About the gravity of a black hole Earth, sun and all the planets and the stars of the universe have a gravity field, which is determined by the second law of Newton. But this law can't explain the gravity of a black hole. So what do we mean by the gravity of a black hole and what is its formula?
 A: But we can understand black holes with Newtonian physics. In fact, black holes were first hypothesized by the English natural philosopher John Michell in the 18th century. To understand black holes with classical physics, we have to understand the Schwarzchild radius . We can derive this by solving for the velocity it takes for some object to break a heavenly body's gravitational field, known as the escape velocity. Consider a rocket that blasts off from the planet's surface. By the conservation of energy, the total energy of the rocket(kinetic plus potential) at the planet's surface will be equal to the total energy when the rocket is infinitely far away. Because the rocket is starting at the surface with some initial velocity, all of its initial energy is kinetic. If the rocket is far enough away from the planet, then its speed will be negligible and we can safely assume all of its final energy will be potential. Be the conservation of energy, we thus find that
\begin{equation}
\frac{mv^2}{2}-\frac{GMm}{r}=0+0\rightarrow v^2=\frac{2GM}{r}
\end{equation}
where $m$ is the mass of the rocket, $G$ is Newton's gravitational constant, $M$ is the mass of the planet, and $r$ is the radius of the planet. $v$ is thus the velocity it takes for the rocket to completely escape the planet's force of gravity.
Now, simply take $v=c$--that is, compact all the mass $M$ into a radius so small that the escape velocity is the speed of light. This "critical" radius in which matter cannot be compacted any further is the Schwarzschild radius:
\begin{equation}
r=\frac{2GM}{c^2}
\end{equation}
When an object of mass $M$ is compacted to this radius, an object would have to travel faster than the speed of light to escape its gravitational pull. Because no object can move faster than the speed of light outside science fiction, nothing can escape a black hole. The Schwarzschild radius thus marks the "point of no return": the event horizon.
Of course, classical mechanics can only go so far. As they age, black holes decay and give off Hawking radiation, and this is a quantum effect. Furthermore, to truly understand the nature of black holes and the nature of the event horizon, we need a quantum theory of gravity. The fact that information gets trapped in a black hole with a finite lifetime causes problems that can't be addressed in classical mechanics, and some people believe that a "firewall" might have to exist at the event horizon to solve these issues. Indeed, some recent experiments from LIGO appear to support some new physics at the event horizon, so we just need to wait and see if the "firewall" is a reality.
So, in short, much of black hole physics can be described with normal Newtonian mechanics. However, though it might be able to explain simple gravitational effects, there is still much to learn concerning its quantum nature.
A: Some parts of your statements in your question are just not right, so your question may get put on hold or deleted. People expect questions to be asked after doing some independent research into the issue in question, and then ask what they don't understand. But I will answer you as though you asked 'why can't Newton's gravitation explain black holes (BH)?'
Well it can't for many reasons. It's not Newton's second law (which is F=ma) but rather his law of gravitation which says there is a force between any two masses. That is, for two masses M and m separated by a distance R the force is (with G the so called Newton's constant)
$F = GMm/R^2$ 
Newton's equation assumes the force is exercised at a distance. If you are on the surface of a planet, with mass M, with R the radius of the planet (assume it perfectly spherical, it's close enough for these purposes), then everything in that equation is given except m, and you can write the equation as F = mg, with g the acceleration of gravity in that planet on the surface. 
For Newton there was no speed limit such as the speed of light. So you could always escape any mass M. But special relativity (SR) discovered that nothing can go faster than light, with speed c. So yes, for a massive enough M, you could not go fast enough to escape it's gravity, it'll pull you back down. 
But that's still not a BH, in a BH you can't even go above the surface. You are trapped inside. The modern BHs were only predicted by using general relativity (GR), that explains gravity as the effect of space and time (called spacetime) being curved and bending the orbits of masses (and actually of any energy, thus also of zero rest mass particles, i.e., radiation). If you are on the surface of some planet, your body feels like it wants to go further into the planet, i.e., it feels like it's being acted upon by a force. GR and Newtonian gravity are explained, as an intro, in the wiki article. 
https://en.m.wikipedia.org/wiki/Gravity
It was the physicist John Wheeler who first used the term 'Black Hole' in 1967. The first GR solution that indicated that a horizon was possible was found by Schwarzschild before 1920, but it was in Wheeler's time that some calculations were done to show the plausibility, and not too long after that that Hawki g and others showed that in fact if a body was massive enough, it had no choice but to form a BH. Less massive ones would form neutron stars or white dwarfs when their fusion fuel got exhausted and they started collapsing, often with a supernova explosion in the middle of all that.  
There's a big difference between Newton and GR. With GR the surface of the BH is just empty space, but the mass M of the BH does not let anything escape above that surface. It's called the horizon. Since nothing escapes, including light, it looks black. Light, in GR, also follows the curvature of spacetime, and cannot escape the horizon. That horizon is a unique entity only defined in GR. [there are also cosmological horizons, one of those defines our observable universe, but that's a different story].
But you have to calculate everything using GR, and when you do calculate relativistically the acceleration at the horizon, it turns out to be infinite. There is a way to normalize it relativistically by multiplying it by the time dilation factor which is 0 at the horizon, and you get a reasonable measure, called the surface gravity of a BH, as k= 1/4M (there's some other constants which are here taken to be 1). See the discussion at wiki in https://en.m.wikipedia.org/wiki/Surface_gravity. It turns out then, from that formula, that if you are falling in to a supermassive BH, then, as M is very big the surface gravity at the horizon is not that big, and you may not even feel any difference as you fall into the horizon of that BH. A stellar mass BH is much worse for you. But either way, once you are inside the horizon you will inexorably continue falling till you hit the singularity (more below).
That's another difference with Newton. There's plenty more. 
BHs colliding and merging with each other release a huge amount of energy in the form of gravitational waves, from outside their horizons, and we've detected them in LIGO from BHs 1.3, 1.4, and 3 billion light years away. All the subsequent analysis is that they in fact obey GR, much to the chagrin of some who said otherwise. You can look up the results and analysis at LIGO.org. 
Other factors:
-gravitational waves, and gravitational effects, also cannot travel faster than light. Action is not at a distance, but takes time to propagate across space. More, Newton's law imply no gravitational waves. 
-Singularity: the gravitational effect becomes so strong at the center (if a perfect sphere) that it theoretically becomes infinite. It is believed that a quantum theory of gravity will resolve that issue. We don't have yet a good quantum gravity theory, but we are researching. String theory is one option, but nothing is firm. 
-a quantum treatment (not a full theory of quantum gravity, just a partial theory of normal quantum fields in gravity) of the space outside but near the horizon of a BH was done by Hawking and he discovered that some radiation can escape the BH, something similar to quantum tunneling (and there's multiple ways to explain it, the best is the quantum calculation). It's not been detected yet, for the kinds of BHs we have detected it is just too weak,  but it is widely thought it has to exist, and that they could be detected when the radiation is stronger, as the BH is near its end of life and may emit that radiation as a strong burst. 
-there are more gravitational wave detectors being built and it is believed they will be able to detect new BHs much more often, and study them more exactly. Space-based detectors will also be built, with much better accuracies and able to see much longer wavelength gravitational waves (i.e., from much bigger objects and including from very early in the universe) but that's much further out in time. 
-for the firewall issue I recommend a wiki article on it. It's its own long story. 
