Classical and semiclassical probes of dimension-dependent effective geometries

Abstract

We introduce and analyze two static, spherically symmetric effective geometries with explicit dependence on the number of spatial dimensions, motivated by defect-like configurations supported by anisotropic stress–energy. The resulting backgrounds exhibit distinct global properties: One is non-asymptotically flat, while the other contains a curvature singularity whose influence on semiclassical observables can be systematically controlled through a near-core expansion. Classical properties are investigated using effective gravitational potentials, null geodesics, and gravitational lensing. We find either saturated or short-ranged deflection profiles that differ qualitatively from the Schwarzschild and Tangherlini cases and depend sensitively on the spatial dimension. The associated effective energy density, isotropic pressure, and anisotropic stress display a pronounced dimension-dependent structure, indicating a crossover in the stress–energy behavior driven by dimensionality. As a semiclassical probe, we study massless scalar two-point functions in a conformal vacuum and obtain a dimension-dependent spectral behavior near the defect core. These results identify a regime in which global geometric features and stress anisotropy, rather than local curvature alone, dominate both classical and semiclassical observables.