Two other important parameters are the radius of the innermost stable circular orbit for a particle (for a non-spinning black hole), and the radius of the innermost circular orbit for a photon (ditto).  Note that everything is fixed by the mass of the black hole; no other parameter enters.  Of course the black hole is a vacuum solution!  The energy associated with the original mass of the system is stored as space-time curvature.  No actual massive object is present.   Also, to external observers, black holes and their event horizons take an infinite time to form.  While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time in the reference frame of infalling matter, a distant observer would see the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms being delayed by an infinite amount of time. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away.  For this reason black holes were originally called "collapsing stars."  The collapse never truly ends, seen by external observers.

Sagittarius A*.  These observations, together with more detailed later ones, have possibly solved the problem of what produces and powers the distinctive immense relativistic jets seen erupting from such black holes.


A famous calculation by Stephen Hawking (1942 - 2018) indicated that black holes might actually emit incandescent radiation, of undetectably low temperature (in the nanokelvin region), due to the difference in spacetime curvature between two close points becoming large enough to produce a real photon.  Various later analyses have confirmed this finding.   Formation of very massive black holes, such as those recently observed to collide and emit detectable gravitational radiation, is not fully understood, and the formation of the incredibly massive black holes (roughly 10⁷ times the “normal” stellar black hole mass) that seem to exist at the centers of all galaxies is difficult to understand in detail, or to model... presumably they result from huge numbers of black-hole mergers and collisions in the very dense galactic cores.  Earlier, some researchers had argued that black holes probably do not actually exist, but it would have been very difficult to understand exotic astronomical objects such as quasars and certain types of X-ray binary systems, except in terms of accretion discs of matter surrounding black holes.  Of course, the direct detection of gravitational radiation from merging black holes, with a “ring-down” spectrum which perfectly fits the numerical predictions of Einstein's theory of gravity, settles that question fairly decisively. At least one of the observed collisions involved black hole masses that overlapped with the typical masses deduced from X-ray binary studies.


It has been suggested (by Hawking, for instance) that extreme density fluctuations in the early universe could have directly generated so-called primordial black holes, with present-day masses ranging from 10^-19 solar masses, to thousands of solar masses, and recent results from the Webb Space Telescope are indeed revealing very massive black holes existing at the centers of very, very early galaxies, black holes that should not have had time to form by accretion of stellar black holes.  The black holes that have so far been studied have obvious origins, directly or indirectly, as the expected endpoints of stellar evolution, and are intimate parts of stellar systems, aside from the monsters found at the cores of galaxies.   There is hardly a more active place, astrophysically speaking, than galactic cores.  The recent discovery of supermassive black holes in the astrophysical Dark Ages does suggest that early in this era, the density of interstellar clouds of gas and dust was so great that density fluctuations could grow to such an extreme as to produce gigantic black holes directly, without any intermediate stellar stage.  Much further research is needed, of course.



Why are we even mentioning black holes in a course called “subatomic physics”? For many reasons, for example because a question relevant to the consistency of Einstein's theory of gravitation with quantum physics was initially raised back in the mid-1970s by Stephen Hawking. This is the so-called “Black Hole information paradox.” The fact that in the more than 40 years(!) that have passed since, there has been no agreement whatsoever as to the resolution of this paradox, or even whether it is a paradox at all, is a prime exhibit of the dismal state of knowledge of the boundaries between gravity and quantum physics! Hawking himself at various times came down on almost all sides of the issue, at one point even claiming the resolution of the paradox was that no actual black holes existed.  It's no exaggeration to say that some new paper "resolving" the paradox is published roughly every 6 months, and no two papers offer even a vaguely similar "solution."  Nor could any solution offered so far be confirmed experimentally.  For a recent comment on this issue, see this video... and an immediate follow-up! Of course there is no reason whatsoever to expect consistency between a classical field theory (of gravity) and any of the aspects of quantum field theory!  This hints that now it is time to face the dismal history of quantum gravity research, coming next.
Hawking in 1975.

Bright elliptical galaxy Messier 87 (M87) is home to a supermassive black hole, 6.5 billion times solar mass, as captured by planet Earth's Event Horizon Telescope in the first-ever "image" of a black hole. Giant of the Virgo galaxy cluster, about 55 million light-years away, M87 is the large galaxy rendered in blue hues in this infrared image from the Spitzer Space telescope. Though M87 appears mostly featureless and cloud-like, the Spitzer image does record details of immense relativistic jets blasting from the galaxy's central region. Shown in the inset at top right, the jets themselves span many thousands of light-years. The brighter jet seen on the right is approaching and close to our line of sight. Opposite, the shock created by the otherwise unseen receding jet lights up a fainter arc of material. Inset at bottom right, the historic black hole image is shown in context, at the center of giant galaxy and relativistic jets. Completely unresolved in the Spitzer image, the supermassive black hole surrounded by an accretion disc of infalling material is the source of the enormous energy driving the jets from the center of  M87. The Schwartzchild radius of the black hole is about 120 astronomical units, while the radius of the photon sphere (the black silhouette seen in the image) is 2.6 times larger.

How are black hole collisions possible in a finite time? Look here!