New Solutions for Topological Defects with Continuous Distributions:A Conformal Metric Perspective
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909679571959808 |
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| author | Carvalho, A. M. de M. Garcia, G. Q. Furtado, C. |
| author_facet | Carvalho, A. M. de M. Garcia, G. Q. Furtado, C. |
| contents | We present new exact solutions for two-dimensional geometries generated by continuous distributions of topological defects within a conformal metric framework. By reformulating Einstein's equations in two dimensions as a Poisson equation for the conformal factor, we analyze how smooth defect densities -- such as Gaussian, exponential, and power-law profiles -- regularize curvature singularities and encode nontrivial topological information. Each distribution yields a well-defined geometry that interpolates between localized curvature near the defect core and asymptotic flatness. We compute the Ricci scalar and total curvature, confirming consistency with the Gauss-Bonnet theorem. Our results provide a unified geometric description of regularized disclination-like defects and offer insights into analog gravity, crystalline materials, and two-dimensional systems with emergent curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06117 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New Solutions for Topological Defects with Continuous Distributions:A Conformal Metric Perspective Carvalho, A. M. de M. Garcia, G. Q. Furtado, C. General Relativity and Quantum Cosmology We present new exact solutions for two-dimensional geometries generated by continuous distributions of topological defects within a conformal metric framework. By reformulating Einstein's equations in two dimensions as a Poisson equation for the conformal factor, we analyze how smooth defect densities -- such as Gaussian, exponential, and power-law profiles -- regularize curvature singularities and encode nontrivial topological information. Each distribution yields a well-defined geometry that interpolates between localized curvature near the defect core and asymptotic flatness. We compute the Ricci scalar and total curvature, confirming consistency with the Gauss-Bonnet theorem. Our results provide a unified geometric description of regularized disclination-like defects and offer insights into analog gravity, crystalline materials, and two-dimensional systems with emergent curvature. |
| title | New Solutions for Topological Defects with Continuous Distributions:A Conformal Metric Perspective |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2507.06117 |