@article{KleinertSchmidt2002, author = {Kleinert, Hagen and Schmidt, Hans-J{\"u}rgen}, title = {Cosmology with curvature-saturated gravitational lagrangian}, year = {2002}, abstract = {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.}, language = {en} } @book{Schmidt1998, author = {Schmidt, Hans-J{\"u}rgen}, title = {Current topics in mathematical cosmology : proceedings of the International Seminar ; Potsdam, Germany 30 March 4 April 1998}, editor = {Rainer, Martin}, publisher = {World Scientific}, address = {Singapore [u.a.]}, isbn = {981-023627-1}, pages = {XVII, 484 S.}, year = {1998}, language = {en} } @book{SchmidtMohazzabRainer1995, author = {Schmidt, Hans-J{\"u}rgen and Mohazzab, Masoud and Rainer, Martin}, title = {Deformations between Bianchi geometries in classical and quantum cosmology}, series = {Report IPM}, volume = {1995, 91}, journal = {Report IPM}, publisher = {IPM}, address = {Teheran}, year = {1995}, language = {en} } @article{SchmidtKasper1995, author = {Schmidt, Hans-J{\"u}rgen and Kasper, Uwe}, title = {Differentialgeometrische Grundlagen der Kosmologie}, year = {1995}, language = {de} } @article{Schmidt2000, author = {Schmidt, Hans-J{\"u}rgen}, title = {Editor's note to A. Sakharov}, year = {2000}, language = {en} } @article{Schmidt1996, author = {Schmidt, Hans-J{\"u}rgen}, title = {Editorial}, year = {1996}, language = {de} } @article{Schmidt1995, author = {Schmidt, Hans-J{\"u}rgen}, title = {Editorial}, year = {1995}, language = {de} } @article{Schmidt1999, author = {Schmidt, Hans-J{\"u}rgen}, title = {Editor{\"i}s note}, year = {1999}, language = {de} } @article{Schmidt2000, author = {Schmidt, Hans-J{\"u}rgen}, title = {Eichfeldtheorie}, year = {2000}, language = {de} } @article{Schmidt2005, author = {Schmidt, Hans-J{\"u}rgen}, title = {Einsteins Arbeiten in Bezug auf die moderne Kosmologie : de Sitters L{\"o}sung der Einsteinschen Feldgleichung mit positivem kosmologischen Glied als Geometrie des inflationaeren Weltmodells}, year = {2005}, abstract = {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.}, language = {de} } @article{Schmidt1998, author = {Schmidt, Hans-J{\"u}rgen}, title = {Exact cosmological solutions of nonlinear F(R)-gravity}, series = {General relativity and quantum cosmology : preprints gr-qc}, volume = {9808060}, journal = {General relativity and quantum cosmology : preprints gr-qc}, year = {1998}, language = {en} } @article{Schmidt1998, author = {Schmidt, Hans-J{\"u}rgen}, title = {Exact cosmological solutions of nonlinear F(R)-gravity}, isbn = {981-023627-1}, year = {1998}, language = {en} } @article{SchmidtSingleton2013, author = {Schmidt, Hans-J{\"u}rgen and Singleton, Douglas}, title = {Exact radial solution in 2+1 gravity with a real scalar field}, series = {Physics letters : B}, volume = {721}, journal = {Physics letters : B}, number = {4-5}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0370-2693}, doi = {10.1016/j.physletb.2013.03.007}, pages = {294 -- 298}, year = {2013}, abstract = {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.}, language = {en} } @article{SchmidtSingleton2013, author = {Schmidt, Hans-J{\"u}rgen and Singleton, Douglas}, title = {Exact radial solution in 2+1 gravity with a real scalar field}, issn = {0370-2693}, year = {2013}, abstract = {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.}, language = {en} } @book{HooftHolsteinMakrietal.2001, author = {Hooft, Gerard and Holstein, Barry and Makri, Nancy and Duru, Ismail and Ruffini, Remo and Janke, Wolfhard and Pelster, Axel and Schmidt, Hans-J{\"u}rgen and Bachmann, Michael}, title = {Fluctuating paths and fields : festschrift dedicated to Hagen Kleinert on the occasion of his 60the birthday}, publisher = {World Scientific}, address = {River Edge, NJ}, isbn = {981-02-4648-X}, pages = {871 S.}, year = {2001}, language = {en} } @article{DzhunushalievSchmidt2000, author = {Dzhunushaliev, Vladimir and Schmidt, Hans-J{\"u}rgen}, title = {Flux Tubes in Weyl Gravity}, year = {2000}, language = {en} } @article{Schmidt2007, author = {Schmidt, Hans-J{\"u}rgen}, title = {Fourth order gravity : equations, history, and application to cosmology}, year = {2007}, abstract = {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.}, language = {en} } @article{Schmidt2011, author = {Schmidt, Hans-J{\"u}rgen}, title = {Gauss-Bonnet Lagrangian G ln G and cosmological exact solutions}, issn = {1550-7998}, year = {2011}, abstract = {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.}, language = {en} } @article{Schmidt2011, author = {Schmidt, Hans-J{\"u}rgen}, title = {Gauss-Bonnet lagrangian G lnG and cosmological exact solutions}, series = {Physical review : D, Particles, fields, gravitation, and cosmology}, volume = {83}, journal = {Physical review : D, Particles, fields, gravitation, and cosmology}, number = {8}, publisher = {American Physical Society}, address = {College Park}, issn = {1550-7998}, doi = {10.1103/PhysRevD.83.083513}, pages = {7}, year = {2011}, abstract = {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.}, language = {en} } @article{Schmidt1995, author = {Schmidt, Hans-J{\"u}rgen}, title = {Gedenkkolloquien anl{\"a}ßlich des 100. Todestages von Hermann von Helmholtz, Kolloquium an der Universit{\"a}t Potsdam}, year = {1995}, language = {de} }