Vacuum polarization by a global monopole with finite core

We investigate the effects of a $(D+1)$-dimensional global monopole core on the behavior of a quantum massive scalar field with general curvature coupling parameter. In the general case of the spherically symmetric static core, formulae are derived for the Wightman function, for the vacuum expectation values of the field square and the energy-momentum tensor in the exterior region. These expectation values are presented as the sum of point-like global monopole part and the core induced one. The asymptotic behavior of the core induced vacuum densities is investigated at large distances from the core, near the core and for small values of the solid angle corresponding to strong gravitational fields. In particular, in the latter case we show that the behavior of the vacuum densities is drastically different for minimally and non-minimally coupled fields. As an application of general results the flower-pot model for the monopole's core is considered and the expectation values inside the core are evaluated.Comment: 22 pages, 4 figures, misprint is corrected, discussion is added, figures are change

Topological Effects in a Fermionic Condensate Induced by a Cosmic String and Compactification on the AdS Bulk

In this paper, we analyzed the fermionic condensate (FC) associated with a massive fermionic field on a five-dimensional anti-de Sitter (AdS) spacetime in the presence of a cosmic string taking into account a magnetic flux running along its core. In addition, a compactified dimension was considered. Due to this compactification, the FC is expressed in terms of two distinct contributions: the first one corresponds to the geometry without compactification, and the second one is induced by the compactification. Depending on the values of the physical parameters, the total FC can be positive or negative. As a limiting case, the expression for the FC on locally Minkowski spacetime was derived. It vanishes for a massless fermionic field, and the nonzero FC on the AdS background space in the massless case is an effect induced by gravitation. This shows that the gravitational field may essentially influence the parameter space for phase transitions. For a massive field, the FC diverges on the string as the inverse cube of the proper distance from the string. In the case of a massless field, depending on the magnetic flux along the string and planar angle deficit, the limiting value of the FC on the string can be either finite or infinite. At large distances, the decay of the FC as a function of the distance from the string is a power law for both cases of massive and massless fields. For a cosmic string on the Minkowski bulk and for a massive field, the decay is exponential. The topological part in the FC vanishes on the AdS boundary. We show that the FCs coincide for the fields realizing two inequivalent irreducible representations of the Clifford algebra. In the special case of the zero planar angle deficit, the results presented in this paper describe Aharonov–Bohm-type effects induced by magnetic fluxes in curved spacetime

Diminishing benefits of urban living for children and adolescents’ growth and development

Optimal growth and development in childhood and adolescence is crucial for lifelong health and well-being1–6. Here we used data from 2,325 population-based studies, with measurements of height and weight from 71 million participants, to report the height and body-mass index (BMI) of children and adolescents aged 5–19 years on the basis of rural and urban place of residence in 200 countries and territories from 1990 to 2020. In 1990, children and adolescents residing in cities were taller than their rural counterparts in all but a few high-income countries. By 2020, the urban height advantage became smaller in most countries, and in many high-income western countries it reversed into a small urban-based disadvantage. The exception was for boys in most countries in sub-Saharan Africa and in some countries in Oceania, south Asia and the region of central Asia, Middle East and north Africa. In these countries, successive cohorts of boys from rural places either did not gain height or possibly became shorter, and hence fell further behind their urban peers. The difference between the age-standardized mean BMI of children in urban and rural areas was <1.1 kg m–2 in the vast majority of countries. Within this small range, BMI increased slightly more in cities than in rural areas, except in south Asia, sub-Saharan Africa and some countries in central and eastern Europe. Our results show that in much of the world, the growth and developmental advantages of living in cities have diminished in the twenty-first century, whereas in much of sub-Saharan Africa they have amplified