How To Calculate A Black Hole

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 black hole, named after German physicist Karl Schwarzschild. 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:

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

Where:

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

Explanation: The formula shows that the event horizon radius is directly proportional to the mass of the black hole and depends on fundamental physical constants.

3. Importance Of Schwarzschild Radius Calculation

Details: Calculating the Schwarzschild radius is essential for understanding black hole physics, general relativity, and the behavior of spacetime around massive objects. It helps determine the size at which an object becomes a black hole.

4. Using The Calculator

Tips: Enter the mass of the object in kilograms. The calculator will compute the Schwarzschild radius in meters. For astronomical objects, use scientific notation or large numbers.

5. Frequently Asked Questions (FAQ)

Q1: What happens at the Schwarzschild radius?
A: The Schwarzschild radius marks the event horizon - the point of no return where the escape velocity equals the speed of light.

Q2: Can anything escape from inside the Schwarzschild radius?
A: No, once matter or radiation crosses the event horizon, it cannot escape the black hole's gravitational pull.

Q3: What is the Schwarzschild radius of Earth?
A: For Earth's mass (5.972 × 10²⁴ kg), the Schwarzschild radius is approximately 8.87 millimeters.

Q4: What is the Schwarzschild radius of the Sun?
A: For the Sun's mass (1.989 × 10³⁰ kg), the Schwarzschild radius is approximately 2.95 kilometers.

Q5: Does the Schwarzschild radius apply to rotating black holes?
A: No, the Schwarzschild solution is for non-rotating black holes. Rotating black holes are described by the Kerr metric.