The term "Applied Relativity" appeared first as the title of a book review by Sciama in 1973 during the golden age of relativity. His review of Weinberg's book about general relativity mentions the term "engineering relativity," but the context is not engineering; it's astrophysics and cosmology. The golden era is when relativistic astrophysics was born to explain discoveries such as quasars, pulsars, and neutron stars. It was a time of renewed interest in relativity, and people were excited to apply it to relativistic problems.
Today, relativity stands firm within the astrophysical and cosmological scientific communities. Gravitational-wave astronomy opened the proverbial window to the universe, and we even have pictures of event horizons.
In this new golden era, applied relativity refers to applying relativity to problems beyond its accepted domains. I'm looking for examples of relativistic techniques in problems where relativistic effects are negligible. These include typical engineering and technology problems with low characteristic speeds and weak gravitational forces.
Do they exist? Let me know.
- Poincaré Embeddings for Learning Hierarchical Representations
- Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry
- An Ocean Drum: quasi-geostrophic energetics from a Riemann geometry perspective: Quasi-geostrophic dynamics from the perspective of geometric analysis. Constructs an effective metric from the stratification and Coriolis ingredients of bulk water mass and recasts QG-equations in terms of the associated 3-dimensional Laplacian. Applies spectral geometry to extract information of the system without explicitly solving the equations. The QG metric in the deep ocean is hyperbolic.
- Mechanics of floating bodies: Robert Beig and Bernd Schmidt, two seasoned relativists, attack the problem of rigid bodies with constant density floating in an incompressible fluid.