Tag Archives: differential geometry
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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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
Comments Off on Spacetime as a Lorentzian Manifold