When two black holes merge, the ensuing black hole has each extra mass and a bigger diameter.
This nonetheless from a simulation exhibits two merging black holes, every with tens of solar lots and one barely bigger than the opposite. When black holes merge, the result’s bigger than the originals in mass, space, and quantity. Credit score: The Simulating eXtreme Spacetimes (SXS) challenge (http://www.black-holes.org)
When black holes merge, does the precise diameter of the brand new black hole improve, or simply its mass?
Richard Robinson
Clay, New York
The quick reply is sure: When two black holes merge, the ensuing black hole has each extra mass and a bigger diameter. How a lot greater? Let’s discover out!
When astronomers discuss concerning the measurement of a black hole, they’re speaking concerning the measurement of its event horizon — the purpose of no return, past which even the velocity of sunshine is just not adequate to flee the black hole’s gravity. This isn’t a bodily construction that you may contact, however a mathematical, spherical boundary. At its middle lies the guts of a black hole: the singularity, which has mass however no quantity.
For a easy, non-spinning black hole, the radius of the event horizon can also be referred to as the Schwarzschild radius, named for German physicist Karl Schwarzschild, who first labored out how large it could be. The Schwarzschild radius of a black hole, referred to as rS, is given by the equation rS = 2GM/c2, the place G is the gravitational constant (6.67 x 10-11 m3 kg-1 s-2), M is the mass of the black hole (in kilograms), and c is the velocity of sunshine in meters per second (3 x 108 m/s).
As a easy instance, if we merge two black holes with the identical mass and assume no mass is misplaced within the smash-up, we find yourself with a ultimate black hole with twice the mass and in addition twice the radius of both of the 2 black holes that went into it.
It’s price noting that in the actual world, black holes can spin, and there are an entire host of different results that finally impression the dimensions and even manner we might outline a black hole’s “diameter.” Moreover, some small fraction of the black holes’ mass is misplaced after they merge, radiated away as power through gravitational waves. So, in apply, you at all times find yourself with a ultimate black hole whose mass is usually not fairly the sum of the 2 progenitor black holes mixed.
Alison Klesman
Senior Editor
Hawking’s space theorem
When Stephen Hawking answered an analogous query about black holes colliding in our December 1998 difficulty, he famous: “An attention-grabbing function that I noticed whereas I used to be stepping into mattress one night time in 1970 is that the realm of the event horizon, or boundary, of the ultimate black hole must be higher than the sum of the areas of the occasion horizons of the unique black holes. This limits the quantity of power that may be radiated in gravitational waves and in addition steered that the realm of the event horizon is just like the thermodynamic amount entropy, a connection that was established after I later confirmed that black holes radiate like scorching our bodies.”
Known as Hawking’s space theorem, this idea states {that a} black hole’s entropy — which is proportional to the realm of its event horizon — can’t lower. So, even when black holes can lose some small quantity of mass throughout the merger, the ultimate event horizon can’t have much less space than the sum of the preliminary occasion horizons mixed.
This theorem was developed some 45 years earlier than the 2015 first detection of gravitational waves. A July 2021 paper in Bodily Overview Letters lastly confirmed Hawking’s theorem observationally. In it, researchers reanalyzed the primary gravitational-wave merger ever seen, referred to as GW150914, and decided with 95 % confidence that the realm of the ensuing black hole’s event horizon had not decreased in comparison with the occasion horizons of the progenitor black holes. — A.Okay.
