### Does the event horizon of a black hole increase or decrease by adding mass?

• Vase Dodevski

6 years ago

So a black hole is a something that has enormous gravity, therefore mass accelerates faster towards it. But if the black hole double it's mass, will it's event horizon increase in length , or will it decrease? Did you read the Wikipedia article about the radius of black holes and its dependence on the mass? Not even a minimal amount of research. As a guide - if you type your headline question into a search engine and the first link it provides directly gives you the answer, then it is not a very interesting stack exchange question.

• 6 years ago

The radius of the event horizon ($r_\mathrm{s}$) is directly proportional to the mass of the black hole (M). More exactly:

$$r_\mathrm{s} = \frac{2 G M}{c^2}$$

The black holes whose merger was detected by LIGO would each have been about 90 km in radius, and after merger, a little less than 180km. So apparently, if my waist line is smaller than $6.5×10^{-25}$ meters, I collapse into a black hole. Wow, thanks a lot for that.Really helpful Additional fun fact: If you consider the density of a black hole $\rho$ as its mass over it's volume given as a sphere with a radius equal to the Schwarzschild-radius $\rho = \frac{M}{\frac{4}{3}\pi r_S^3}$, than you′ll find $\rho \sim M^{-2}$. It's getting less dense, the more massive it becomes.