@article{DzhunushalievSchmidt1999, author = {Dzhunushaliev, Vladimir and Schmidt, Hans-J{\"u}rgen}, title = {2+2-decomposable solutions of weyl gravity}, year = {1999}, language = {en} } @article{Schmidt1998, author = {Schmidt, Hans-J{\"u}rgen}, title = {2-dimensional representations of 4-dimensional gravitational waves}, year = {1998}, language = {en} } @article{DzhunushalievSchmidt1999, author = {Dzhunushaliev, Vladimir and Schmidt, Hans-J{\"u}rgen}, title = {4D wormhole with signature change in the presence of extra dimensions}, series = {General relativity and quantum cosmology : preprints gr-qc}, volume = {9908076}, journal = {General relativity and quantum cosmology : preprints gr-qc}, year = {1999}, language = {en} } @article{Schmidt1997, author = {Schmidt, Hans-J{\"u}rgen}, title = {A new duality transformation for fouth-order gravity}, year = {1997}, language = {en} } @article{Schmidt1997, author = {Schmidt, Hans-J{\"u}rgen}, title = {A new proof of Birkhoff{\"i}s theorem}, year = {1997}, language = {en} } @article{Schmidt1998, author = {Schmidt, Hans-J{\"u}rgen}, title = {A two-dimensional representation of four-dimensional graviational waves}, year = {1998}, language = {en} } @article{Schmidt2000, author = {Schmidt, Hans-J{\"u}rgen}, title = {Allgemeine Relativit{\"a}tstheorie}, year = {2000}, language = {de} } @article{Schmidt1994, author = {Schmidt, Hans-J{\"u}rgen}, title = {Aufgaben zur Kosmologie}, year = {1994}, language = {de} } @article{Schmidt1996, author = {Schmidt, Hans-J{\"u}rgen}, title = {Classical mechanics with lapse}, year = {1996}, language = {en} } @article{MignemiSchmidt1998, author = {Mignemi, Salvatore and Schmidt, Hans-J{\"u}rgen}, title = {Classification of multidimensional inflationary models}, year = {1998}, language = {en} } @article{Schmidt1995, author = {Schmidt, Hans-J{\"u}rgen}, title = {Comment on conformal transformations single out a unique measure of distance}, year = {1995}, language = {en} } @article{Schmidt1994, author = {Schmidt, Hans-J{\"u}rgen}, title = {Comment on stability of the semiclassical Einstein equation}, year = {1994}, language = {en} } @article{Schmidt1997, author = {Schmidt, Hans-J{\"u}rgen}, title = {Conformal relations and Hamiltonian formlation of fourth-order gravity}, year = {1997}, language = {en} } @article{Schmidt1998, author = {Schmidt, Hans-J{\"u}rgen}, title = {Consequences of the noncompactness of the Lorentz group}, year = {1998}, language = {en} } @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} } @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} } @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} } @article{AmendolaBattagliaMayerCapozzielloetal.1992, author = {Amendola, Luca and Battaglia Mayer, Alexandra and Capozziello, Salvatore and Gottl{\"o}ber, Stefan and M{\"u}ller, Volker and Occhionero, Franco and Schmidt, Hans-J{\"u}rgen}, title = {Generalized sixth-order gravity and inflation}, series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, volume = {1992, 04}, journal = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {7 S.}, year = {1992}, language = {en} } @article{Schmidt1998, author = {Schmidt, Hans-J{\"u}rgen}, title = {Gravitation in 1+1 Dimensionen : exacte L{\"o}sungen, Konformrelationen und Beziehungen zum 3+1 -dimensionalen Fall}, year = {1998}, language = {de} } @article{Schmidt1996, author = {Schmidt, Hans-J{\"u}rgen}, title = {How should we measure spatial distances?}, year = {1996}, language = {en} } @article{SchmidtRainer1995, author = {Schmidt, Hans-J{\"u}rgen and Rainer, Martin}, title = {Inhomogeneous cosmological models with homogeneous inner hypersurface geometry}, year = {1995}, language = {en} } @article{SchmidtSingleton2013, author = {Schmidt, Hans-J{\"u}rgen and Singleton, Douglas}, title = {Isotropic universe with almost scale-invariant fourth-order gravity}, series = {Journal of mathematical physics}, volume = {54}, journal = {Journal of mathematical physics}, number = {6}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0022-2488}, doi = {10.1063/1.4808255}, pages = {14}, year = {2013}, abstract = {We study a class of isotropic cosmologies in the fourth-order gravity with Lagrangians of the form L = f(R) + k(G) where R and G are the Ricci and Gauss-Bonnet scalars, respectively. A general discussion is given on the conditions under which this gravitational Lagrangian is scale-invariant or almost scale-invariant. We then apply this general background to the specific case L = alpha R-2 + beta Gln G with constants alpha, beta. We find closed form cosmological solutions for this case. One interesting feature of this choice of f(R) and k(G) is that for very small negative value of the parameter beta, the Lagrangian L = R-2/3 + beta Gln G leads to the replacement of the exact de Sitter solution coming from L = R-2 (which is a local attractor) to an exact, power-law inflation solution a(t) = t(p) = t(-3/beta) which is also a local attractor. This shows how one can modify the dynamics from de Sitter to power-law inflation by the addition of a Gln G-term.}, language = {en} } @article{SchmidtSingleton2013, author = {Schmidt, Hans-J{\"u}rgen and Singleton, Douglas}, title = {Isotropic universe with almost scale-invariant fourth-order gravity}, year = {2013}, abstract = {We study a broad class of isotropic vacuum cosmologies in fourth-order gravity under the condition that the gravitational Lagrangian be scale-invariant or almost scale-invariant. The gravitational Lagrangians considered will be of the form L = f(R) + k(G) where R and G are the Ricci and Gauss-Bonnet scalars respectively. Specifically we take f(R) = R^2n and k(G) = G^n or k(G) = G ln G. We find solutions in closed form for a spatially flat Friedmann space-time and interpret their asymptotic early-time and late-time behaviour as well as their inflationary stages. One unique example which we discuss is the case of a very small negative value of the parameter b in the Lagrangian L = R^2 + b G ln G which leads to the replacement of the exact de Sitter solution from L = R^2 (being a local attractor) to a power-law inflation exact solution also representing a local attractor. This shows how one can modify the dynamics from de Sitter to power-law inflation by the addition of the G ln G-term.}, language = {en} } @article{Schmidt1994, author = {Schmidt, Hans-J{\"u}rgen}, title = {Jahresbericht 1993}, year = {1994}, language = {de} } @article{MeisterSchmidt1997, author = {Meister, Claudia-Veronika and Schmidt, Hans-J{\"u}rgen}, title = {Jahresberichte 1996}, year = {1997}, language = {de} } @article{Schmidt1997, author = {Schmidt, Hans-J{\"u}rgen}, title = {Janyska, Josef [u.a.](Ed.) Differential geometry and applications : proceedings of the 6th international conference Brno, August 28 - September 1, 1995; Brno, Masaryk Univ., 1996}, year = {1997}, language = {en} } @article{Schmidt1997, author = {Schmidt, Hans-J{\"u}rgen}, title = {Klassiker der Kosmologie}, year = {1997}, language = {de} } @article{SchmidtReuter1994, author = {Schmidt, Hans-J{\"u}rgen and Reuter, Stefan}, title = {Klassisch konform{\"a}quivalente Gravitationstheorien und deren korrespondierende Wheeler-de Witt-Gleichungen}, year = {1994}, language = {de} } @article{Schmidt1995, author = {Schmidt, Hans-J{\"u}rgen}, title = {Kurzautobiographie}, year = {1995}, language = {de} } @article{Schmidt1997, author = {Schmidt, Hans-J{\"u}rgen}, title = {Memorial notice to J. Huang}, year = {1997}, language = {en} } @article{GottloeberSchmidtStarobinskyetal.1992, author = {Gottl{\"o}ber, Stefan and Schmidt, Hans-J{\"u}rgen and Starobinsky, A. A. and M{\"u}ller, Volker}, title = {Models of chaotic inflation}, series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, volume = {1992, 08}, journal = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {24 S.}, year = {1992}, language = {en} } @article{Schmidt1997, author = {Schmidt, Hans-J{\"u}rgen}, title = {New conformal relations in fourth-order gravity}, year = {1997}, language = {en} } @article{Schmidt1997, author = {Schmidt, Hans-J{\"u}rgen}, title = {New steps towards a proof of the cosmological "no hair" theorem}, isbn = {981-023499-6}, year = {1997}, language = {en} } @article{DzhunushalievSchmidt2000, author = {Dzhunushaliev, Vladimir and Schmidt, Hans-J{\"u}rgen}, title = {New vacuum solutions of conformal Weyl gravity}, year = {2000}, language = {en} } @article{CapozzielloLambiaseSchmidt2000, author = {Capozziello, Salvatore and Lambiase, G. and Schmidt, Hans-J{\"u}rgen}, title = {Nonminimal derivative couplings and inflation in generalized theories of gravity}, year = {2000}, language = {en} } @article{Schmidt2000, author = {Schmidt, Hans-J{\"u}rgen}, title = {On a new conformal duality of spherically symmetric space-times}, year = {2000}, language = {en} } @article{Schmidt2000, author = {Schmidt, Hans-J{\"u}rgen}, title = {On a new conformal duality of spherically symmetric space-times}, year = {2000}, language = {en} } @article{GorbatenkoPushkinSchmidt2002, author = {Gorbatenko, M. V. and Pushkin, A. V. and Schmidt, Hans-J{\"u}rgen}, title = {On a relation between the Bach equation and the equation of geometrodynamics}, year = {2002}, abstract = {The Bach equation and the equation of geometrodynamics are based on two quite different physical motivations, but in both approaches, the conformal properties of gravitation plays the key role. In this paper we present an analysis of the relation between these two equations and show that the solutions of the equation of geometrodynamics are of a more general nature. We show the following non-trivial result: there exists a conformally invariant Lagrangian, whose field equation generalizes the Bach equation and has as solutions those Ricci tensors which are solutions to the equation of geometrodynamics.}, language = {en} } @article{Schmidt1995, author = {Schmidt, Hans-J{\"u}rgen}, title = {On space-times which cannot be distinguished by curvature invariants}, year = {1995}, language = {en} } @article{Schmidt1995, author = {Schmidt, Hans-J{\"u}rgen}, title = {On the space of 3-dimensional homogeneous Riemannian manifolds}, year = {1995}, language = {en} } @article{Schmidt2011, author = {Schmidt, Hans-J{\"u}rgen}, title = {Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole}, issn = {1550-7998}, year = {2011}, abstract = {We deduce a new formula for the perihelion advance \$Theta\$ of a test particle in the Schwarzschild black hole by applying a newly developed non-linear transformation within the Schwarzschild space-time. By this transformation we are able to apply the well-known formula valid in the weak-field approximation near infinity also to trajectories in the strong-field regime near the horizon of the black hole. The resulting formula has the structure \$Theta = c_1 - c_2 ln(c^2_3 - e^2) \$ with positive constants \$c_{1,2,3}\$ depending on the angular momentum of the test particle. It is especially useful for orbits with large eccentricities \$e < c_3 < 1\$ showing that \$Theta o infty\$ as \$e o c_3\$.}, language = {en} } @article{Schmidt2011, author = {Schmidt, Hans-J{\"u}rgen}, title = {Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole}, series = {Physical review : D, Particles, fields, gravitation, and cosmology}, volume = {83}, journal = {Physical review : D, Particles, fields, gravitation, and cosmology}, number = {12}, publisher = {American Physical Society}, address = {College Park}, issn = {1550-7998}, doi = {10.1103/PhysRevD.83.124010}, pages = {9}, year = {2011}, abstract = {We deduce a new formula for the perihelion advance Theta of a test particle in the Schwarzschild black hole by applying a newly developed nonlinear transformation within the Schwarzschild space-time. By this transformation we are able to apply the well-known formula valid in the weak-field approximation near infinity also to trajectories in the strong-field regime near the horizon of the black hole. The resulting formula has the structure Theta = c(1) - c(2) ln(c(3)(2) - e(2)) with positive constants c(1,2,3) depending on the angular momentum of the test particle. It is especially useful for orbits with large eccentricities e < c(3) < 1 showing that Theta -> infinity as e -> c(3).}, language = {en} } @article{Schmidt2008, author = {Schmidt, Hans-J{\"u}rgen}, title = {Perihelion precession for modified Newtonian gravity}, issn = {1550-7998}, year = {2008}, abstract = {We calculate the perihelion precession for nearly circular orbits in a central potential V(r). Differently from other approaches to this problem, we do not assume that the potential is close to the Newtonian one. The main idea in the deduction is to apply the underlying symmetries of the system, and to use the transformation behaviour in a rotating system of reference. This is equivalent to say, that the effective potential can be written in a one-parameter set of possibilities as sum of centrifugal potential and potential of the central force.}, language = {en} } @article{BachmannSchmidt2000, author = {Bachmann, Michael and Schmidt, Hans-J{\"u}rgen}, title = {Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology}, year = {2000}, language = {en} } @article{BachmannSchmidt1999, author = {Bachmann, Michael and Schmidt, Hans-J{\"u}rgen}, title = {Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology}, series = {General relativity and quantum cosmology : preprints gr-qc}, volume = {9912068}, journal = {General relativity and quantum cosmology : preprints gr-qc}, year = {1999}, language = {en} } @article{Schmidt1994, author = {Schmidt, Hans-J{\"u}rgen}, title = {Personengenau und sehr prononciert : Leserbrief}, year = {1994}, language = {de} } @article{Schmidt1997, author = {Schmidt, Hans-J{\"u}rgen}, title = {Pictorial examples that distinguish covariant and contravariant vectors}, year = {1997}, language = {en} } @article{Schmidt2005, author = {Schmidt, Hans-J{\"u}rgen}, title = {Schwarzschild and Synge once again}, issn = {0001-7701}, year = {2005}, abstract = {We complete the historical overview about the geometry of a Schwarzschild black hole at its horizon by emphasizing the contribution made by Synge in [6] to its clarification}, language = {en} } @article{DzhunushalievRurenkoSchmidt2002, author = {Dzhunushaliev, Vladimir and Rurenko, O. and Schmidt, Hans-J{\"u}rgen}, title = {Spherically symmetric solutions in multidimensional gravity with the SU(2) gauge group as the extra dimensions}, year = {2002}, language = {en} } @article{Schmidt1994, author = {Schmidt, Hans-J{\"u}rgen}, title = {Stability and Hamiltonian formulation of higher derivative theories}, year = {1994}, language = {en} } @article{SchmidtKasperKluskeetal.1995, author = {Schmidt, Hans-J{\"u}rgen and Kasper, Uwe and Kluske, Sabine and Rainer, Martin and Reuter, Stefan}, title = {Stability properties of the Starobinsky cosmological model}, year = {1995}, language = {en} } @article{Schmidt1999, author = {Schmidt, Hans-J{\"u}rgen}, title = {The classical solutions of two-dimensional gravity}, year = {1999}, language = {en} } @article{SchmidtRainer1995, author = {Schmidt, Hans-J{\"u}rgen and Rainer, Martin}, title = {The natural classification of real lie algebras}, year = {1995}, language = {en} } @article{Schmidt2003, author = {Schmidt, Hans-J{\"u}rgen}, title = {The square of the Weyl tensor can be negative}, year = {2003}, abstract = {We show that the square of the Weyl tensor can be negative by giving an example}, language = {en} } @article{Schmidt2013, author = {Schmidt, Hans-J{\"u}rgen}, title = {The tetralogy of Birkhoff theorems}, series = {General relativity and gravitation}, volume = {45}, journal = {General relativity and gravitation}, number = {2}, publisher = {Springer}, address = {New York}, issn = {0001-7701}, doi = {10.1007/s10714-012-1478-5}, pages = {395 -- 410}, year = {2013}, abstract = {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.}, language = {en} } @article{Schmidt2013, author = {Schmidt, Hans-J{\"u}rgen}, title = {The tetralogy of Birkhoff theorems}, issn = {0001-7701}, year = {2013}, abstract = {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.}, language = {en} } @article{Schmidt2000, author = {Schmidt, Hans-J{\"u}rgen}, title = {Topologische Aspekte in der Kosmologie}, year = {2000}, language = {de} } @article{KluskeSchmidt1996, author = {Kluske, Sabine and Schmidt, Hans-J{\"u}rgen}, title = {Towards a cosmic no hair theorem for higher-order gravity}, year = {1996}, language = {en} } @article{GurovichSchmidtTokareva2001, author = {Gurovich, Viktor and Schmidt, Hans-J{\"u}rgen and Tokareva, Ira}, title = {Tunneling of the closed Friedmann Universe with generation of scalar waves}, year = {2001}, abstract = {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.}, language = {en} } @article{SchmidtMignemi1995, author = {Schmidt, Hans-J{\"u}rgen and Mignemi, Salvatore}, title = {Two-dimensional higher-derivative gravity and conformal transformations}, year = {1995}, language = {en} } @article{Schmidt2005, author = {Schmidt, Hans-J{\"u}rgen}, title = {Untitled}, year = {2005}, language = {de} } @article{CanforaSchmidt2003, author = {Canfora, Fabrizio and Schmidt, Hans-J{\"u}rgen}, title = {Vacuum solutions which cannot be written in diagonal form}, year = {2003}, abstract = {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.}, language = {en} } @article{Schmidt1996, author = {Schmidt, Hans-J{\"u}rgen}, title = {Why do all the curvature invariants of a gravitational wave vanish?}, year = {1996}, language = {en} } @article{Schmidt1994, author = {Schmidt, Hans-J{\"u}rgen}, title = {WIP-Projekt "Kosmologie"}, year = {1994}, language = {de} } @article{DzhunushalievSchmidt2000, author = {Dzhunushaliev, Vladimir and Schmidt, Hans-J{\"u}rgen}, title = {Wormholes and Flux Tubes in the 7D Gravity on the Principal Bundle with SU(2) Gauge Group as the Extra Dimensions}, year = {2000}, language = {en} } @article{SchmidtBaierBleyeretal.1994, author = {Schmidt, Hans-J{\"u}rgen and Baier, Frank W. and Bleyer, Ulrich and Hubrig, Swetlana and Meister, Claudia-Veronika and Schilbach, Elena and Tiersch, Heinz}, title = {Zum Wissenschaftler-Integrationsprogramm}, year = {1994}, language = {de} }