Exploring Torus Black-Holes In (1+3)- Dimensions: A Novel Approach to Higher Genus Solution

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E. GarcÌa-Rodriguez
E. GarcÌa-Rodriguez
2
M. Medina
M. Medina
3
J. A. Nieto
J. A. Nieto

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A torus black-hole solution of the vacuum gravitational field equation of general relativity in (1 + 3)-dimensions is obtained. Starting with a metric ansatz associated with the torus, our method is based on straightforward computations the usual geometric mathematical tools of the Christoffel symbols and the Riemann tensor. Specifically, after deriving such mathematical tools the field equations of general relativity are considered. The resultatning equations are properly combained to find the solution. Moreover, the novelty and potential implications of this solution emerges from the fact that is based on a coordinate transformation metric ansatz. This provides with broad implications and future research directions. In particular we argue that our formalism can properly be used for a search of higher genus black-hole solution.

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No external funding was declared for this work.

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The authors declare no conflict of interest.

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E. GarcÌa-Rodriguez. 2026. \u201cExploring Torus Black-Holes In (1+3)- Dimensions: A Novel Approach to Higher Genus Solution\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 24 (GJSFR Volume 24 Issue F2): .

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High-quality image of a black hole torus structure in complex 3D space.
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Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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January 20, 2025

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A torus black-hole solution of the vacuum gravitational field equation of general relativity in (1 + 3)-dimensions is obtained. Starting with a metric ansatz associated with the torus, our method is based on straightforward computations the usual geometric mathematical tools of the Christoffel symbols and the Riemann tensor. Specifically, after deriving such mathematical tools the field equations of general relativity are considered. The resultatning equations are properly combained to find the solution. Moreover, the novelty and potential implications of this solution emerges from the fact that is based on a coordinate transformation metric ansatz. This provides with broad implications and future research directions. In particular we argue that our formalism can properly be used for a search of higher genus black-hole solution.

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Exploring Torus Black-Holes In (1+3)- Dimensions: A Novel Approach to Higher Genus Solution

E. GarcÌa-Rodriguez
E. GarcÌa-Rodriguez
M. Medina
M. Medina
J. A. Nieto
J. A. Nieto

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