Black Holes

Black holes are regions of spacetime where gravity is so strong that nothing, not even light, can escape once it crosses the event horizon.

Black Hole Event Horizon Simulation

Interactive simulation of a Schwarzschild black hole with accretion disk, photon sphere, and gravitational lensing effects.

Event Horizon (r = 1.0 r_s)

Photon Sphere (r = 1.5 r_s)

Accretion Disk (ISCO at 3 r_s)

Einstein Ring (lensed light)

Black Hole Mass: 1.0 M_☉

Physics notes: The event horizon is at the Schwarzschild radius r_s = 2GM/c². The photon sphere at 1.5r_s is where light can orbit. The innermost stable circular orbit (ISCO) is at 3r_s - matter inside this radius spirals into the black hole.

The Event Horizon

The event horizon is the boundary of a black hole - the point of no return. For a non-rotating (Schwarzschild) black hole, it occurs at the Schwarzschild radius:

Schwarzschild Radius

r_s = \frac{2GM}{c^2}

For the Sun, this would be about 3 km. For Earth, only 9 mm! At the event horizon, the escape velocity equals the speed of light.

The Photon Sphere

At $r = 1.5 r_s$ , light can orbit the black hole in unstable circular orbits. This is the photon sphere:

Photon Sphere Radius

r_{\text{photon}} = \frac{3GM}{c^2} = 1.5 \, r_s

If you stood here (somehow), you could see the back of your own head - light would orbit around and return to you!

Innermost Stable Circular Orbit (ISCO)

The ISCO at $r = 3r_s$ is the closest stable orbit for matter:

ISCO Radius

r_{\text{ISCO}} = \frac{6GM}{c^2} = 3 \, r_s

Inside this radius, orbits are unstable - any perturbation sends matter spiraling into the black hole. This defines the inner edge of the accretion disk.

Accretion Disks

Matter falling toward a black hole forms a flat, rotating accretion disk. As gas spirals inward:

Friction heats the gas to millions of degrees
Inner regions glow white-hot, outer regions are cooler (redder)
The disk emits X-rays and other high-energy radiation
Up to 40% of the rest mass energy can be released (vs 0.7% for nuclear fusion!)

Disk Temperature Profile

T(r) \propto r^{-3/4}

Gravitational Lensing

Black holes bend light dramatically. Light from behind the black hole curves around, creating Einstein rings - circular images of background objects.

Einstein Ring Angular Radius

\theta_E = \sqrt{\frac{4GM}{c^2} \frac{D_{LS}}{D_L D_S}}

The black hole also creates multiple images of background stars and galaxies, magnifying and distorting them in characteristic ways.

Time Dilation

Near a black hole, time passes more slowly due to gravitational time dilation:

Gravitational Time Dilation

\frac{d\tau}{dt} = \sqrt{1 - \frac{r_s}{r}}

At the event horizon ( $r = r_s$ ), time appears to stop for a distant observer. An infalling astronaut would see the outside universe speed up dramatically, while observers outside would see them freeze at the horizon (redshifting to invisibility).

Tidal Forces and Spaghettification

The difference in gravitational pull between your head and feet creates tidal forces. For a stellar-mass black hole, these become lethal well outside the event horizon:

Tidal Acceleration

\Delta a \approx \frac{2GM}{r^3} \Delta r

This "spaghettification" would stretch you into a long, thin strand. For supermassive black holes, tidal forces at the horizon are gentler - you could cross intact!

Types of Black Holes

Stellar (3-100 M_☉): Formed from collapsed massive stars
Intermediate (100-10⁵ M_☉): Possibly from mergers
Supermassive (10⁶-10¹⁰ M_☉): Found in galaxy centers
Primordial (hypothetical): Formed in the early universe

Hawking Radiation

Stephen Hawking showed that black holes aren't completely black - they emit thermal radiation due to quantum effects near the horizon:

Hawking Temperature

T_H = \frac{\hbar c^3}{8\pi G M k_B} \approx \frac{6 \times 10^{-8}}{M/M_\odot} \text{ K}

For stellar black holes, this is far colder than the cosmic microwave background, so they grow rather than evaporate. Only tiny primordial black holes would have evaporated by now.

First Image of a Black Hole

In 2019, the Event Horizon Telescope captured the first image of a black hole - the supermassive black hole M87* with 6.5 billion solar masses. The bright ring is the photon sphere and lensed accretion disk; the dark center is the "shadow" of the event horizon. This confirmed GR predictions with stunning precision!

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