General relativity is not just a theory, it is a complete reimagining of what space, time, and gravity mean.
Most GR resources either drown you in formalism with no physical intuition, or strip out all the mathematics and leave you with metaphors. This series does neither. Each post builds one rigorous layer at a time from the equivalence principle through tensors, geodesics, and Einstein's field equations, all the way to black holes, gravitational waves, and the frontiers of spacetime physics. If you are comfortable with calculus and linear algebra, you have everything you need to start at Post 01.
Follow the order below each post builds on the last.
A structured journey from tensors to black holes, spacetime curvature, and cosmology. Follow the order below each post builds on the last.
Arc I: Foundations
Why General Relativity Exists
From Newtonian gravity to Einstein's revolution why gravity is not a force but geometry. Covers the equivalence principle, inertial vs gravitational mass, and Einstein's elevator thought experiment.
Equivalence principle Curved spacetime Thought experiments↑ Read post 01 first
The Mathematics of Curved Spacetime
Build the mathematical language of GR from the ground up scalars, vectors, tensors, index notation, the metric tensor, and Einstein summation convention.
Tensors Metric tensor Index notation↑ Read post 02 first
Geodesics and Curvature
How matter moves in curved spacetime and how curvature is mathematically defined geodesics, Christoffel symbols, parallel transport, and the Riemann curvature tensor.
Geodesics Riemann tensor Parallel transport↑ Read posts 01–03 first
Einstein's Field Equations Explained
Deriving and understanding the equations that connect matter with spacetime curvature the stress-energy tensor, Einstein tensor, cosmological constant, and the weak-field limit.
Arc II: Astrophysical GR
↑ Arc I recommended
Schwarzschild Geometry and Black Holes
The first exact solution to Einstein's equations and the physics of black holes event horizons, gravitational time dilation, photon spheres, and orbits near singularities.
Schwarzschild metric Event horizon Time dilation↑ Arc I recommended
Gravitational Waves: Ripples in Spacetime
How accelerating masses create spacetime waves linearised gravity, wave solutions, binary inspirals, and how humanity detected them with LIGO and Virgo.
Linearised gravity LIGO GW150914↑ Arc I recommended
Cosmology and the Expanding Universe
Applying GR to the universe itself the FLRW metric, Friedmann equations, Hubble expansion, dark matter, dark energy, and Big Bang cosmology.
FLRW metric Friedmann equations Dark energy↑ Read post 05 first
Rotating Black Holes and Extreme Gravity
Kerr spacetime, frame dragging, ergospheres, accretion disks, and relativistic astrophysics around the most extreme objects in the universe.
Kerr metric Frame dragging ErgosphereArc III: Frontiers of Gravity
↑ Arcs I and II recommended
Testing Gravity Beyond Einstein
Modern precision tests of GR pulsar timing, black hole imaging, modified gravity theories, and multi-messenger constraints in the post-LIGO era.
Pulsar timing Modified gravity Black hole imaging↑ Full series recommended
The Future of Spacetime Physics
Where GR breaks down Hawking radiation, the information paradox, quantum spacetime, string theory, and loop quantum gravity.
Hawking radiation Quantum gravity Information paradoxPosts are released monthly. Each post assumes familiarity with the ones listed in its prerequisite. If you are new to the series, start at post 01 no prior knowledge of GR is assumed, though comfort with calculus and linear algebra will help from post 02 onward.
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