Black Hole Mass Calculator

Schwarzschild Radius Mass Formula:

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

Schwarzschild Radius (r_s):

meters

Speed of Light (c):

m/s

Gravitational Constant (G):

m³/kg s²

Black Hole Mass (M):

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1. What is the Schwarzschild Radius Mass Formula?

The Schwarzschild radius formula calculates the mass of a black hole from its event horizon radius. This fundamental equation in general relativity describes the relationship between a black hole's mass and the radius at which light cannot escape its gravitational pull.

2. How Does the Calculator Work?

The calculator uses the Schwarzschild radius mass formula:

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

Where:

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

Explanation: This formula derives from Einstein's field equations and represents the mass required to create an event horizon of given radius in spacetime.

3. Importance of Black Hole Mass Calculation

Details: Calculating black hole mass is essential for understanding gravitational effects, accretion disk behavior, gravitational wave predictions, and studying cosmic evolution. Mass determines the black hole's influence on surrounding matter and spacetime curvature.

4. Using the Calculator

Tips: Enter Schwarzschild radius in meters. The calculator pre-fills standard values for speed of light and gravitational constant, but these 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 - the boundary beyond which nothing, not even light, can escape the black hole's gravity.

Q2: How is this formula derived?
A: It comes from solving Einstein's field equations for a spherically symmetric, non-rotating mass in vacuum, first derived by Karl Schwarzschild in 1916.

Q3: Does this work for rotating black holes?
A: No, this formula is for non-rotating (Schwarzschild) black holes. Rotating black holes require the Kerr metric.

Q4: What are typical black hole masses?
A: Stellar black holes: 3-20 solar masses, supermassive black holes: millions to billions of solar masses.

Q5: How is Schwarzschild radius measured in practice?
A: Through observations of orbiting objects, gravitational lensing, accretion disk dynamics, or more recently, gravitational wave detections.