Tag Archives: Mathematical Physics
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
Posted in Expository
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
Posted in Expository
Tagged Black holes, general relativity, Mathematical Physics, theoretical physics
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Recent notes on covariance-weighted consistency tests for Kerr parameter estimates
A recurring issue in strong-field tests of General Relativity is the question of how one should compare parameter estimates inferred from genuinely independent observational sectors. In the case of stationary black hole spacetimes, the Kerr hypothesis predicts that all sufficiently … Continue reading
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