Black Holes

The Ultimate Enigma: Regions of spacetime where gravity is so strong that nothing, not even light, can escape.

Black Holes

An in-depth exploration of the most extreme objects in the universe—from Schwarzschild and Kerr solutions through Hawking radiation and thermodynamics to astrophysical observations and gravitational wave detections.

Course Overview

Black holes are regions of spacetime where gravity is so strong that nothing, not even light, can escape. They are exact solutions to Einstein's field equations of General Relativity and represent some of the most extreme environments in the universe. This course provides rigorous mathematical treatment from the basic Schwarzschild solution through rotating Kerr black holes, quantum effects (Hawking radiation), thermodynamics, and modern astrophysical observations including LIGO gravitational wave detections and Event Horizon Telescope imaging.

What You'll Learn

  • • Schwarzschild solution and event horizons
  • • Geodesics, photon sphere, and ISCO
  • • Kerr metric for rotating black holes
  • • Ergosphere and Penrose process
  • • Reissner-Nordström charged solutions
  • • Hawking radiation and black hole evaporation
  • • Black hole thermodynamics and entropy
  • • No-hair theorem and information paradox
  • • Astrophysical observations (LIGO, EHT)
  • • Accretion disks and quasars

Prerequisites

Course Structure

4 Parts covering 24 chapters • From Schwarzschild basics to quantum effects and observations • Includes 9 detailed derivation pages with step-by-step calculations • Features Nobel laureate video lectures (Sir Roger Penrose) • Suitable for advanced undergraduates and graduate students

Course Parts

⚫

Part I: Black Hole Basics

Schwarzschild solution derivation from Einstein equations, event horizons, surface gravity, singularities, geodesics and particle motion, photon sphere, ISCO, coordinate systems (Eddington-Finkelstein, Kruskal).

Schwarzschild MetricEvent HorizonsGeodesics6 Chapters
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Part II: Rotating & Charged Black Holes

Kerr metric derivation in Boyer-Lindquist coordinates, ergosphere and frame dragging, Penrose process for energy extraction (29% efficiency), Reissner-Nordström charged solutions, Kerr-Newman, no-hair theorem.

Kerr MetricErgospherePenrose Process6 Chapters
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Part III: Black Hole Thermodynamics & Quantum Effects

Four laws of black hole mechanics, Bekenstein entropy and area theorem, Hawking radiation derivation, black hole temperature and evaporation, information paradox, holographic principle, AdS/CFT correspondence.

Hawking RadiationBH ThermodynamicsInformation Paradox6 Chapters
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Part IV: Astrophysics & Observations

Stellar collapse and formation, supermassive black holes at galactic centers, accretion disks and jets, X-ray binaries (Cygnus X-1), Event Horizon Telescope M87* imaging, LIGO/Virgo gravitational wave detections.

Accretion DisksLIGO DetectionsEHT Imaging6 Chapters

Key Equations

Schwarzschild Metric

$ds^2 = -\left(1-\frac{2GM}{c^2r}\right)c^2dt^2 + \left(1-\frac{2GM}{c^2r}\right)^{-1}dr^2 + r^2 d\Omega^2$

Describes spacetime outside a spherically symmetric, non-rotating black hole. Event horizon at rs = 2GM/c².

Kerr Metric (Rotating Black Holes)

$ds^2 = -\left(1-\frac{r_sr}{\Sigma}\right)c^2dt^2 - \frac{r_sr\sin^2\theta}{\Sigma}(c\,dt)(a\,d\phi) + \frac{\Sigma}{\Delta}dr^2 + \Sigma d\theta^2 + \sin^2\theta\left(r^2+a^2+\frac{r_sra^2\sin^2\theta}{\Sigma}\right)d\phi^2$

Most astrophysical black holes rotate. Features ergosphere where rotational energy can be extracted.

Hawking Temperature

$T_H = \frac{\hbar c^3}{8\pi GMk_B} = \frac{\hbar c}{4\pi k_Br_s}$

Black holes radiate as blackbodies due to quantum effects near the horizon. For solar mass: TH ≈ 60 nK.

Bekenstein-Hawking Entropy

$S_{BH} = \frac{k_BAc^3}{4\hbar G} = \frac{k_BA}{4\ell_P^2}$

Black hole entropy is proportional to the area of the event horizon, not volume—a key insight for quantum gravity.

📺 Video Lectures

World-class lectures on black hole physics, Hawking radiation, and conformal cyclic cosmology from Nobel laureates.

Professor Sir Roger Penrose: Hawking Points & CCC

Nobel laureate explores Hawking points in CMB, conformal cyclic cosmology, and black hole entropy.

Sir Roger Penrose & Prof Janna Levin: A Universe of Black Holes

Discussion on singularities, gravitational waves, LIGO detections, and supermassive black holes.

The Astrophysics of Supermassive Black Holes by Prof. Ballantyne

Comprehensive lecture on AGN, quasars, M-sigma relation, and co-evolution with galaxies.

Related Courses

General Relativity

Einstein field equations, Riemann tensor, and spacetime curvature

Special Relativity

Foundation: Lorentz transformations, spacetime, and relativistic mechanics

Cosmology

Universe evolution, dark matter, dark energy, and the Big Bang

Quantum Gravity

Beyond classical GR: string theory, loop quantum gravity, holography

"Black holes are where God divided by zero."— Steven Wright