TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Baier, Frank W. A1 - Bleyer, Ulrich A1 - Hubrig, Swetlana A1 - Meister, Claudia-Veronika A1 - Schilbach, Elena A1 - Tiersch, Heinz T1 - Zum Wissenschaftler-Integrationsprogramm Y1 - 1994 ER - TY - JOUR A1 - Dzhunushaliev, Vladimir A1 - Schmidt, Hans-Jürgen T1 - Wormholes and Flux Tubes in the 7D Gravity on the Principal Bundle with SU(2) Gauge Group as the Extra Dimensions Y1 - 2000 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - WIP-Projekt "Kosmologie" Y1 - 1994 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 - 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 - JOUR A1 - Schmidt, Hans-Jürgen T1 - Untitled Y1 - 2005 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 - 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 - Kluske, Sabine T1 - Towards a no hair theorem for higher order gravit Y1 - 1995 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 - JOUR A1 - Schmidt, Hans-Jürgen T1 - Topologische Aspekte in der Kosmologie Y1 - 2000 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 - 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 A1 - Rainer, Martin T1 - The natural classification of real lie algebras Y1 - 1995 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 T1 - The classical solutions of two-dimensional gravity Y1 - 1999 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 - 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 - 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 - JOUR A1 - Schmidt, Hans-Jürgen T1 - Schwarzschild and Synge once again N2 - 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 Y1 - 2005 UR - http://arXiv.org/abs/gr-qc/0408017 SN - 0001-7701 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - Scale-invariant gravity in two dimensions II T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 03 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schmidt, Hans-Jürgen A1 - Wang, Anzhong T1 - Plane domain walls when coupled with the Brans-Dicke scalar field T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 06 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Pictorial examples that distinguish covariant and contravariant vectors Y1 - 1997 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - Physikalische Konsequenzen von Gravitationsfeldgleichungen vierter Ordnung bei der Beschreibung des frühen Universums und isolierter Gravitationsfelder Y1 - 1994 PB - Tectum CY - Marburg ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Personengenau und sehr prononciert : Leserbrief Y1 - 1994 ER - TY - JOUR A1 - Bachmann, Michael A1 - Schmidt, Hans-Jürgen T1 - Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology Y1 - 2000 ER - TY - JOUR A1 - Bachmann, Michael A1 - Schmidt, Hans-Jürgen T1 - Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology JF - General relativity and quantum cosmology : preprints gr-qc Y1 - 1999 VL - 9912068 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Perihelion precession for modified Newtonian gravity N2 - 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. Y1 - 2008 UR - http://arXiv.org/abs/0803.0920 SN - 1550-7998 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole N2 - 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 $e o c_3$. Y1 - 2011 UR - http://link.aps.org/doi/10.1103/PhysRevD.83.124010 SN - 1550-7998 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole JF - Physical review : D, Particles, fields, gravitation, and cosmology N2 - 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). Y1 - 2011 U6 - https://doi.org/10.1103/PhysRevD.83.124010 SN - 1550-7998 VL - 83 IS - 12 PB - American Physical Society CY - College Park ER - TY - BOOK A1 - Reuter, Stefan A1 - Schmidt, Hans-Jürgen T1 - On the Wheeler-de Witt equation for homogeneous cosmological models T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 11 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - On the space of 3-dimensional homogeneous Riemannian manifolds Y1 - 1995 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - On the de Sitter space-time : the geometric foundation of infaltionary cosmology T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 10 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - On space-times which cannot be distinguished by curvature invariants Y1 - 1995 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - On inflation within closed Fiedmann universe models T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 02 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Gorbatenko, M. V. A1 - Pushkin, A. V. A1 - Schmidt, Hans-Jürgen T1 - On a relation between the Bach equation and the equation of geometrodynamics N2 - 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. Y1 - 2002 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - On a new conformal duality of spherically symmetric space-times Y1 - 2000 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - On a new conformal duality of spherically symmetric space-times Y1 - 2000 ER - TY - JOUR A1 - Capozziello, Salvatore A1 - Lambiase, G. A1 - Schmidt, Hans-Jürgen T1 - Nonminimal derivative couplings and inflation in generalized theories of gravity Y1 - 2000 ER - TY - JOUR A1 - Dzhunushaliev, Vladimir A1 - Schmidt, Hans-Jürgen T1 - New vacuum solutions of conformal Weyl gravity Y1 - 2000 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - New steps towards a proof of the cosmological "no hair" theorem Y1 - 1997 SN - 981-023499-6 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - New conformal relations in fourth-order gravity Y1 - 1997 ER - TY - JOUR A1 - Gottlöber, Stefan A1 - Schmidt, Hans-Jürgen A1 - Starobinsky, A. A. A1 - Müller, Volker T1 - Models of chaotic inflation JF - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 08 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Memorial notice to J. Huang Y1 - 1997 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Kurzautobiographie Y1 - 1995 ER - TY - BOOK A1 - Reuter, Stefan A1 - Schmidt, Hans-Jürgen T1 - Klassisch konformäquivalente Gravitationstheorien und deren korrespondierende Wheeler-de-Witt-Gleichungen T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 05 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Reuter, Stefan T1 - Klassisch konformäquivalente Gravitationstheorien und deren korrespondierende Wheeler-de Witt-Gleichungen Y1 - 1994 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Klassiker der Kosmologie Y1 - 1997 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Karsinski, A., Inhomogeneous cosmological models; Cambridge, Univ. Press, 1997 BT - Inhomogeneous cosmological models Y1 - 1998 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - 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 BT - Differential geometry and applications : proceedings of the 6th international conference Brno, August 28 - September 1, 1995 Y1 - 1997 ER - TY - JOUR A1 - Meister, Claudia-Veronika A1 - Schmidt, Hans-Jürgen T1 - Jahresberichte 1996 Y1 - 1997 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Jahresbericht 1993 Y1 - 1994 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Singleton, Douglas T1 - Isotropic universe with almost scale-invariant fourth-order gravity JF - Journal of mathematical physics N2 - 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. Y1 - 2013 U6 - https://doi.org/10.1063/1.4808255 SN - 0022-2488 VL - 54 IS - 6 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Singleton, Douglas T1 - Isotropic universe with almost scale-invariant fourth-order gravity N2 - 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. Y1 - 2013 UR - http://arxiv.org/abs/1212.1769 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Rainer, Martin T1 - Inhomogeneous cosmological models with homogeneous inner hypersurface geometry Y1 - 1995 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - How to measure spatial distances? T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1995 VL - 1995, 10 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - How should we measure spatial distances? Y1 - 1996 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Gravitation in 1+1 Dimensionen : exacte Lösungen, Konformrelationen und Beziehungen zum 3+1 -dimensionalen Fall Y1 - 1998 ER - TY - JOUR A1 - Amendola, Luca A1 - Battaglia Mayer, Alexandra A1 - Capozziello, Salvatore A1 - Gottlöber, Stefan A1 - Müller, Volker A1 - Occhionero, Franco A1 - Schmidt, Hans-Jürgen T1 - Generalized sixth-order gravity and inflation JF - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 04 PB - Univ. CY - Potsdam 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 - 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 - 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 - 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 - Dzhunushaliev, Vladimir A1 - Schmidt, Hans-Jürgen T1 - Flux Tubes in Weyl Gravity Y1 - 2000 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 - 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 - 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 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 - Eichfeldtheorie Y1 - 2000 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Editorïs note Y1 - 1999 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 - Editor's note to A. Sakharov Y1 - 2000 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen A1 - Kasper, Uwe T1 - Differentialgeometrische Grundlagen der Kosmologie Y1 - 1995 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 - 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 - 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 - JOUR A1 - Schmidt, Hans-Jürgen T1 - Consequences of the noncompactness of the Lorentz group Y1 - 1998 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - Consequences of the noncompactness of the Lorentz group Y1 - 1995 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - Consequences of the noncompactness of the Lorentz group T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1995 VL - 1995, 09 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Conformal relations and Hamiltonian formlation of fourth-order gravity Y1 - 1997 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - Comment to a paper by J. Simon in Phys. Rev. D 45 (1992) 1953 T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1993 VL - 1993, 06 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Comment on stability of the semiclassical Einstein equation Y1 - 1994 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Comment on conformal transformations single out a unique measure of distance Y1 - 1995 ER - TY - JOUR A1 - Mignemi, Salvatore A1 - Schmidt, Hans-Jürgen T1 - Classification of multidimensional inflationary models Y1 - 1998 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Classical mechanics with lapse Y1 - 1996 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Cercignani, C., Scaling limits and models in physical process; Basel, Birkhäuser, 1998 BT - Scaling limits and models in physical process Y1 - 1999 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Aufgaben zur Kosmologie Y1 - 1994 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - An alternate Hamiltonian formulation of fourth-order theories Y1 - 1995 CY - Potsdam ER - TY - BOOK A1 - Schmidt, Hans-Jürgen T1 - An alternate Hamiltonian formulation of fourth-order theories T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 12 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Allgemeine Relativitätstheorie Y1 - 2000 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - A two-dimensional representation of four-dimensional graviational waves Y1 - 1998 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - A new proof of Birkhoffïs theorem Y1 - 1997 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - A new duality transformation for fouth-order gravity Y1 - 1997 ER -