How To Calculate A Black Hole Mass

Black Hole Mass Formula:

\[ M = \frac{c^3 \times r_s}{2G} \]

Black Hole Mass (M):

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1. What is the Black Hole Mass Formula?

The black hole mass formula calculates the mass of a Schwarzschild black hole from its Schwarzschild radius. This fundamental relationship in general relativity connects the geometry of spacetime around a non-rotating black hole with its mass.

2. How Does the Calculator Work?

The calculator uses the black hole mass formula:

\[ M = \frac{c^3 \times r_s}{2G} \]

Where:

\( M \) — Black hole mass (kg)
\( c \) — Speed of light (3×10⁸ m/s)
\( r_s \) — Schwarzschild radius (meters)
\( G \) — Gravitational constant (6.67430×10⁻¹¹ m³ kg⁻¹ s⁻²)

Explanation: The Schwarzschild radius represents the event horizon of a non-rotating black hole, beyond which nothing can escape the gravitational pull.

3. Importance of Black Hole Mass Calculation

Details: Calculating black hole mass is essential for understanding gravitational effects, predicting spacetime curvature, studying accretion disk behavior, and analyzing gravitational wave emissions from black hole mergers.

4. Using the Calculator

Tips: Enter the Schwarzschild radius in meters. The value must be positive and non-zero. The calculator uses fundamental physical constants to compute the corresponding black hole mass.

5. Frequently Asked Questions (FAQ)

Q1: What is the Schwarzschild radius?
A: The Schwarzschild radius is the radius of the event horizon of a non-rotating black hole, defining the boundary beyond which escape velocity exceeds the speed of light.

Q2: How is this formula derived?
A: The formula is derived from Einstein's field equations of general relativity for a spherically symmetric, non-rotating mass distribution.

Q3: What are typical Schwarzschild radius values?
A: For a solar mass black hole (2×10³⁰ kg), the Schwarzschild radius is approximately 3 kilometers. Larger masses have proportionally larger Schwarzschild radii.

Q4: Does this work for rotating black holes?
A: No, this formula applies only to Schwarzschild (non-rotating) black holes. Rotating black holes require the Kerr metric and are more complex.

Q5: What are the practical applications?
A: This calculation is used in astrophysics research, gravitational wave astronomy, black hole imaging, and testing general relativity predictions.