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New conformal-metric solutions for continuous distributions of disclination-like defects.

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Title: New conformal-metric solutions for continuous distributions of disclination-like defects.
Authors: Carvalho, A. M. de M.1 (AUTHOR) alexandre@fis.ufal.br, Garcia, G. Q.2 (AUTHOR) gqgarcia99@gmail.com, Furtado, C.3 (AUTHOR) furtado@fisica.ufpb.br
Source: International Journal of Modern Physics A: Particles & Fields; Gravitation; Cosmology; Nuclear Physics. 2/20/2026, Vol. 41 Issue 5, p1-16. 16p.
Subjects: Disclinations, Conformal geometry, Poisson's equation, Gauss-Bonnet theorem, Gaussian distribution, Topological defects (Physics)
Abstract: In this paper, we develop a conformal formulation for two-dimensional geometries sourced by continuous distributions of topological defects, reducing the problem to a Poisson equation for the conformal factor. Throughout, we focus on radially symmetric, curvature-type (disclination-like) defect distributions in a torsion-free geometry. Closed-form solutions are obtained for Gaussian, exponential and power-law (1 ∕ r) profiles. The Gaussian profile yields a regular core and an asymptotically flat far field. The exponential profile is treated on the punctured plane (r > 0), producing sharply localized curvature with finite total flux. For the 1 ∕ r case, we work on the punctured plane (or on annuli), obtaining an exterior logarithmic solution that encodes a conical geometry; more general power-law profiles require finite domains or decay to ensure integrability. In all cases, Gauss–Bonnet on annuli provides a global relation equating total curvature (holonomy/deficit angle) to the integrated defect density, while the δ -limit reproduces the standard conical geometry with distributional curvature. The framework offers a unified, physically motivated description of finite-core disclination-like defects relevant to analog gravity and two-dimensional material systems. [ABSTRACT FROM AUTHOR]
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Abstract:In this paper, we develop a conformal formulation for two-dimensional geometries sourced by continuous distributions of topological defects, reducing the problem to a Poisson equation for the conformal factor. Throughout, we focus on radially symmetric, curvature-type (disclination-like) defect distributions in a torsion-free geometry. Closed-form solutions are obtained for Gaussian, exponential and power-law (1 ∕ r) profiles. The Gaussian profile yields a regular core and an asymptotically flat far field. The exponential profile is treated on the punctured plane (r > 0), producing sharply localized curvature with finite total flux. For the 1 ∕ r case, we work on the punctured plane (or on annuli), obtaining an exterior logarithmic solution that encodes a conical geometry; more general power-law profiles require finite domains or decay to ensure integrability. In all cases, Gauss–Bonnet on annuli provides a global relation equating total curvature (holonomy/deficit angle) to the integrated defect density, while the δ -limit reproduces the standard conical geometry with distributional curvature. The framework offers a unified, physically motivated description of finite-core disclination-like defects relevant to analog gravity and two-dimensional material systems. [ABSTRACT FROM AUTHOR]
ISSN:0217751X
DOI:10.1142/S0217751X26500454