General Relativity: From Differential Geometry to Gravitational Waves
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".
Deadline for manuscript submissions: 31 December 2024 | Viewed by 126
Special Issue Editor
Special Issue Information
Dear Colleagues,
General Relativity, as introduced by Einstein in 1915, has not only quantitatively improved on Newtonian Mechanics, but it has also shown that some of its basic concepts, such as force, absolute time and space, and gravitation as a direct and instantaneous action of one body on another, are essentially meaningless even if sometimes convenient for approximate calculation. Seemingly reasonable intuition was replaced by a set of physical postulates and mathematical axioms. This in turn led not only to advances in related fields such as relativistic cosmology, but also to new methods in differential geometry, and to technological advances such as GPS, differential–geometric methods in computer vision, and, more recently, interferometry in relation to the detection of gravitational waves.
Thanks to the Pound–Rebka experiment (1959), relativistic effects may now be measured on Earth, giving General Relativity an experimental basis, in addition to an observational one. These and other experiments in turn imply that the physical interpretation of the equivalence principle needs to be modified into the C-equivalence principle (1963). As a consequence, the axiomatics of manifold theory needs to be revisited, as recently illustrated in Axioms. General Relativity has also played a major role in the development of differential geometry and the theory of partial differential equations, especially with regard to the formation of singularities. It therefore seems useful to bring to a mathematical audience some of these developments, in relation to mathematical or non-mathematical issues, outlining open problems. Papers that focus on observational or experimental work are welcome; however, they should spell out the modeling assumptions in mathematical form, preferably as a set of axioms.
Prof. Dr. Satyanad Kichenassamy
Guest Editor
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Keywords
- general relativity
- differential geometry
- gravitational waves
- conformal geometry
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