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Black Holes: Physics, Structure, and Theory

1Introduction to Black Holes and Historical Context2Foundations of General Relativity3The Schwarzschild Solution4Geometry of Spacetime and Tidal Forces5Rotating Black Holes: The Kerr Metric6Black Hole Thermodynamics7Hawking Radiation and Quantum Effects8The Information Paradox9Formation and Astrophysical Evidence10Direct Imaging and Future Horizons
Foundations of General Relativity

Special Relativity Review

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Before tackling General Relativity, we briefly recall Special Relativity. It rests on two pillars: first, the laws of physics are identical in all inertial frames; second, the speed of light is constant for everyone. In this framework, space and time are unified into spacetime. While different observers may disagree on distances or durations, they agree on the spacetime interval, which serves as the absolute geometric backbone of our universe.
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Postulates of Special Relativity

  • The laws of physics are the same in all inertial reference frames.
  • The speed of light in a vacuum (\(c\)) is constant for all observers, independent of the motion of the source or observer.

Invariant Spacetime Interval

While space and time measurements vary between observers, the spacetime interval (\(ds^2\)) remains invariant:

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