TY - JOUR A1 - Kleinert, Hagen A1 - Schmidt, Hans-Jürgen T1 - Cosmology with curvature-saturated gravitational lagrangian N2 - We argue that the Lagrangian L(R) for gravity should remain bounded at large curvature, and interpolate between the weak-field tested Einstein-Hilbert Lagrangian and a pure cosmological constant for large R with the curvature- saturated ansatz. The curvature-dependent effective gravitational constant tends to infinity for large R, in contrast to most other approaches where it tends to 0. The theory possesses neither ghosts nor tachyons, but it fails to be linearization stable. On the technical side we show that two different conformal transformations make L asymptotically equivalent to the Gurovich-ansatz on the one hand, and to Einstein's theory with a minimally coupled scalar field with self-interaction on the other. Y1 - 2002 UR - http://arXiv.org/abs/gr-qc/0006074 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen ED - Rainer, Martin T1 - Current topics in mathematical cosmology : proceedings of the International Seminar ; Potsdam, Germany 30 March 4 April 1998 Y1 - 1998 SN - 981-023627-1 PB - World Scientific CY - Singapore [u.a.] ER - TY - BOOK A1 - Schmidt, Hans-Jürgen A1 - Mohazzab, Masoud A1 - Rainer, Martin T1 - Deformations between Bianchi geometries in classical and quantum cosmology T3 - Report IPM Y1 - 1995 VL - 1995, 91 PB - IPM CY - Teheran ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Kasper, Uwe T1 - Differentialgeometrische Grundlagen der Kosmologie Y1 - 1995 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Editor's note to A. Sakharov Y1 - 2000 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Editorial Y1 - 1996 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Editorial Y1 - 1995 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Editorïs note Y1 - 1999 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Eichfeldtheorie Y1 - 2000 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Einsteins Arbeiten in Bezug auf die moderne Kosmologie : de Sitters Lösung der Einsteinschen Feldgleichung mit positivem kosmologischen Glied als Geometrie des inflationaeren Weltmodells N2 - Die Arbeit von Albert Einstein von 1918 zu Willem De Sitters Loesung der Einsteinschen Feldgleichung wird unter heutigem Gesichtspunkt kommentiert. Dazu wird zunaechst die Geometrie der De Sitterschen Raum-Zeit beschrieben, sowie ihre Bedeutung fuer das inflationaere Weltmodell erlaeutert. Y1 - 2005 UR - http://arXiv.org/abs/gr-qc/0506121 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Exact cosmological solutions of nonlinear F(R)-gravity JF - General relativity and quantum cosmology : preprints gr-qc Y1 - 1998 UR - http://xxx.soton.ac.uk/form/gr-qc? VL - 9808060 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Exact cosmological solutions of nonlinear F(R)-gravity Y1 - 1998 SN - 981-023627-1 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Singleton, Douglas T1 - Exact radial solution in 2+1 gravity with a real scalar field JF - Physics letters : B N2 - In this Letter we give some general considerations about circularly symmetric, static space-times in 2 + 1 dimensions, focusing first on the surprising (at the time) existence of the BTZ black hole solution. We show that BTZ black holes and Schwarzschild black holes in 3 + 1 dimensions originate from different definitions of a black hole. There are two by-products of this general discussion: (i) we give a new and simple derivation of (2 + 1)-dimensional Anti-de Sitter (AdS) space-time; (ii) we present an exact solution to (2 + 1)-dimensional gravity coupled to a self-interacting real scalar field. The spatial part of the metric of this solution is flat but the temporal part behaves asymptotically like AdS space-time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space-time. The solution can be compared to gravitating scalar field solutions in 3 + 1 dimensions but with certain oddities connected with the (2 + 1)-dimensional character of the space-time. The solution is unique to 2 + 1 dimensions; it does not carry over to 3 + 1 dimensions. KW - (2+1)-dimensional gravity KW - Exact solution KW - BTZ black hole KW - Self-interacting scalar field Y1 - 2013 U6 - https://doi.org/10.1016/j.physletb.2013.03.007 SN - 0370-2693 VL - 721 IS - 4-5 SP - 294 EP - 298 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Singleton, Douglas T1 - Exact radial solution in 2+1 gravity with a real scalar field N2 - In this paper we give some general considerations about circularly symmetric, static space-times in 2+1 dimensions, focusing first on the surprising (at the time) existence of the BTZ black hole solution. We show that BTZ black holes and Schwarzschild black holes in 3+1 dimensions originate from different definitions of a black hole. There are two by-products of this general discussion: (i) we give a new and simple derivation of 2+1 dimensional Anti-de Sitter (AdS) space-time; (ii) we present an exact solution to 2+1 dimensional gravity coupled to a self-interacting real scalar field. The spatial part of the metric of this solution is flat but the temporal part behaves asymptotically like AdS space-time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space- time. The solution can be compared to gravitating scalar field solutions in 3+1 dimensions but with certain oddities connected with the 2+1 dimensional character of the space-time. The solution is unique to 2+1 dimensions; it does not carry over to 3+1 dimensions. Y1 - 2013 UR - http://arXiv.org/abs/1212.1285 SN - 0370-2693 ER - TY - BOOK A1 - Hooft, Gerard A1 - Holstein, Barry A1 - Makri, Nancy A1 - Duru, Ismail A1 - Ruffini, Remo A1 - Janke, Wolfhard A1 - Pelster, Axel A1 - Schmidt, Hans-Jürgen A1 - Bachmann, Michael T1 - Fluctuating paths and fields : festschrift dedicated to Hagen Kleinert on the occasion of his 60the birthday Y1 - 2001 SN - 981-02-4648-X PB - World Scientific CY - River Edge, NJ ER - TY - JOUR A1 - Dzhunushaliev, Vladimir A1 - Schmidt, Hans-Jürgen T1 - Flux Tubes in Weyl Gravity Y1 - 2000 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Fourth order gravity : equations, history, and application to cosmology N2 - The field equations following from a Lagrangian L(R) will be deduced and solved for special cases. If L is a non-linear function of the curvature scalar, then these equations are of fourth order in the metric. In the introduction we present the history of these equations beginning with the paper of H. Weyl from 1918, who first discussed them as alternative to Einstein's theory. In the third part, we give details about the cosmic no hair theorem, i.e., the details how within fourth order gravity with L= R + R^2 the inflationary phase of cosmic evolution turns out to be a transient attractor. Finally, the Bicknell theorem, i.e. the conformal relation from fourth order gravity to scalar- tensor theory, will be shortly presented. Y1 - 2007 UR - http://arxiv.org/abs/gr-qc/0602017 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Gauss-Bonnet Lagrangian G ln G and cosmological exact solutions N2 - For the Lagrangian L = G ln G where G is the Gauss-Bonnet curvature scalar we deduce the field equation and solve it in closed form for 3-flat Friedman models using a statefinder parametrization. Further we show, that among all lagrangians F(G) this L is the only one not having the form G^r with a real constant r but possessing a scale-invariant field equation. This turns out to be one of its analogies to f(R)-theories in 2-dimensional space-time. In the appendix, we systematically list several formulas for the decomposition of the Riemann tensor in arbitrary dimensions n, which are applied in the main deduction for n=4. Y1 - 2011 UR - http://arxiv.org/pdf/1102.0241v2 SN - 1550-7998 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Gauss-Bonnet lagrangian G lnG and cosmological exact solutions JF - Physical review : D, Particles, fields, gravitation, and cosmology N2 - For the Lagrangian L = G lnG where G is the Gauss-Bonnet curvature scalar we deduce the field equation and solve it in closed form for 3-flat Friedmann models using a state-finder parametrization. Further we show that among all Lagrangians F(G) this L is the only one not having the form G(r) with a real constant r but possessing a scale-invariant field equation. This turns out to be one of its analogies to f(R) theories in two-dimensional space-time. In the appendix, we systematically list several formulas for the decomposition of the Riemann tensor in arbitrary dimensions n, which are applied in the main deduction for n = 4. Y1 - 2011 U6 - https://doi.org/10.1103/PhysRevD.83.083513 SN - 1550-7998 VL - 83 IS - 8 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Gedenkkolloquien anläßlich des 100. Todestages von Hermann von Helmholtz, Kolloquium an der Universität Potsdam Y1 - 1995 ER -