If the Sun were compressed to its $r$_s (Schwarzschild radius), what would happen to it?

• A. It would become a neutron star.
• B. It would explode in a supernova.
• C. It would remain unchanged.
• D. It would become a black hole.

Answer: (D)

Verified step by step guidance

1. Understand the concept of the Schwarzschild radius, which is the radius defining the event horizon of a black hole. It is given by the formula: \(r_{s} = \frac{2GM}{c^{2}}\), where \(G\) is the gravitational constant, \(M\) is the mass of the object, and \(c\) is the speed of light.
2. Recognize that if an object with mass \(M\) is compressed within its Schwarzschild radius \(r_{s}\), the escape velocity from its surface exceeds the speed of light, meaning nothing, not even light, can escape its gravitational pull.
3. Apply this understanding to the Sun: if the Sun were compressed to a radius equal to or smaller than its Schwarzschild radius, it would form an event horizon, effectively becoming a black hole.
4. Note that becoming a neutron star or exploding in a supernova are different astrophysical processes that occur under different conditions, typically involving stars with different masses or evolutionary stages.
5. Conclude that compressing the Sun to its Schwarzschild radius means it would become a black hole, as this radius marks the boundary beyond which gravitational collapse leads to a black hole.