If 2 black holes were to merge, would the event horizon double in size?

Question

also, am I correct in thinking that the schwarzschild radius (event horizon) is about 3 times the mass (i.e. 10m(sun) = 30km and 3m(sun) = 10km)? is it always about 3 times the mass?

Serious answers, please. If you don't believe that black holes exist, go annoy someone else with your pointless replies.

Answer 1

schwarzschild radius formula is:

r = (2Gm)/c^2

where

G = gravitational constant (or 6.67* 10^-11 m^3/kg/s)

m = mass

c = speed of light.

So if an object doubles in mass, it's schwarzschild radius would double as well. That doesn't mean a sphere that is twice as big of course, the volume of the event horizon would be eight times as large. This is universally constant, but you might be able the see that not all objects will generate an event horizon.

the event horizon of your sun is about 3km from the middle, much smaller then the sun itself is. Our sun won't form a black hole, but suppose it does.

It will have to shrink down to a radius of less then 3km at it's current mass in order for us to see the event horizon (pun semi-intended)

ps, congratualtions on asking an actual, proper question on YA, that's a rare thing..

EDIT: as a bonus, the Schwarzschild radius is

1.484942 × 10^-27 m / kg

give or take a little for the accuracy of the gravitational constant.

Answer 2

No, the bigger one would swollow the smaller one and then the mass is still the same for the big one.

Answer 3

Alcari is correct, of course.  But that is for black holes that  are not rotating (Schwarzschild BH).  For a  rotating  (Kerr) BH, the size is more complicated; two equal-sized Kerr BHs that merged would NOT double in size.  The merged BH would be much smaller than double.

The situation for BHs with electric charge, or  with charge and spin, is much more complex.