Category Archives: Expository
So what are tensors, really?
I want to start with a confession. When I first heard the word “tensor,” I assumed it was one of those words that exists to make physicists sound clever. Something you learn in graduate school, surrounded by people who already … Continue reading
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Tagged classical mechanics, general relativity, Mathematical Physics, Tensors
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The mathematics behind a “wormhole”
Let me tell you something that will sound ridiculous at first. Take a piece of paper. Draw a dot on the left and a dot on the right. The shortest path between them, if you are a little ant walking … Continue reading
How many solutions of Einstein’s equations are there?
How many solutions does the most beautiful equation in physics have? More than you’d think… probably infinitely many, and most of them will never have names. Continue reading
Posted in Expository, Notes
Tagged Astrophysics, Black holes, differential geometry, Einstein equation, general relativity, Kerr spacetime, Lorentzian Geometry, manifolds, Mathematical Physics, riemannian geometry, Schwarzschild spacetime, Tensor Calculus, theoretical physics, Wormholes
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On the Consistency of Published M87* Mass Measurements
A useful way to test a black hole spacetime is not only to ask whether one observational method agrees with Kerr, but to ask whether several independent methods agree with each other. In the case of M87*, this question is … Continue reading
Some remarks on quasinormal modes for Euler–Heisenberg black holes in a PFDM background
One of the recurring themes in black hole perturbation theory is that many apparently complicated dynamical questions eventually reduce to a rather geometric spectral problem. One begins with a black hole spacetime, perturbs it slightly, separates variables, and discovers that … Continue reading
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Tagged Black holes, general relativity, Mathematical Physics, theoretical physics
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Inspiral-merger-ringdown consistency tests and the reconstruction of Kerr geometry
One of the more conceptually interesting developments in gravitational wave astronomy is the inspiral-merger-ringdown (IMR) consistency test. At a heuristic level, the idea is rather simple: different sectors of a binary black hole coalescence should reconstruct the same final spacetime … Continue reading
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Tagged Astrophysics, Black holes, consistency tests, general relativity
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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 Dark Halo That Almost Became a Galaxy
One of the cleanest ideas in modern cosmology is also one of the easiest to overlook. According to the standard ΛCDM model, structure in the Universe forms hierarchically, with dark matter collapsing under gravity into bound halos over an enormous … 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
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Tagged consistency tests, general relativity, gravitational waves, KTC, theoretical physics
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Overdetermined parameter interference in physics
In many areas of physics, a system is described by a small number of fundamental parameters, while the available observations greatly exceed this number. When this occurs, the problem of parameter inference becomes overdetermined. Rather than being a drawback, this … Continue reading
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Tagged consistency tests, general relativity, KTC
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