Thermodynamics and Phase Transition in Shapere-Wilczek {\it fgh} model: Cosmological Time Crystal in Quadratic Gravity

The Shapere-Wilczek model \cite{wil}, or so called $fgh$ model, enjoys the remarkable features of a Time Crystal (TC) that has a non-trivial time dependence in its lowest energy state (or the classical ground state). We construct a particular form of $fgh$ model (with specified $f,g,h$ functions) that is derived from a Mini-superspace version of a quadratic $f(R,R_{\mu\nu})$ gravity theory. Main part of the investigation deals with thermodynamic properties of such systems from classical statistical mechanics perspective. Our analysis reveals the possibility of a {\it phase transition}. Because of the higher (time) derivative nature of the model computation of the partial function is non-trivial and requires newly discovered techniques. We speculate about possible connection between our model and the Multiverse scenario.Comment: 9 pages including supplements, 6 captioned figures; title has been changed, some references are added; version accepted for publication in Physics Letters

Motion of charged particle in Reissner–Nordström spacetime: a Jacobi-metric approach

Abstract The present work discusses motion of neutral and charged particles in Reissner–Nordström spacetime. The constant energy paths are derived in a variational principle framework using the Jacobi metric which is parameterized by conserved particle energy. Of particular interest is the case of particle charge and Reissner–Nordström black hole charge being of same sign, since this leads to a clash of opposing forces—gravitational (attractive) and Coulomb (repulsive). Our paper aims to complement the recent work of Pugliese et al. (Eur Phys J C 77:206. arXiv:1304.2940 , 2017; Phys Rev D 88:024042. arXiv:1303.6250 , 2013). The energy dependent Gaussian curvature (induced by the Jacobi metric) plays an important role in classifying the trajectories