This question is the first part of a multi$-$part problem.

The Schwarzschild radius is the critical radius at which the escape velocity from a massive object equals the speed of light. Beyond this radius, not even light can escape the gravitational pull of the object, forming a black hole.

The Schwarzschild radius is also referred to as the event horizon of a black hole in the case of non$-$rotating, uncharged black holes $($also known as Schwarzschild black holes$).$

Equivalently, the event horizon is the boundary around the black hole where the escape velocity equals the speed of light. Beyond this boundary, not even light can escape the gravitational pull, making the black hole $$invisible$$ to external observers.

The Schwarzschild radius r$$ is given by the formula

r $=(2$GM$)/($c$^2)$

where$$ G$$ is the gravitational constant,$$ M$$ is the mass of the object, and$$ c$$ is the speed of light.

If the mass of an object doubles, how does its Schwarzschild radius change?