Speed of gravity is infinite? If fastest thing is light then how universe is spreading faster than the speed of light?
Gravity waves cannot escape from a black hole.
The gravitation field (i.e. the amount of curvature of spacetime at each event) outside the horizon of a black hole was set up in the past as the black hole formed. The black hole in the present is the name we give to the set of locations where, in consequence of this past behaviour, there is now a region of spacetime from which no causal influence can escape. So you see at no time did any gravitational influence have to propagate from inside to outside the horizon of the black hole. Rather, the curvature is set up in the past and then it simply stays constant (until further matter falls to the horizon and then changes the curvature as it passes by).
Questions make sense to me. But question in title should match question in body.
Q: If light and gravity same-speed, why light cant escape
A: If the gravity field had not already been set up, then yes it would be a race between the light and the expanding gravity field. But the light is already in gravity that has been there a long time.
Q2: Does this mean speed of gravity is infinite?
A2: No. Right the first time: propagates at speed of light.
I have edited the question to eliminate the duplicate question. But here’s the answer to it:
Q3: If fastest thing is light then how universe is spreading faster than the speed of light?
A3: This is a totally separate question that has been asked and answered elsewhere. Superluminal expansion of the early universe how is this possible?
Light fastest thing in the universe. Doesnt mean the universe’s boundary cannot grow faster.
Nothing that happens inside the event horizon of a black hole can affect or be detected by a distant observer.
However, from the point of view of a distant observer nothing actually crosses the event horizon of a black hole - everything slows down as it approaches the event horizon, where gravitational time dilation becomes unbounded.
The gravitational field of a black hole seen by a distant observer is actually the gravitational field of everything “frozen” at its event horizon. The reason an external observer cannot see the event horizon (i.e. the reason that black holes are black) is that any photons that are emitted close to the event horizon are hugely redshifted before they reach a distant observer, and eventually become undetectable.
You are asking if the "speed of gravity is infinite" because you may be thinking from a purely Newtonian gravity standpoint, where this would be true (in Newtonian gravity).
It is important to note that Newtonian gravity has been superseded by General relativity, which takes the speed of gravitational interactions to be equal to the speed of light. We note that some galaxies appear to be receding faster than the speed of light, and there is no contradiction. This phenomena is a result of universal expansion, and the restriction imposed by relativity that no signal can be transmitted faster than light is still not violated.
We define the Hubble sphere or Hubble volume, which is a sphere centered where we are, and everything outside this sphere recedes faster than the speed of light due to expansion of the universe.
As to the the other question in your title, light cannot escape from a black hole because a black hole is a region of highly curved spacetime, and light has to follow the geometry of this curved spacetime, so that inside the event horizon all paths are directed to the center and all light rays will always move toward the center. In the language of relativity, all future light cones within a black hole lie within its event horizon.
A black hole does not necessarily emit gravitational waves, and if one did that is not the reason light cannot escape. What causes things to fall for any massive object is Einstein's description of gravity with General Relativity. What he tells us is space and time curve around massive objects, hence any object moving in a gravitational field will be influenced to curve with spacetime. We have observed light curve around other massive objects too, light just isn't trapped into any of those objects. Blackholes create a large enough weld in spacetime that when light passes through it curves just as it curves around any other object however it just curves hard enough that it directs in word.