@book{SchmidtWang1992, author = {Schmidt, Hans-J{\"u}rgen and Wang, Anzhong}, title = {Plane domain walls when coupled with the Brans-Dicke scalar field}, series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, volume = {1992, 06}, journal = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {27 S.}, year = {1992}, 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 = {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{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{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{SchmidtRainer1995, author = {Schmidt, Hans-J{\"u}rgen and Rainer, Martin}, title = {Inhomogeneous cosmological models with homogeneous inner hypersurface geometry}, year = {1995}, 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} } @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} } @book{SchmidtMignemi1995, author = {Schmidt, Hans-J{\"u}rgen and Mignemi, Salvatore}, title = {Two-dimensional higher-derivative gravity and conformal transformations}, year = {1995}, language = {en} }