Black holes

A black hole is a region where spacetime curvature is severe enough that no path leads outward. It is characterised completely by three numbers: mass, spin and charge. Everything else about whatever formed it is lost.

The horizon

The simplest solution, found by Schwarzschild in 1916 within months of general relativity’s publication, describes a non-rotating uncharged mass. Its event horizon lies at

The horizon is not a surface in any material sense. Nothing special happens locally to an infalling observer crossing it; there is no wall and no sudden force. What changes is causal structure: beyond the horizon every future-directed path leads inward. A distant observer sees infalling material slow, redden and fade, never quite crossing, while the infalling observer crosses in finite proper time.

Real black holes rotate, and the appropriate solution is Kerr’s, found in 1963. Rotation introduces two features with no Newtonian analogue. The ergosphere is a region outside the horizon where spacetime is dragged so strongly that no observer can remain stationary relative to distant stars. Energy can be extracted from it, which is the leading mechanism for powering jets. And the innermost stable circular orbit moves inward with spin, from $6GM/c^2$ for a non-rotating hole to about $1.24GM/c^2$ for a maximally rotating one, which raises the efficiency of accretion substantially.

Formation and growth

The supermassive origin problem is genuine and unresolved. Quasars powered by holes of a billion solar masses are observed at redshifts corresponding to less than a billion years after the Big Bang. Growing from a stellar-mass seed at the Eddington-limited rate does not obviously fit in the time available, which motivates either heavy seeds from direct collapse of primordial gas clouds or episodes of accretion above the Eddington limit.

The intermediate mass gap was long conspicuous. Gravitational wave detections have begun to populate it: GW190521 produced a remnant of about 142 M☉, the first firm object in the range.

Accretion and jets

Material falling toward a black hole carries angular momentum, so it settles into a disc rather than falling straight in. Viscous friction within the disc transports angular momentum outward and lets matter spiral inward, converting gravitational potential energy into heat and radiation.

The efficiency is remarkable. Between 6% and 42% of rest mass energy is radiated, depending on spin, against 0.7% for hydrogen fusion. This is why accreting black holes are the most luminous persistent objects in the universe.

Many accreting systems launch relativistic jets: collimated outflows moving at very nearly the speed of light, extending in some cases far beyond the host galaxy. The Blandford-Znajek mechanism is the standard explanation, extracting rotational energy from the hole through magnetic field lines threading the horizon. The jets deposit enormous energy into the surrounding medium and are the feedback channel that couples black hole growth to galaxy evolution. See Galaxies.

Direct imaging

The Event Horizon Telescope produced the first image of a black hole’s shadow in 2019, for M87*, and of Sgr A* in 2022.

The technique is very long baseline interferometry: radio telescopes across Earth observe simultaneously, and the signals are combined afterwards to synthesise an aperture the size of the baseline. At 1.3 mm wavelength on an Earth-diameter baseline, the angular resolution is

which is roughly the angle subtended by an orange on the Moon.

Two targets are within reach, and for the same reason. M87* is enormous but distant; Sgr A* is small but close. Their apparent angular sizes are comparable, and both are near the resolution limit. Sgr A* proved harder despite being nearer, because its light-crossing time is minutes rather than days, so the source changes while being observed and the image must be reconstructed from a varying object.

What the images show is not the horizon but the shadow: a dark region of about 2.6 times the Schwarzschild radius, caused by light rays that fall in rather than reaching the observer, surrounded by a bright ring of lensed emission. The measured sizes match general relativity’s prediction.

Gravitational waves

The 2015 detection of GW150914 was the first direct observation of a black hole merger and of gravitational waves themselves. Two holes of about 36 and 29 solar masses merged into one of about 62, radiating roughly three solar masses of energy as gravitational waves in a fraction of a second.

The peak power exceeded the combined electromagnetic output of every star in the observable universe, and none of it was light.

The observational significance is that this probes the strong-field, dynamical regime of general relativity, which no other measurement reaches. Solar system tests probe weak fields; the merger of two black holes tests the theory where curvature is extreme and time-dependent. So far it has passed.

Detections now number in the hundreds and have established a population of stellar-mass black holes considerably more massive than those known from X-ray binaries, which changed the understanding of massive star evolution.

Information

The theoretical problem that keeps black holes at the centre of fundamental physics is that Hawking radiation appears to be thermal, carrying no information about what fell in. If the hole eventually evaporates completely, the information seems to be destroyed, which quantum mechanics forbids.

Proposed resolutions include information encoded in subtle correlations within the radiation, holographic duality in which the interior is encoded on the boundary, and modifications to the horizon’s structure. There is no consensus.

For astrophysical black holes this is entirely academic, since a stellar-mass hole’s Hawking temperature is far below that of the cosmic microwave background and it absorbs more than it emits. The paradox matters because it is one of the few places where quantum mechanics and general relativity make incompatible statements about the same situation.

References

• Misner, C. W., Thorne, K. S. and Wheeler, J. A. Gravitation, Princeton University Press, 2017 reprint.
• Event Horizon Telescope Collaboration, “First M87 Event Horizon Telescope Results”, The Astrophysical Journal Letters, 875:L1, 2019, and the Sgr A* series, *ApJL*, 930:L12, 2022.
• Abbott, B. P. et al. “Observation of Gravitational Waves from a Binary Black Hole Merger”, Physical Review Letters, 116:061102, 2016.
• Blandford, R. D. and Znajek, R. L. “Electromagnetic extraction of energy from Kerr black holes”, MNRAS, 179:433, 1977.
• Hawking, S. W. “Particle creation by black holes”, Communications in Mathematical Physics, 43:199, 1975.