Multi-body spherically symmetric steady states of Newtonian self-gravitating elastic matter

We study the problem of static, spherically symmetric, self-gravitating elastic matter distributions in Newtonian gravity. To this purpose we first introduce a new definition of homogeneous, spherically symmetric (hyper)elastic body in Euler coordinates, i.e., in terms of matter fields defined on the current physical state of the body. We show that our definition is equivalent to the classical one existing in the literature and which is given in Lagrangian coordinates, i.e., in terms of the deformation of the body from a given reference state. After a number of well-known examples of constitutive functions of elastic bodies are re-defined in our new formulation, a detailed study of the Seth model is presented. For this type of material the existence of single and multi-body solutions is established.Comment: 33 pages, 1 figure. v2 matches final published versio

On dynamical systems approaches and methods in f(R)f(R) cosmology

We discuss dynamical systems approaches and methods applied to flat Robertson-Walker models in $f(R)$-gravity. We argue that a complete description of the solution space of a model requires a global state space analysis that motivates globally covering state space adapted variables. This is shown explicitly by an illustrative example, $f(R) = R + \alpha R^2$, $\alpha > 0$, for which we introduce new regular dynamical systems on global compactly extended state spaces for the Jordan and Einstein frames. This example also allows us to illustrate several local and global dynamical systems techniques involving, e.g., blow ups of nilpotent fixed points, center manifold analysis, averaging, and use of monotone functions. As a result of applying dynamical systems methods to globally state space adapted dynamical systems formulations, we obtain pictures of the entire solution spaces in both the Jordan and the Einstein frames. This shows, e.g., that due to the domain of the conformal transformation between the Jordan and Einstein frames, not all the solutions in the Jordan frame are completely contained in the Einstein frame. We also make comparisons with previous dynamical systems approaches to $f(R)$ cosmology and discuss their advantages and disadvantages.Comment: 36 pages, 7 figures. v2: references added, matches published versio

Dynamic AdS/QCD and the spectrum of walking gauge theories

We present a simple AdS/QCD model in which the formation of the chiral condensate is dynamically determined. The gauge dynamics is input through the running of the quark bilinear’s anomalous dimension, ?. The condensate provides a dynamically generated infrared wall in the computation of mesonic bound state masses and decay constants. As an example, we use the model, with perturbative computations of the running of ?, to study SU(3) gauge theory with a continuous number of quark flavors, Nf. We follow the behavior of the spectrum as we approach the conformal window through a walking gauge theory regime. We show such walking theories display a Berezinskii–Kosterlitz–Thoules phase transition, with Miransky scaling, as one approaches the edge of the conformal window at the critical value of Nf. We show that these walking theories possess an enhanced quark condensate, a light Higgs-like excitation, and argue that the nonperturbative contribution to S falls to zero. We also study the deformation of the Berezinskii–Kosterlitz–Thoules transition when the quarks have a current mass, which may be of use for understanding lattice simulations of walking theories