1. What is Schwarzschild Radius?

The Schwarzschild radius is the radius of the event horizon of a non-rotating black hole. It represents the boundary beyond which nothing, not even light, can escape the black hole's gravitational pull.

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·s²)
• \( M \) — Mass of the object (kg)
• \( c \) — Speed of light (3 × 10⁸ m/s)

Explanation: The formula shows the relationship between an object's mass and the radius at which its escape velocity equals the speed of light.

3. Importance of Schwarzschild Radius

Details: The Schwarzschild radius is fundamental in general relativity and black hole physics. It helps determine whether an object of a given mass could theoretically become a black hole if compressed within this radius.

4. Using the Calculator

Tips: Enter the mass of the object in kilograms. The result will show the Schwarzschild radius in meters. For example, the Sun's mass would be 1.989 × 10³⁰ kg.

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 anything have a natural Schwarzschild radius?
A: Only objects that have collapsed into black holes naturally have sizes smaller than their Schwarzschild radii.

Q4: Can a human have a Schwarzschild radius?
A: Yes, but it's extremely small (about 10^-25 meters for a 70 kg person) - far smaller than any known elementary particle.

Q5: Does rotation affect the Schwarzschild radius?
A: The original formula is for non-rotating black holes. Rotating black holes (Kerr black holes) have more complex event horizons.