What is meant by Schwarzschild radius ? Why
do we call Schwarzschild radius the event
horizon ? Calculate the Schwarzschild radius for
the Sun.
The Schwarzschild radius, named after the German astronomer Karl Schwarzschild, is a critical parameter in the field of general relativity, a fundamental theory in the realm of astronomy and astrophysics. It defines the size of the spherical region around a non-rotating, spherically symmetric mass at which the escape velocity equals the speed of light. Beyond this radius, not even light can escape, marking a boundary known as the event horizon. The concept of the Schwarzschild radius is intimately connected to the understanding of black holes.
In simple terms, the Schwarzschild radius (Rs) is calculated using the formula:
\[ R_s = \frac{{2GM}}{{c^2}} \]
where:
- \( G \) is the gravitational constant (\( G \approx 6.674 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2} \)),
- \( M \) is the mass of the object (in kilograms),
- \( c \) is the speed of light (\( c \approx 3 \times 10^8
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