Mathematical Journey to Relativity

Euclidean and Non--Euclidean Geometries: How they appear.- Basic Facts in Euclidean and Minkowski Plane Geometry.- From Projective Geometry to Poincare Disk. How to carry out a Non-Euclidean Geometry Model.- Revisiting the Differential Geometry of Surfaces in 3D-Spaces.- Basic Differential Geometry Concepts and their Applications.- Differential Geometry at Work: Two Ways of Thinking the Gravity. The Einstein Field Equations from a Geometric Point of View.- Differential Geometry at Work: Euclidean, Non-Euclidean and Elliptic Geometric Models from Geometry and Physics.- Gravity in Newtonian Mechanics.- Special Relativity.- General Relativity and Relativistic Cosmology.- A Geometric Realization of Relativity: the de Sitter Spacetime.- Another Geometric Realization of Relativity: the Anti-de Sitter Spacetime.- More than Metric: Geometric Objects for Alternative Pictures of Gravity.- Metric-Affine Theories of Gravity.- Conclusions

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• A física quântica (mecânica quântica e teoria quântica de campos)
• Física Matemática
• Física relativística
• Geometria diferencial e riemaniana

Euclidean Geometry;Relativity Graduate Textbook;Non-Euclidean Geometry;Minkowski Plane Geometry;Minkowski Differential Geometry;Poincare Disk Model;Newtonian Gravity;Kepler's Laws;Special Relativity;General Relativity;Einstein Field Equations;De Sitter Spacetime