Question

The formula for the Schwarzschild radius is RSch = 2GM c2 = 2.9532 M M⊙km , where G = 6.67384 × 10⁻¹¹ (in MKS units) is the gravitational constant, M is the mass of an object, c is the speed of light, and M⊙ = 1.9885 × 10³⁰ kg is the mass of the Sun. This formula follows from general relativity for a non-rotating, spherically symmetric mass distribution, but it also accidently can be obtained by setting the escape velocity equal to the speed of light in the Newtonian formula for the escape velocity from a spherically symmetric mass distribution. According to general relativity if any object is compressed within its Schwarzschild radius it:.

Answer 1

When an object is compressed within its Schwarzschild radius, it becomes a black hole, with Sgr A* having a Schwarzschild radius of approximately 11,848,000 kilometers.

Step-by-step explanation:

According to general relativity, if any object is compressed within its Schwarzschild radius, it becomes a black hole—a region in space where the escape velocity exceeds the speed of light, and therefore, not even light can escape. The Schwarzschild radius (Rs) is calculated using the formula Rs = 2GM/c², where G is the gravitational constant, M is the mass of the body, and c is the speed of light. For the center of our Galaxy, the supermassive black hole named Sgr A*, with a reported mass of around 4 million solar masses, the calculation of its Schwarzschild radius would be:

Rs = 2(6.67384 × 10⁻¹¹)(4 × 10⁶)(1.9885 × 10³⁰) / (3.00 × 10⁸)² = 11,848,000 km.

This radius represents the boundary of the event horizon for Sgr A*, beyond which no information or matter can return.