**When black holes merge, does the actual diameter of the new black hole increase, or just its mass?**

*Richard Robinson**Clay, New York*

The short answer is yes: When two black holes merge, the resulting black hole has both more mass and a larger diameter. How much bigger? Let’s find out!

When astronomers talk about the size of a black hole, they’re talking about the size of its event horizon — the point of no return, beyond which even the speed of light is not sufficient to escape the black hole’s gravity. This is not a physical structure that you could touch, but a mathematical, spherical boundary. At its center lies the heart of a black hole: the singularity, which has mass but no volume.

For a simple, non-spinning black hole, the radius of the event horizon is also called the Schwarzschild radius, named for German physicist Karl Schwarzschild, who first worked out how big it would be. The Schwarzschild radius of a black hole, called *r _{S}*, is given by the equation

*r*= 2

_{S}*GM*/

*c*

^{2}, where

*G*is the gravitational constant (6.67 x 10

^{-11}m

^{3}kg

^{-1}s

^{-2}),

*M*is the mass of the black hole (in kilograms), and

*c*is the speed of light in meters per second (3 x 10

^{8}m/s).

As a simple example, if we merge two black holes with the same mass and assume no mass is lost in the smash-up, we end up with a final black hole with twice the mass and also twice the radius of either of the two black holes that went into it.

It’s worth noting that in the real world, black holes *can* spin, and there are a whole host of other effects that ultimately impact the size and even way we would define a black hole’s “diameter.” Furthermore, some small fraction of the black holes’ mass is lost when they merge, radiated away as energy via gravitational waves. So, in practice, you always end up with a final black hole whose mass is generally not *quite* the sum of the two progenitor black holes combined.

*Alison Klesman**Senior Editor*