Inside the Event Horizon: Why Time Stops at the Singularity

00:00 — What Is the Schwarzschild Radius of a Black Hole?

Derived by Karl Schwarzschild in 1916 as an exact solution to Einstein's field equations, the Schwarzschild radius (r_s = 2GM / c²) defines the spherical boundary where escape velocity equals the speed of light (c = 299,792,458 m/s). For a non-rotating stellar black hole of 10 solar masses (10 M☉), the event horizon radius is approximately 29.5 kilometers.

03:15 — Why Does Gravitational Time Dilation Freeze Clocks at the Horizon?

For an observer at radial distance r outside a non-rotating black hole, proper time dτ relates to coordinate time dt measured far from the black hole via: dτ = dt × √(1 - r_s / r). As r approaches r_s, the term inside the square root approaches zero. One second on an infalling spacecraft's clock corresponds to an increasingly vast span of time for a telescope watching from Earth.

08:40 — What Happens Inside the Event Horizon? (Space and Time Swap Roles)

Once an observer crosses r < r_s, the metric coefficients of radial space (dr²) and time (dt²) reverse algebraic signs. Inside the event horizon, the radial direction becomes time-like: avoiding the central singularity is as physically impossible as avoiding moving forward into tomorrow.

13:20 — How Does Hawking Radiation Evaporate Black Holes?

In 1974, Stephen Hawking demonstrated that quantum vacuum fluctuations near the event horizon cause black holes to emit thermal radiation at temperature T_H = ħc³ / (8πGMk_B). Because temperature is inversely proportional to mass, a solar-mass black hole radiates at ~60 nanokelvin—far colder than the 2.7255 K Cosmic Microwave Background—meaning it currently absorbs more energy than it emits until the universe cools further.

Black Hole Mass vs. Event Horizon Telemetry Table