1. What is the Schwarzschild Radius?

The Schwarzschild radius is the radius of the event horizon of a non-rotating black hole. It represents the point of no return where the escape velocity equals the speed of light.

2. How Does the Calculator Work?

The calculator uses the Schwarzschild radius formula:

Where:

• \( r_s \) — Schwarzschild radius (meters)
• \( G \) — Gravitational constant (6.67430 × 10^-11 m³ kg^-1 s^-2)
• \( M \) — Mass of the black hole (kg)
• \( c \) — Speed of light (299,792,458 m/s)

Explanation: The formula shows that the radius of a black hole's event horizon is directly proportional to its mass.

3. Importance of Schwarzschild Radius

Details: The Schwarzschild radius is fundamental in general relativity and black hole physics. It defines the size of a black hole's event horizon and helps classify compact objects.

4. Using the Calculator

Tips: Enter the mass of the black hole in kilograms. The calculator will compute the Schwarzschild radius in meters.

5. Frequently Asked Questions (FAQ)

Q1: What's the Schwarzschild radius of Earth?
A: For Earth's mass (5.972 × 10²⁴ kg), the Schwarzschild radius is about 8.87 millimeters.

Q2: What's the Schwarzschild radius of the Sun?
A: For the Sun's mass (1.989 × 10³⁰ kg), it's approximately 2.95 kilometers.

Q3: Does rotation affect the Schwarzschild radius?
A: The formula given is for non-rotating black holes. Rotating black holes (Kerr black holes) have a more complex structure.

Q4: What happens at the Schwarzschild radius?
A: It's the point where space-time becomes so curved that all paths lead inward, and not even light can escape.

Q5: Can anything have a smaller radius than its Schwarzschild radius?
A: Objects compressed below their Schwarzschild radius collapse into a black hole according to general relativity.