Gravitational difference between a black hole and a star

[Tatest]

How come the gravity of a stellar- mass black hole is strong enough to trap light but the gravity of a stellar-mass star (eg the sun) is not strong enough to trap light ?

 

[Nugatory]

This question is easier to think about if you start with ordinary classical Newtonian gravity: ##F=Gm/r^2## is the formula for the strength of the gravitational field at a distance ##r## from the center of a spherical object (like a star) with mass ##m##. So if we have two objects with the same mass, but one of them is much denser (so is much smaller) than the other, what does that tell us about the strength of the gravitational force at the surface?

 

[Tatest]

Thankyou Nugatory. I think that your marvellous formula tells me that the strength of the gravitational force is greater at the surface of the smaller object compared to a larger object with the same mass.

Doesn't that mean that the smaller object has stronger gravity ?

 

[Nugatory]

Doesn't that mean that the smaller object has stronger gravity ?

It means that the gravitational field is stronger at the surface of the smaller object, because the surface is closer to the center.

You can attach the words "the smaller object has stronger gravity" to this fact if you want, but not everyone is going to understand those words the same way. The math is precise and unambiguous, and that's part of why mathematics is the language of physics.