
Explore how gravity slows time, making clocks tick slower deeper in a gravitational well. See GPS evidence and experiments that compare sea level and mountain elevations.
Explore how gravity emerges from spacetime curvature, and how the Schwarzschild metric shows time slows near massive bodies, affecting clocks, GPS, and satellite physics.
Explore how Riemannian geometry uses manifolds and metric tensors to measure distances and angles in curved space-time, with Christoffel symbols and curvature tensors guiding geodesics.
Explore how Einstein's field equation links spacetime curvature, via the Einstein tensor and metric tensor, to energy and momentum through the stress-energy tensor and cosmological constant.
Explore how Einstein's field equations, the same equation, produce black holes, white holes, gravitational waves, and wormholes under different energy distributions and boundary conditions.
Explain how Einstein added the cosmological constant lambda to keep the universe static, then showed that Hubble's expansion revealed space itself is stretching, making lambda unnecessary.
Trace the evolution from Chandrasekhar's limit on white dwarfs to stellar-mass and supermassive black holes, highlighting gravity, accretion disk heat, and imaging by the Event Horizon Telescope.
Explores how classical relativity yields a black hole singularity and how quantum gravity ideas like string theory and loop quantum gravity aim to replace it with a finite region.
Laser interferometer gravitational wave observatory detects the gravitational wave from merging black holes. It reveals masses of 36 and 29 and a 62 mass remnant, with energy radiated as waves.
This course contains the use of artificial intelligence
This course is a comprehensive exploration of Albert Einstein’s most profound legacy: the reimagining of the universe as a geometric masterpiece. We begin by tracing the historic shift from Isaac Newton’s "invisible force" of gravity to Einstein’s radical realization that space and time are not separate entities, but are woven together into a single, four-dimensional fabric called spacetime. You will discover how mass and energy actually warp this fabric, turning gravity from a mysterious pull into a physical property of the world around us.
The curriculum then dives into the mind-bending reality of Gravitational Time Dilation, proving that your sense of time is dictated by your location in a gravitational well. You will explore the "living mathematics" of Riemannian geometry, where we define geodesics—the straightest possible paths in a curved world—to understand why planets orbit and apples fall. We simplify the intimidating Einstein Field Equations, breaking down the symbols that serve as the universal rulebook: telling mass-energy how to curve spacetime, and curved spacetime how to move mass-energy.
Finally, we venture into the most extreme corners of the cosmos, from the "blunder" of the Cosmological Constant that now explains the accelerating expansion of our universe to the terrifying reality of Black Holes. You will stand at the edge of the Event Horizon and Peer into the Singularity, where our current equations fail and the search for a "Theory of Everything" begins.