What happens to matter in extremely high gravity? Though I am a software engineer, I have bit interest in sciences as well. I was reading about black holes and I thought if there is any existing research results on How matter gets affected because of extremely high gravity. I tried searching but these long equations really didn't help me. Can someone please put it in layman terms?
More specifically if I ask Why the infinite gravity doesn't tear down the atoms in to quarks and does it have enough potential that it can affect something a Planck scale?
 A: Extreme gravity essentially equates to extreme pressure. We see a progression in stellar evolution.
The high pressures of the huge gravitational pull of a star is at first counteracted by electromagnetic/thermal interactions between gas particles. However, at a certain point (with enough gravitational pull) these interactions are not enough and the gravitational force overwhelms electromagnetic forces. Positively charged nuclei collide into positively charged nuclei and hydrogen fusion occurs. The star is supported from further collapse via electron degeneracy pressure, where two electrons cannot occupy the same quantum state.
As elements bind into heavier elements, fusion becomes more and more difficult and requires more energy. Eventually the nuclear forces are not sufficient and the star collapses further, allowing carbon to fuse. This carbon fusion is much more energetic than the proceeding fusion and the star explodes. If there is sufficient mass, a supernova occurs and the remnant could be a neutron star (if the star exceeds the Chandrashankar limit of about 1.44 solar masses) or a black hole (if the star exceeds the Tolman-Oppenheimer-Volkoff Limit of 3 solar masses).
In a neutron star, fermi-degeneracy pressure keeps the particles from collapsing down to a gravitational singularity. Essentially there is enough pressure to force electrons into protons and form neutrons (inverse beta decay), and the neutrons are only stopped from colliding with each other by neutron degeneracy pressure. With a large enough mass though, even this is not enough to stop collapse, to either a theoretical quark star or even to a black hole.
So essentially we see as pressure increases, the various forces that keep matter matter-like get overcome. First electromagnetic interactions, then electron degenerecy pressure, then neutron degenercy pressure, and finally a collapse into a singularity/black hole (or something like that).
Edit: In response to the original poster's question, they can theoretically condense further to a quark degenerate matter. The specifics at this level get more fuzzy, since the strong force is difficult to model accurately due to asymptotic freedom. Unless there are particles that make up quarks, this is the lowest level of possible degeneracy. 
A: Tidal disruptions
The single most distinctive feature of the gravitational field around massive compact objects such as black holes is the presence of strong tidal forces. These forces arise when the gravitational pull on one portion of an object differs significantly in strength from the pull on another portion of an object. Mathematically, tidal forces arise from the presence of sizable second derivatives of the gravitational potential (or, strictly speaking from the perspective of general relativity, second derivatives of the metric tensor).
As is well discussed in many other answers on this site and elsewhere on the Internet, an object falling directly toward a black hole will be stretched and ripped apart from the tidal forces acting on it. If the object is a person falling feet first, the gravitational attraction will be stronger on the feet than on the head, which is what causes the stretching.
A current hot topic in astrophysical research is the tidal disruption of stars orbiting compact objects. Only within the last year or two, such events have begun to be directly observed.
Accretion-powered luminous objects
The gravitational field of a massive compact object provides a tremendous potential energy well. This potential energy can be released as electromagnetic radiation when objects fall into hot accretion disks surrounding the compact object. A quasar is the brightest example of an accretion-powered luminous source - indeed, quasars are the among the most energetic light sources in the universe and are among the most distant objects we can observe on earth.
Accretion into a gravitational potential well is the universe's most efficient mechanism for releasing energy. On average, 10% of the total mass-energy ($m c^2$) that falls into quasars gets radiated away as light. In extreme cases, especially when the black hole has a large amount of angular momentum, this efficiency can rise even closer to unity. Compare to this to efficiency of hydrogen fusion into helium in the sun, which only converts 0.7% of the mass-energy into radiation.
Wrapping up magnetic fields
Einstein's theory of general relativity interprets gravity as curvature in four-dimensional spacetime. An example of a purely relativistic gravitational effect is a type of 'twisting' or wrapping up of space known as frame-dragging. Frame dragging can have a number of interesting effects. One of the most dramatic is the wrapping of magnetic fields into coils which can then launch matter from an accretion disk at relativistic speeds. The details of this magnetic jet-launching are explained either by the so-called Blandford-Znajek mechanism or the Penrose process.
Emission of gravitational waves
When two massive objects such as black holes get close to each other, as often happens to the central super-massive black holes in galaxies following a major galaxy merger, their orbital motion can send out waves of stretching and compression of spacetime called gravitational radiation. Very soon (it is June 2012 as of the time of this writing), scientists can expect to detect these gravitational waves directly at the Laser Interferometer Gravitational-Wave Observatory (LIGO).
A: Let us separate the matter into two branches:
a)Black Holes, which are governed by those equations you are loath to delve into
b)matter in high gravity fields , if the mass is low enough so that a black hole cannot form, according to the equations.

Gravitational collapse is at the heart of structure formation in the universe. An initial smooth distribution of matter will eventually collapse and cause a hierarchy of structures, such as clusters of galaxies, stellar groups, stars and planets. For example, a star is born through the gradual gravitational collapse of a cloud of interstellar matter. The compression caused by the collapse raises the temperature until nuclear fuel reignites in the center of the star and the collapse comes to a halt. The thermal pressure gradient (leading to expansion) compensates the gravity (leading to compression) and a star is in dynamical equilibrium between these two forces.
Gravitational collapse of a star occurs at the end of its lifetime, also called the death of the star. When all stellar energy sources are exhausted, the star will undergo a gravitational collapse. In this sense a star is in a "temporary" equilibrium state between a gravitational collapse at stellar birth and a further gravitational collapse at stellar death. The end states are called compact stars.
The types of compact stars are:
White dwarfs, in which gravity is opposed by electron degeneracy pressure;
Neutron stars, in which gravity is opposed by neutron degeneracy pressure and short-range repulsive neutron–neutron interactions mediated by the strong force;
Black holes, when the mass is high enough, and where the  the physics at the center is unknown.

The link from which the quote is taken can inform further.
