How Is Black Holes Mass Calculated

Schwarzschild Radius Mass Formula:

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

Black Hole Mass (M):

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1. What Is The Schwarzschild Radius Mass Formula?

The Schwarzschild radius mass formula calculates the mass of a black hole from its Schwarzschild radius using fundamental physical constants. This formula derives from Einstein's field equations of general relativity and describes the relationship between a black hole's mass and its event horizon size.

2. How Does The Calculator Work?

The calculator uses the Schwarzschild radius mass formula:

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

Where:

\( M \) — Black hole mass (kg)
\( c \) — Speed of light in vacuum (299,792,458 m/s)
\( r_s \) — Schwarzschild radius (m)
\( G \) — Gravitational constant (6.6743 × 10⁻¹¹ m³/kg s²)

Explanation: This formula shows that a black hole's mass is directly proportional to its Schwarzschild radius, with the proportionality constant involving the speed of light and gravitational constant.

3. Importance Of Black Hole Mass Calculation

Details: Calculating black hole mass is fundamental to understanding gravitational physics, testing general relativity, studying galaxy formation, and analyzing gravitational wave observations from merging black holes.

4. Using The Calculator

Tips: Enter Schwarzschild radius in meters. The speed of light and gravitational constant are pre-filled with standard values but can be adjusted if needed. All values must be positive.

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, beyond which nothing can escape, not even light.

Q2: How is Schwarzschild radius related to mass?
A: The Schwarzschild radius is directly proportional to mass: \( r_s = \frac{2GM}{c^2} \). Our calculator solves for mass given the radius.

Q3: What are typical black hole masses?
A: Stellar black holes: 3-20 solar masses (1 solar mass ≈ 2×10³⁰ kg). Supermassive black holes: millions to billions of solar masses.

Q4: Does this work for rotating black holes?
A: No, this formula is for non-rotating (Schwarzschild) black holes. Rotating (Kerr) black holes require more complex calculations.

Q5: How is Schwarzschild radius measured?
A: For supermassive black holes, it can be estimated from observations of orbiting stars or gas, or through techniques like very-long-baseline interferometry.