Modeling Wormholes Generated by Dark Matter Galactic Halos in f(R)$f(R)$ Modified Gravity

Wormholes (WHs) are hypothetical topologically non-trivial spacetime structures that can be freely traversed by observers and connect two asymptotic regions or infinities. From the current theoretical development, the prospect of their existence is challenging but cannot be excluded. In this paper, generalized Ellis–Bronikov (GEB) traversable WH geometries for static and spherically symmetric spacetime in the background of $f(R)$ gravity is explored. First, the Tsujikawa-like $f(R)$ model and the shape function for the GEB model is considered, which depend on a sequence of simple Lorentzian WHs with two parameters: a free even integer exponent, n, besides the throat radius, r₀. One also consider that these WHs are generated by dark matter galactic halos (DMGHs), based on the three most common phenomenological models, viz., Navarro–Frenk–White (NFW), Thomas–Fermi (TF), and pseudo-isothermal (PI). In this concern, the satisfaction of the energy conditions (ECs) which are dependent on the dark matter (DM) models, viz., dominant energy condition (DEC) and strong energy condition (SEC) and those which are not dependent viz., null energy condition (NEC) and WEC at the WH throat and its neighborhood is investigated. Finally, the presence of exotic matter is confirmed by the violation of the NEC in all cases, revealing the supremacy and physical acceptability to support the existence of the WHs and making them compatible and traversable in Tsujikawa's-like $f(R)$ model.     

Static and Dynamic Magnetic Properties of a Co(II)-Complex with N2O2 Donor Set – A Theoretical and Experimental Study

A representative Co(II) based single ion magnet (SIM) with N₂O₂ donor set and distorted pseudo-tetrahedral geometry has been synthesized and characterized to study the atomic and electronic structure. DC magnetometry results have been evaluated by means of a phenomenological Hamiltonian approach regarding zero field splitting (ZFS) parameters and compared with results from ab-initio multi-reference CASSCF (complete active space self-consistent field) calculations and qualitative ligand field theory (AILFT). Profound investigation of spin-lattice relaxation with the variation of temperature (from 1.8 to about 8 K) and magnetic field (at 14 different fields from zero up to 1 T) have been performed based on AC magnetometry. Under an applied dc magnetic field, spin-lattice relaxation occurs via a direct process with T² temperature dependence due to limited heat transfer at very low temperature and above 5 K relaxation by an Orbach process with an energy barrier of ≈80 K dominates.