Tag Archives: theoretical physics
Traversable wormholes and the geometry of effective exoticity
One of the useful lessons of general relativity is that the Einstein equations are not, by themselves, especially conservative about the kinds of geometries they permit. Smooth Lorentzian metrics can describe black holes, gravitational waves, expanding cosmologies, singularity formation, and … Continue reading
A Consistency Test for Kerr Black Holes via Orbital Motion, Ringdown, and Imaging
Kerr Trisector Closure (KTC) is a consistency test for the Kerr hypothesis that tries to stay honest about what is actually being inferred from data. The guiding principle is simple: if the exterior spacetime of an astrophysical, stationary, uncharged black … Continue reading
Posted in Expository, Notes
Tagged consistency tests, general relativity, gravitational waves, KTC, theoretical physics
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Towards a derivation of the metric tensor in general relativity
One of the central tasks in differential geometry is to make precise the notion of length and angle on a smooth manifold. Unlike $\mathbb R^n$, a general manifold comes with no preferred inner product. The metric tensor is not something … Continue reading
Posted in Notes
Tagged differential geometry, general relativity, manifolds, riemannian geometry, theoretical physics
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Spacetime as a Lorentzian Manifold
One of the central tasks in differential geometry is to make precise the notion of length and angle on a smooth manifold. Unlike $\mathbb R^n$, a general manifold comes with no preferred inner product. The metric tensor is not something … Continue reading
Posted in Notes
Tagged differential geometry, general relativity, theoretical physics
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