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 - 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 - 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 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 -