Recent Posts
- The Eddington Luminosity in Spherical Accretion and Beyond
- How a Molecular Cloud Collapses Into a Star
- Why $R_{\mu\nu}=0$ does not imply $R_{\mu\nu\rho\sigma}=0$
- Derivation of the Cosmic-Ray Diffusion Coefficient from Pitch-Angle Scattering
- The rubber sheet gets the geometry right and the mechanism wrong!
Tag Archives: Mathematical Physics
Why $R_{\mu\nu}=0$ does not imply $R_{\mu\nu\rho\sigma}=0$
Almost everyone makes this mistake once, and it’s a good one to make. You learn the Einstein field equations. You learn that in vacuum, with no matter and no energy and no cosmological constant, they collapse down to something very … Continue reading
Derivation of the Cosmic-Ray Diffusion Coefficient from Pitch-Angle Scattering
Cosmic rays arrive at Earth from every direction almost perfectly evenly, to about one part in a thousand. That’s a disaster if you wanted to know where they came from, because they’re charged and the Galaxy is magnetised, so whatever … Continue reading
Posted in Expository, Projects, Research
Tagged astronomy, Astrophysics, Mathematical Physics, physics, science, theoretical physics
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The rubber sheet gets the geometry right and the mechanism wrong!
You have seen this demonstration. Somebody stretches a rubber sheet over a frame, drops a bowling ball in the middle, and the sheet sags. Then they roll a marble across it and the marble curves toward the bowling ball, maybe … Continue reading
Posted in Diary, Expository, Notes, Scratch essays
Tagged Astrophysics, debunking, equivalence principle, general relativity, Geodesics, gravitational waves, gravity, manifolds, Mathematical Physics, philosophy of science, physics, Schwarzschild metric, science, science writing, spacetime, spacetime curvature, theoretical physics
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So, what is a vector?
In my first year of undergraduate physics, one of my professors walked into the lecture hall, placed his notes on the desk, looked around the room, and asked a question that, at first, seemed almost too easy. “What is a … Continue reading
Posted in Expository
Tagged classical mechanics, Math, Mathematical Physics, motion, What Is...
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Deriving the Euler–Lagrange Equation for Particles, Fields, and Curved Spacetime
A good way to understand the laws of motion is not to memorize a separate equation for each situation, but to notice there is really only one trick, and every equation of motion is what falls out when you apply … Continue reading
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, What Is...
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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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