# Mathematicians conceived of black holes long before astronomers actually found any?How?

I read this statement in Lockhart's - "A Mathematician's Lament". But how could mathematicians figure out something like black holes even before astronomers noticing any of them?

• General relativity! May 19 '13 at 19:33
• Any more details would be wonderful!! May 19 '13 at 19:39
• One issue is that the escape velocity can be greater than the speed of light. What happens then? May 19 '13 at 19:42
• Google the keywords "Schwarzschild solution". And it is in fact in the very FIRST place black hole exists in math (some object has a smaller radius than its Schwarzschild radius), then astronomers went on to design methods to detect them (like exploiting gravity lens effect). May 19 '13 at 20:22
• A word of caution about the looseness of that claim: Most everyone involved in developing the theory of black holes would be described primarily as a theoretical physicist/astrophysicist, not a mathematician. You could ask how does any theorist make predictions prior to having observations, but that's just what a prediction is, and it's exactly what theoretical scientists do all day long.
– user43318
May 19 '13 at 22:31

$$\dot{x}=x^2,\quad x(0)=1$$ The solution to this equation is the function
$$x(t)=\frac{1}{1-t}$$
This function exhibits finite time blow-up, since when $t=1$, we have a singularity - a place where $x(t)$ becomes infinite. If the ODE models our system accurately, we should be able to observe this blow-up with measurements. The same is true of gravitational singularities - the model predicts a blow-up, so astronomers went looking for (and found) those singularities.