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: general relativity
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
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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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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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
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
Posted in Expository, Notes
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