How To Calculate Density Of A Black Hole

Black Hole Density Formula:

\[ \rho = \frac{3c^6}{32\pi G^3 M^2} \]

Black Hole Density (ρ):

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1. What is Black Hole Density?

Black hole density refers to the mass per unit volume of a black hole, calculated based on its Schwarzschild radius. It represents an average density since black holes are singularities with theoretically infinite density at their centers.

2. How Does the Calculator Work?

The calculator uses the black hole density formula:

\[ \rho = \frac{3c^6}{32\pi G^3 M^2} \]

Where:

\( \rho \) — Black hole density (kg/m³)
\( c \) — Speed of light in vacuum (299,792,458 m/s)
\( G \) — Gravitational constant (6.6743 × 10⁻¹¹ m³/kg s²)
\( M \) — Black hole mass (kg)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula derives from the Schwarzschild radius formula \( r_s = \frac{2GM}{c^2} \) and the volume of a sphere \( V = \frac{4}{3}\pi r^3 \), with density \( \rho = \frac{M}{V} \).

3. Importance of Black Hole Density Calculation

Details: Calculating black hole density helps understand the extreme nature of these cosmic objects, their gravitational effects, and provides insights into general relativity and quantum gravity theories.

4. Using the Calculator

Tips: Enter black hole mass in kilograms. 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: Why does black hole density decrease with increasing mass?
A: Larger black holes have Schwarzschild radii that increase linearly with mass, but volume increases with the cube of radius, causing average density to decrease.

Q2: What is the density of a stellar-mass black hole?
A: A 10 solar mass black hole has a density of approximately 2 × 10¹⁹ kg/m³, much denser than atomic nuclei.

Q3: What about supermassive black holes?
A: Supermassive black holes can have densities comparable to or even less than water. For example, Sagittarius A* has density ~10⁵ kg/m³.

Q4: Is this the actual density throughout the black hole?
A: No, this is an average density. Black holes are thought to be singularities with infinite density at the center within an event horizon.

Q5: Can anything escape a black hole's density?
A: Nothing can escape from within the event horizon due to the extreme gravitational pull, which is related to the black hole's density and mass.