Calculating The Mass Of A Black Hole

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 mass formula calculates the mass of a black hole from its Schwarzschild radius using fundamental physical constants. This equation is derived from Karl Schwarzschild's solution to Einstein's field equations of general relativity.

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 (meters)
\( c \) — Speed of light in vacuum (299,792,458 m/s)
\( G \) — Gravitational constant (6.6743 × 10⁻¹¹ m³/kg s²)

Explanation: The Schwarzschild radius represents the radius of the event horizon, beyond which nothing can escape the black hole's gravitational pull.

3. Importance of Black Hole Mass Calculation

Details: Calculating black hole mass is essential for understanding black hole properties, gravitational effects, accretion disk behavior, and studying general relativity predictions in extreme gravitational fields.

4. Using the Calculator

Tips: Enter Schwarzschild radius in meters, speed of light in m/s (default: 299,792,458), and gravitational constant in m³/kg s² (default: 6.6743e-11). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the Schwarzschild radius?
A: The Schwarzschild radius is the radius of a sphere such that, if all the mass of an object were compressed within that sphere, the escape velocity would equal the speed of light.

Q2: How is Schwarzschild radius related to black hole mass?
A: The Schwarzschild radius is directly proportional to the black hole's mass - doubling the mass doubles the Schwarzschild radius.

Q3: What are typical Schwarzschild radii for astronomical black holes?
A: Stellar black holes: ~3 km per solar mass; supermassive black holes: millions to billions of kilometers.

Q4: Can this formula be used for any mass?
A: Yes, but for non-black hole objects, the Schwarzschild radius is usually much smaller than the object's actual radius.

Q5: What are the limitations of this calculation?
A: This assumes a non-rotating, uncharged black hole (Schwarzschild metric). Rotating black holes require the Kerr metric.