Physics / research
Black holes, thermodynamics, and quantum fields
Connect horizons and classical black-hole mechanics to Hawking radiation and entropy, clearly identifying semiclassical assumptions and unresolved information questions.
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Module 01 research
Black holes, thermodynamics, and quantum fields
Connect horizons and classical black-hole mechanics to Hawking radiation and entropy, clearly identifying semiclassical assumptions and unresolved information questions.
- 01
Penrose diagrams and maximal extensions
Read the causal content of Schwarzschild extensions without confusing coordinate boundaries, singularities, and a collapse spacetime.
38 min - 02
Null congruences and Raychaudhuri focusing
Track a bundle of affinely parameterized light rays and identify the geometric and energy assumptions behind focusing.
38 min - 03
Trapped surfaces and singularity-theorem assumptions
Compute null expansions on spheres and distinguish slice-based trapping from global incompleteness and event-horizon claims.
38 min - 04
The black-hole area theorem and energy conditions
Explain the global step behind classical horizon-area increase and use it as a bound on mergers and rotational extraction.
38 min - 05
Surface gravity and stationary horizon laws
Normalize the horizon generator and apply stationary first-law variations without mistaking them for general horizon dynamics.
38 min - 06
Bogoliubov transformations and particle definitions
Relate positive-frequency mode choices while preserving commutators, and distinguish particle number from a state-independent local observable.
38 min - 07
Unruh detectors and acceleration temperature
Derive the thermal detailed-balance ratio for a uniformly accelerated detector while keeping its state, trajectory, and switching assumptions explicit.
38 min - 08
Hawking radiation from horizon redshift
Connect the exponential late-time ray relation to Hawking occupation while specifying the quantum state, greybody filtering, and semiclassical regime.
38 min - 09
Generalized entropy and evaporating black holes
Combine renormalized horizon and exterior entropy, and use a controlled large-mass evaporation model without extrapolating it through the quantum-gravity endpoint.
38 min - 10
The information-loss paradox and the status of proposals
Formulate the tension among semiclassical radiation, complete evaporation, and unitarity, and assess what Page curves and island calculations actually establish.
38 min