How can we say star mass affects event horizon diameter ?

[PhyHunter]

PLEASE LOOK ATTACHMENT!
Star mass affects event horizons diameter.But we know that Black hole's foundation is singularity so we can understand that singularity affects event horizon diameter.
Example:Imagine there are two stars, first star mass is 5 star mass second one is 7 star mass so If we think when they transform black hole both of them wiil be create singularity.So there are two same singularity.We know singularity affects event horizon diameter. How can we say star mass affects event horizon diameter.
How can we understand that r₁ is longer than r ? (please look attachment)

 

[mathman]

The concept of the singularity is purely theoretical. Since it is contradicted by quantum theory, no one really knows what happens inside a black hole. The diameter of the event horizon is determined by the mass, irrespective of what happens inside.

 

[PhyHunter]

How did Physicists find this equations ? Have you any idea about this subject ?

 

[Mordred]

Look at the Shwartzchild metrics.

http://jila.colorado.edu/~ajsh/insidebh/schw.html

http://en.m.wikipedia.org/wiki/Schwarzschild_metric

the second link covers Shwartzchild metric. The first link has some decent videos based on simulations

 

[Chronos]

The Schwarzschild metric is an exact solution to Einstein's field equations.

 

[Naty1]

You can only understand [or maybe 'accept'] the relationship between mass and the radius of an event horizon from the mathematics of general relativity.

There are some good general insights here in sections 5 and 6 which may be of interest.

http://en.wikipedia.org/wiki/General_relativity#Black_holes_and_other_compact_objects

But especially when starting out, there is not a lot of 'logic' to an event horizon. It is useful to keep in mind that, as always in relativity, different observers may record different observations. And different geometries expose different aspects of black holes and horizons.

Massive gas clouds may coalesce to form a stellar object, like a star. After sufficient energy and heat is expelled from a stellar object, after billions upon billions of years when it's nuclear fuel is largely used, then gravity has sufficient strength to cause some collapse of the remaining matter. What we think we understand is that highly compressed matter, called degenerate matter, might prevent the formation of a black hole in a stellar object with insufficient mass. But once the mass is sufficiently large, collapse to a singularity with an event horizon seems inevitable. Exactly what remains is uncertain.

For more reading, check out supermassive black hole in Wikipedia.