of the type: every member of a family of pseudo-Riemannian space-times has more isometries than expected from the original metric ansatz, carries the name Birkhoff-type theorem. Within the fourth of these classes we present some new results with further values of dimension and signature of the related spaces; including them are some counterexamples: families of space-times where no Birkhoff-type theorem is valid. These counterexamples further confirm the conjecture, that the Birkhoff-type theorems have their origin in the property, that the two eigenvalues of the Ricci tensor of two- dimensional pseudo-Riemannian spaces always coincide, a property not having an analogy in higher dimensions. Hence, Birkhoff-type theorems exist only for those physical situations which are reducible to two dimensions. Y1 - 2013 UR - http://arXiv.org/abs/1208.5237 SN - 0001-7701 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Topologische Aspekte in der Kosmologie Y1 - 2000 ER - TY - JOUR A1 - Kluske, Sabine A1 - Schmidt, Hans-Jürgen T1 - Towards a cosmic no hair theorem for higher-order gravity Y1 - 1996 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen A1 - Kluske, Sabine T1 - Towards a no hair theorem for higher order gravit Y1 - 1995 ER - TY - JOUR A1 - Gurovich, Viktor A1 - Schmidt, Hans-Jürgen A1 - Tokareva, Ira T1 - Tunneling of the closed Friedmann Universe with generation of scalar waves N2 - The evolution of the closed Friedmann Universe with a packet of short scalar waves is considered with the help of the Wheeler-DeWitt equation. The packet ensures conservation of homogeneity and isotropy of the metric on average. It is shown that during tunneling the amplitudes of short waves of a scalar field can increase catastrophically promptly if their influence to the metric is not taken into account. This effect is similar to the Rubakov-effect of catastrophic particle creation calculated already in 1984. In our approach to the problem it is possible to consider a self- consistent dynamics of the expansion of the Universe and amplification of short waves. It results in a decrease of the barrier and interruption of amplification of waves, and we get an exit of the wave function from the quantum to the classically available region. Y1 - 2001 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen A1 - Mignemi, Salvatore T1 - Two-dimensional higher-derivative gravity and conformal transformations Y1 - 1995 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Mignemi, Salvatore T1 - Two-dimensional higher-derivative gravity and conformal transformations Y1 - 1995 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Untitled Y1 - 2005 ER - TY - JOUR A1 - Canfora, Fabrizio A1 - Schmidt, Hans-Jürgen T1 - Vacuum solutions which cannot be written in diagonal form N2 - A vacuum solution of the Einstein gravitational field equation is shown to follow from a general ansatz but fails to follow from it if the symmetric matrix in it is assumed to be in diagonal form. Y1 - 2003 UR - http://arXiv.org/abs/gr-qc/0305107 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - Why do all the curvature invariants of a gravitational wave vanish? T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 03 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Why do all the curvature invariants of a gravitational wave vanish? Y1 - 1996 ER -