Global monopole in Palatinif(R)gravity

Abstract

We consider the space-time metric generated by a global monopole in an extension of General Relativity (GR) of the form f (R) = R − λR 2 . The theory is formulated in the metric-affine (or Palatini) formalism and exact analytical solutions are obtained. For λ < 0, one finds that the solution has the same characteristics as the Schwarzschild black hole with a monopole charge in Einstein's GR. For λ > 0, instead, the metric is more closely related to the Reissner-Nordström metric with a monopole charge and, in addition, it possesses a wormhole-like structure that allows for the geodesic completeness of the space-time. Our solution recovers the expected limits when λ = 0 and also at the asymptotic far limit. The angular deflection of light in this spacetime in the weak field regime is also calculated. *

Kinetics of crystalline nuclei growth in glassy systems

“…In the given study, we focus on the crystalline nuclei growth in glasses at deep levels of supercooling. At such the thermodynamic conditions, the steady-state growth rate υ (st) is defined mainly by the kinetic term g + (N ) and, thereby, it increases with the temperature T , that is opposite to well-known behavior of the growth rate observable experimentally in the systems at low and moderate levels of supercooling [42][43][44].…”

“…General patterns in the temperature dependencies of the growth rate detectable for various crystallizing systems [42,44] indicates that a unified theoretical description of the growth rate as a function of the tempera-ture as well as direct comparison of the experimental data for the systems by means of scaling relations are possible. As an attempt to do such the comparison, one can mention the corresponding part in Langer's review [51] (Fig.…”

“…The mixed growth regimes can also arise with the noninteger values of the parameter p [25,26]. This is seen from kinetic growth models (41), (42) and (43) given in Appendix. In particular, it is quite reasonable to expect that non-integer values of the parameter p will be at growth of a nucleus of near-critical sizes, since there is no clearly defined regime of growth at such sizes, while stochastic effects in the post-nucleation growth are significant.…”

“…Tm Tg υ (g) R χ g (g) Nc ς Dz (at P = 14ε/σ 3 ) 1.51 ε/kB 0.65 ε/kB (23.8 ± 2.7) · 10 −4 σ/τ 0.37 ± 0.06 (13.9 ± 1.6) · τ −1 0.31 ± 0.04 bLJ (at P = 17ε/σ 3 ) 1.65 ε/kB 0.92 ε/kB (4.7 ± 0.7) · 10 −4 σ/τ 0.41 ± 0.07 (13.1 ± 1.5) · τ −1 0.58 ± 0.06 [ vs. reduced temperature T . Such the plot allows one to compare the simulation results for the glassy Dz-and bLJ-systems, the simulation results for the supercooled LJ-system [41] and tantal [15], the experimental data for the supercooled SiO2 [42], PbO·SiO2 [42], Li2O·2SiO2 [6], Li2O·3SiO2 [43], CaO·MgO·2SiO2 [44] and 2MgO·2Al2O3 · 5SiO2 [44]. The dashed line reproduces the master-curve (20).…”

Static traversable wormholes in f(R,T)=R+2αlnT gravity

“…(r + 2) − e r 0 −r r 2 (sinh(r) − 1) − α r + sinh(r) + 1 (36) p r = (r + 2) sinh(r) 16π − e r 0 −r r 2 (sinh(r) − 1) − α r + sinh(r) + 1 (37) ρ = ((r − 2) sinh(r) − 2r) 16π − e r 0 −r r 2 (sinh(r) − 1) − α r + sinh(r) + 1 (38) Using Equations (36)- (38), we get the following terms:…”