Tag Archives: Einstein equations
From the Equivalence Principle to Curved Geometry of Spacetime
Newtonian mechanics contains two masses with no obvious reason to be related. One appears in the law of gravitation, $$\mathbf{F}=-\frac{GMm_g}{r^{2}}\hat{\mathbf r},$$ where $m_g$ measures how strongly a body couples to a gravitational field. The other appears in the second law, … Continue reading
Posted in Expository, Notes
Tagged Classical Gravity, curvature, differential geometry, Einstein equations, equivalence principle, general relativity, geodesic deviation, Geodesics, gravity, Lorentzian Geometry, manifolds, Mathematical Physics, spacetime, Tensors, theoretical physics
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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