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To give some context for the general reader, the naive expectation for asymptotically flat spacetime symmetries, i.e., symmetries of spacetime seen by observers located far away from all sources of the gravitational field, would be to extend and reproduce the symmetries of flat spacetime of special relativity, viz., the Poincaré group, also called the inhomogeneous Lorentz group, [2] which is ...
In general relativity, four-dimensional vectors, or four-vectors, are required. These four dimensions are length, height, width and time. A "point" in this context would be an event, as it has both a location and a time. Similar to vectors, tensors in relativity require four dimensions. One example is the Riemann curvature tensor.
The Poincaré group, named after Henri Poincaré (1905), [1] was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. [2] [3] It is a ten-dimensional non-abelian Lie group that is of importance as a model in our understanding of the most basic fundamentals of physics.
In special relativity, energy is closely connected to momentum. In special relativity, just as space and time are different aspects of a more comprehensive entity called spacetime, energy and momentum are merely different aspects of a unified, four-dimensional quantity that physicists call four-momentum. In consequence, if energy is a source of ...
The spacetime symmetry group for special relativity is the Poincaré group, which is a ten-dimensional group of three Lorentz boosts, three rotations, and four spacetime translations. It is logical to ask what symmetries, if any, might apply in General Relativity.
Lie groups – Group that is also a differentiable manifold with group operations that are smooth; Lorentz group – Lie group of Lorentz transformations; Poincaré group – Group of flat spacetime symmetries; Bondi–Metzner–Sachs group – Asymptotic symmetry group of General Relativity
The time it takes light to traverse back-and-forth along the Lorentz–contracted length of the longitudinal arm is given by: = + = / + / + = / = where T 1 is the travel time in direction of motion, T 2 in the opposite direction, v is the velocity component with respect to the luminiferous aether, c is the speed of light, and L L the length of the longitudinal interferometer arm.
Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity.This physical theory models gravitation as the curvature of a four dimensional Lorentzian manifold (a spacetime) and the concepts of topology thus become important in analysing local as well as global aspects of spacetime.