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General relativity, formulated by Albert Einstein, is a theory of gravitation that describes gravity as the warping of spacetime by mass and energy, rather than as a force acting at a distance. It fundamentally changed our understanding of the universe, predicting phenomena such as the bending of light around massive objects and the existence of black holes.
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Torsion refers to the twisting of an object due to an applied torque, which results in shear stress over the material's cross-section. It is a critical consideration in engineering and structural design to ensure that components can withstand rotational forces without failing.
Concept
Curvature is a measure of how much a geometric object deviates from being flat or straight. It is a fundamental concept in differential geometry, with applications ranging from analyzing the shape of curves and surfaces to understanding the structure of spacetime in general relativity.
Spacetime geometry is a foundational framework in general relativity that combines the three dimensions of space with the dimension of time into a single four-dimensional manifold. It describes how matter and energy influence the curvature of spacetime, which in turn dictates the motion of objects and the propagation of light.
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Spin is a fundamental quantum property of particles, akin to intrinsic angular momentum, that plays a crucial role in the behavior of quantum systems and underpins the Pauli exclusion principle. It is quantized, meaning it can take on discrete values, and is essential for understanding phenomena such as magnetism and the structure of atoms.
A black hole singularity is a point in space where gravitational forces compress matter to an infinitely small point, resulting in infinite density and zero volume. This enigmatic region challenges the current understanding of physics, indicating a breakdown of spacetime as described by general relativity.
A Cartan connection generalizes the notion of linear connections by allowing for curved or deformed geometry, thus providing a framework for describing the geometry of a manifold with a wider scope. It enables a more flexible treatment of geometrical and physical contexts, such as in the theory of general relativity and gauge theories, by incorporating the group-theoretical approach to differential geometry.
Exotic matter refers to theoretical substances that possess properties outside the realm of normal matter, such as negative mass or energy density. These properties could potentially allow for phenomena like faster-than-light travel or the creation of stable wormholes, according to speculative theories in physics.
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