Schwarzschild Black Hole Calculator

Schwarzschild Radius Formula:

\[ r_s = \frac{2 G M}{c^2} \]

Schwarzschild Radius (r_s):

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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:

\[ r_s = \frac{2 G M}{c^2} \]

Where:

\( r_s \) — Schwarzschild radius (m)
\( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)
\( M \) — Mass of the object (kg)
\( c \) — Speed of light (299,792,458 m/s)

Explanation: The formula shows the relationship between a black hole's mass and the size of its event horizon.

3. Importance of Schwarzschild Radius

Details: The Schwarzschild radius is fundamental in general relativity and black hole physics. It defines the size at which an object becomes a black hole for a given mass.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What happens at the Schwarzschild radius?
A: At this radius, the escape velocity equals the speed of light, making it impossible for anything, including light, to escape.

Q2: What's the Schwarzschild radius of Earth?
A: For Earth's mass (5.972 × 10²⁴ kg), it's about 8.87 mm - meaning Earth would become a black hole if compressed to this size.

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

Q4: Can anything escape from inside the Schwarzschild radius?
A: No, not even light can escape from within the event horizon.

Q5: How was this radius discovered?
A: Karl Schwarzschild derived this solution to Einstein's field equations in 1916, shortly after Einstein published general relativity.