gen-define-black-hole-event-horizons-and-give-one-short-worked-e-6ab3

Define black hole event horizons and give one short worked example.

# Black Hole Event Horizons ## Definition An **event horizon** is the boundary surrounding a black hole beyond which nothing—not even light—can escape. It represents the point of no return where the escape velocity equals the speed of light. For a non-rotating (Schwarzschild) black hole, the event horizon radius is given by the **Schwarzschild radius**: $$r_s = \frac{2GM}{c^2}$$ where: - G = gravitational constant (6.67 × 10⁻¹¹ m³ kg⁻¹ s⁻²) - M = mass of the black hole - c = speed of light (3 × 10⁸ m/s) --- ## Worked Example **Find the event horizon radius of a black hole with mass equal to 10 solar masses.** **Given:** - M = 10 M☉ = 10 × (2 × 10³⁰ kg) = 2 × 10³¹ kg **Solution:** $$r_s = \frac{2GM}{c^2}$$ $$r_s = \frac{2 × (6.67 × 10^{-11}) × (2 × 10^{31})}{(3 × 10^8)^2}$$ $$r_s = \frac{2.67 × 10^{21}}{9 × 10^{16}}$$ $$r_s ≈ 30,000 \text{ m} = 30 \text{ km}$$ **Answer:** The event horizon has a radius of approximately **30 km** (about the size of a small city).