The formula to calculate the Schwarzschild Radius (R) is:
\[ R = \frac{2GM}{c^2} \]
Where:
Let's say the mass of the black hole (\( M \)) is 10 solar masses. Using the formula:
\[ R = \frac{2 \cdot 6.67430 \times 10^{-11} \cdot (10 \cdot 1.98847 \times 10^{30})}{(299792458)^2} \]
We get:
\[ R \approx 29.53 \text{ kilometers} \]
So, the Schwarzschild Radius (\( R \)) is approximately 29.53 kilometers.
The Schwarzschild radius, also known as the black hole radius, is the distance from the center of a black hole to its event horizon, the point beyond which nothing, not even light, can escape its gravitational pull. It is a critical measure in astrophysics for understanding the size and boundary of a black hole.
Definition: The radius of a black hole, also known as the Schwarzschild radius, is the radius of the event horizon beyond which nothing can escape the gravitational pull of the black hole.
Formula: \( R_s = \frac{2GM}{c^2} \)
Example: \( R_s = \frac{2 \times 6.674 \times 10^{-11} \times 10^{30}}{(3 \times 10^8)^2} \)
Definition: A tool to estimate the lifetime of a black hole based on its radius.
Formula: \( T = \frac{5120 \pi G^2 M^3}{\hbar c^4} \)
Example: \( T = \frac{5120 \pi \times (6.674 \times 10^{-11})^2 \times (10^{30})^3}{(1.054 \times 10^{-34}) \times (3 \times 10^8)^4} \)
Definition: A tool to calculate the diameter of a black hole based on its mass.
Formula: \( D = \frac{4GM}{c^2} \)
Example: \( D = \frac{4 \times 6.674 \times 10^{-11} \times 10^{30}}{(3 \times 10^8)^2} \)
Definition: A tool to calculate the density of a black hole based on its mass and radius.
Formula: \( \rho = \frac{3M}{4 \pi R_s^3} \)
Example: \( \rho = \frac{3 \times 10^{30}}{4 \pi \times (2.95 \times 10^3)^3} \)
