The renowned astronomer Arthur Eddington called them a cosmological absurdity. GR and its equations predicted their outcome, yet Einstein originally thought that there would always be a physical barrier to prevent such catastrophic collapse. John Michell theorised BH of sorts as far back as the late 1700's while working on collapsed star densities and mass. He called them "Dark Stars" but was not really taken seriously and his work was pigeon holed until many years later when Neutron stars were discovered and questions were asked about further possible collapse of stellar objects. When a star uses up its available fuel for fusion, it has one of three paths to take, based on the original mass of that star. It can end up a White Dwarf as our own Sun will eventually see out its life. These WD's are held up from further collapse by EDP [Electron Degeneracy Pressure] Larger mass stars finish their lives as Neutron/Pulsar stars, held up from further collapse by NDP. [Neutron Degeneracy Pressure] Inevitably even larger mass stars are monstrous enough to overcome both EDP and NDP, and forming what was to be known as Black Holes. First known as Gravitationally Completely Collapsed Objects, John Wheeler coined the BH. Simply put a BH's EH [Event Horizon] is where the escape velocity equals "c" the speed of light in a vacuum. Beyond this point nothing can escape, including light. A BH's size can vary from those predicted to have occurred at the BB, microscopic quantum sized BH's, to stellar collapse BH's a few 10s of kms in diameter, and the monsters that lurk at the centers of galaxies ranging from millions to billions of solar masses. These are termed Super Massive BH's. BH's can only have three properties of mass, charge and angular momentum. Charge would obviously be quickly negated, leaving mass and angular momentum. Angular momentum also would gradually be negated, but over much slower rates. This leaves the end state of all BH's as the Schwarzchild variety, or a BH with no spin or charge, also the most mathematically convenient to work with. If we were to categorise all the BH's we have in our Universe today, the most common would be the Kerr BH, or the one with angular momentum, first suggested by Roy Kerr. GR tells us that once any massive object is forced to undergo collapse, once it reaches a point called the Schwarzchild radius [which for a BH is the EH] then further collapse is compulsory. This means that if we squeeze the Sun into a volume of around 5 kms, it would reach its Schwarzchild radius, further collapse would continue and it would become a BH. The Schwarzchild radius is the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light. An example of an object where the mass is within its Schwarzschild radius is a BH. Once a stellar remnant collapses to or below this radius, light cannot escape and the object is no longer directly visible, thereby forming a BH. It is a characteristic radius associated with every quantity of mass. The name itself results from Karl Schwarzchild a German astronomer, who calculated the exact solution during the first world war in 1916. This compulsory collapse leads us to what we refer to as the Singularity. Mathematically speaking, the Singularity is where all our known laws, including GR break down, or are not applicable. Many other seemingly weird aspects of BH's are known, but as weird as they are, they are aligned with the facts borne out by SR that space and time are not absolute and that all frames of references are as valid as each other. An example of one of these seemingly paradoxical scenarios is as follows...... If myself and a companion travel towards a BH and I stay a safe distance away, while my curious friend travels on towards the BH and its EH, due to gravitational time dilation, I will from my position in space, never see him cross the EH to his doom, only slowly and gently just be redshifted beyond my instrumental viewable ranges. From my friends point of view though, he proceeds towards the EH, and crosses it with no changes from his perspective in time, ignoring tidal gravitational effects which depend on the BH's size...the smaller the BH, the more critical and soonerwill be the effect of spaghettification as it has become known. Physically speaking the Singularity lies at the heart of the BH, and is where all its mass is concentrated in a form that as yet we have no description for. It lies at the quantum/Planck level of spacetime, and may in the future have more light shed upon it by a validated QGT [ Quantum Gravity Theory] Is there a surface of sorts there or does it lead to infinity? WE do not as yet know, but the QGT should help sort that out. A quantum effect called Hawking radiation which theorises on particle pair creation at near a BH's EH, where one escapes and the other succumbs to the BH, tells us that over the lifetime of the Universe, BH's should evaporate. Hawking radiation though, just like BH's have never been observed. Though we still have some that will claim that BH's do not exist, none can ever describe the effects on matter/energy and spacetime, that are observed in any other logical scientific way, the effects that can only ever be attributed to BH's. BH's for all intents and purposes, and based on the current laws of physics and GR, most certainly do exist. Likewise Hawking radiation, and what we know about the quantum world, tells us that logically it is a real concept, but in most cases, would be only evident over the lifetime of the Universe, and we are talking time frames of many hundreds and even trillions of years. Stephen Hawking once used a phrase from a poem by Dante, about the gates of Hell. "Abandon all hope ye, that enter here" probably aptly describes a BH.