Question

Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all these have definitive answers, so your explanation is more important than your chosen answer. If two black holes merge together, the resulting black hole is even smaller than the original ones because of its stronger gravity.

Short answer

The statement does not make sense; a merged black hole is larger, not smaller.

Step-by-step solution

Understanding Black Holes

A black hole is a region of space where the gravitational pull is so strong that nothing, not even light, can escape it. The size of a black hole is determined by its event horizon, the boundary beyond which nothing can escape. In physics, the mass and size are critical factors when discussing black holes.

Basics of Black Hole Merging

When two black holes merge, their masses combine. According to the laws of physics, especially the conservation of mass and energy, the total mass of the new black hole formed by the merger is approximately the sum of the masses of the original two black holes, minus some energy lost in the form of gravitational waves.

Implication of Combined Mass on Size

As black holes merge, their combined mass results in a new event horizon that is larger than the original black holes. The event horizon's size increases because the Schwarzschild radius, which determines the size of a black hole's event horizon, is directly proportional to its mass.

Analyzing the Statement

The statement suggests that a merged black hole is smaller due to its stronger gravity. However, stronger gravity due to increased mass typically results in a larger event horizon, not smaller. Thus, the statement seems to contradict established scientific understanding.

Key concepts

Event Horizon

The event horizon is a crucial concept when it comes to understanding black holes. It is essentially the boundary surrounding a black hole beyond which nothing can escape, not even light. This means if something crosses this boundary, it will inevitably be sucked into the black hole because the gravitational pull is too strong.
Imagine the event horizon as the edge of a waterfall. If you stay on the bank or swim away strong enough, you can avoid being pulled over. However, once you cross it, the pull of the waterfall will take you down.

• It's an imaginary line - not something physical you can touch.
• The size of the event horizon is determined by the mass of the black hole.
• The larger the mass, the larger the event horizon.

When two black holes merge, their masses combine and create a larger event horizon, not a smaller one.

Gravitational Waves

Gravitational waves are ripples in the fabric of spacetime that are caused by some of the most violent and energetic processes in the universe. When black holes merge, a part of their mass is converted into gravitational waves.
This may sound complicated, but in simple terms, it’s like throwing a heavy rock into a pond and watching ripples spread out across the water. This is a way to visualize how gravitational waves ripple throughout space.

• They were first predicted by Albert Einstein in 1916.
• Gravitational waves are created when massive bodies like black holes, move quickly and change their configuration in space.
• The detection of these waves helps scientists confirm black hole mergers and learn more about the universe.

Even though some mass is lost as energy in the form of these waves during a black hole merger, the resulting black hole is still larger than either of the original black holes.

Schwarzschild Radius

The Schwarzschild radius is a term used to describe the size of the event horizon of a black hole based on its mass. It determines the boundary from which nothing can escape the black hole's pull.
It's like a measure of how much space can be contained within a certain amount of mass if it were compressed to its very limit. Imagine taking the Earth and making it extremely dense. Its Schwarzschild radius would be very small, indicating how much space it would occupy as a black hole.

• The formula for the Schwarzschild radius is: \[ r_s = \frac{2GM}{c^2} \] where \( r_s \) is the Schwarzschild radius, \( G \) is the gravitational constant, \( M \) is the mass, and \( c \) is the speed of light.
• Hence, larger mass means a larger Schwarzschild radius.
• This is why when two black holes merge, the resultant black hole has a larger Schwarzschild radius.

By understanding the Schwarzschild radius, it becomes clear why a black hole becomes larger after merging with another, despite some mass being transformed into gravitational waves.