Diamonds are not forever. They may be very hard, but are quite rigid and will shatter like glass if hit hard enough. At high temperatures they can be melted, and jewelers regularly use steel tools to cut diamond.
The closest that any compact physical object comes to being eternal is the black hole. The remnant of the collapse of a giant star, black holes are basically untouchable. They have the same mass as their parent star, shoved into an area that is usually treated as a zero-dimensional point. Stars can die through supernovae or collisions with other stars - black holes cannot.
Black holes very slowly evaporate over time due to a phenomenon called Hawking radiation, named after Stephen Hawking, who first postulated it. The length of time it would require for a black hole with mass equal to the Sun to evaporate is about 1067 years, which is about as close to forever as anything in this universe can get. Supermassive black holes take much, much longer to evaporate. These will be around for more centuries than there are particles in the universe.
According to the "No Hair theorem," any black hole can be exhaustively characterized by only three variables: mass, angular momentum, and electric charge. To simplify, we can call these mass, spin and charge.
In the mass variable, there are two main categories of black hole: solar-mass black holes, between about 2.5 and 20 solar masses, and supermassive black holes, between a hundred thousand and tens of billions of solar masses. Solar-mass black holes are formed when giant stars collapse after a supernova, supermassive black holes are formed at the center of galaxy-sized accretion discs. Astronomers believe that almost all galaxies have central black holes, including the Milky Way, our galaxy, the central black hole of which has already been pinpointed.
Angular momentum, or spin, not to be confused with the variable of spin in quantum mechanics, has to do with how fast the black hole is rotating. Most black holes rotate very rapidly, because they retain all the angular momentum of their parent star, but condensed into a much smaller space. This is similar to the way in which a skater accelerates her rotation speed when she brings her arms in closer. Rotating black holes are called Kerr black holes.
The last variable used to describe black holes is charge. Very few black holes have any appreciable charge, because the electromagnetic force is many times more powerful than gravity, preventing any charged object from collapsing due to self-repulsion. Imagine trying to press together two star-sized magnets on the sides with the same magnetic orientation, using nothing but gravity as the compressive force. It can't be done. Charged black holes are known as Reissner-Nordström or Kerr-Newman black holes, which are non-rotating and rotating, respectively.
Non-rotating, non-charged black holes are known as Schwarzschild black holes.
