8.2 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Black hole | 7/13 | https://en.wikipedia.org/wiki/Black_hole | reference | science, encyclopedia | 2026-05-05T13:31:52.244381+00:00 | kb-cron |
==== Innermost stable circular orbit (ISCO) ====
In Newtonian gravity, test particles can stably orbit at arbitrary distances from a central object. In general relativity, however, there exists a smallest possible radius for which a massive particle can orbit stably. Any infinitesimal inward perturbations to this orbit will lead to the particle spiraling into the black hole, and any outward perturbations will, depending on the energy, cause the particle to spiral in, move to a stable orbit further from the black hole, or escape to infinity. This orbit is called the innermost stable circular orbit, or ISCO. In the case of a Schwarzschild black hole (spin zero) and a particle without spin, the location of the ISCO is:
r
I
S
C
O
=
3
r
s
=
6
G
M
c
2
,
{\displaystyle r_{\rm {ISCO}}=3\,r_{\text{s}}={\frac {6\,GM}{c^{2}}},}
where
r
I
S
C
O
{\displaystyle r_{\rm {_{ISCO}}}}
is the radius of the ISCO,
r
s
{\displaystyle r_{\text{s}}}
is the Schwarzschild radius of the black hole,
G
{\displaystyle G}
is the gravitational constant, and
c
{\displaystyle c}
is the speed of light. For spinning black holes, the ISCO is moved inwards for particles orbiting in the same direction that the black hole is spinning (prograde) and outwards for particles orbiting in the opposite direction (retrograde). For example, the ISCO for a particle orbiting retrograde can be as far out as about
4.5
r
s
{\displaystyle 4.5r_{\text{s}}}
, while the ISCO for a particle orbiting prograde can be as close as at the event horizon itself. The radius of this orbit changes slightly based on particle spin. For charged black holes, the ISCO moves inwards.
==== Photon sphere and shadow ====
The photon sphere is a spherical boundary for which photons moving on tangents to that sphere are bent completely around the black hole, possibly orbiting multiple times. For Schwarzschild black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. While light can still escape from the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Therefore, any light that reaches an outside observer from the photon sphere must have been emitted by objects between the photon sphere and the event horizon. Light emitted towards the photon sphere may also curve around the black hole and return to the emitter. For a rotating, uncharged black hole, the radius of the photon sphere depends on the spin parameter and whether the photon is orbiting prograde or retrograde. For a photon orbiting prograde, the photon sphere will be 0.5-1.5 Schwarzschild radii from the center of the black hole, while for a photon orbiting retrograde, the photon sphere will be between 3-4 Schwarzschild radii from the center of the black hole. The exact locations of the photon spheres depend on the magnitude of the black hole's rotation. For a charged, nonrotating black hole, there will only be one photon sphere, and the radius of the photon sphere will decrease for increasing black hole charge. For non-extremal, charged, rotating black holes, there will always be two photon spheres, with the exact radii depending on the parameters of the black hole. When viewed from a great distance, the photon sphere creates an observable black hole shadow, a dark silhouette of the black hole against the background stars. Images such as those taken by the Event Horizon Telescope show the black hole shadow, not the event horizon itself. Since no light emerges from within the black hole, this shadow is the limit for possible observations. The shadow of colliding black holes should have characteristic warped shapes, allowing scientists to detect black holes that are about to merge.
==== Ergosphere ====
Near a rotating black hole, spacetime rotates similar to a vortex. The rotating spacetime will drag any matter and light into rotation around the spinning black hole. This effect of general relativity, called frame dragging, gets stronger closer to the spinning mass. The region of spacetime in which it is impossible to stay still is called the ergosphere. The ergosphere of a black hole is a volume bounded by the black hole's event horizon and the ergosurface or stationary limit surface, which coincides with the event horizon at the poles but bulges out from it around the equator. Matter and radiation can escape from the ergosphere. Through the Penrose process, objects can emerge from the ergosphere with more energy than they entered with. The extra energy is taken from the rotational energy of the black hole, slowing down the rotation of the black hole.
==== Plunging region ====
The observable region of spacetime around a black hole closest to its event horizon is called the plunging region. In this area it is no longer possible for free falling matter to follow circular orbits or stop a final descent into the black hole. Instead, it will rapidly plunge toward the black hole at close to the speed of light, growing increasingly hot and producing a characteristic, detectable thermal emission. However, light and radiation emitted from this region can still escape from the black hole's gravitational pull.
=== Radius === For a nonspinning, uncharged black hole, the radius of the event horizon, or Schwarzschild radius, is proportional to the mass, M, through
r
s
=
2
G
M
c
2
≈
2.95
M
M
⊙
k
m
,
{\displaystyle r_{\mathrm {s} }={\frac {2GM}{c^{2}}}\approx 2.95\,{\frac {M}{M_{\odot }}}~\mathrm {km,} }
where rs is the Schwarzschild radius, G is the gravitational constant, c is the speed of light, and M☉ is the mass of the Sun. A black hole of the same mass with nonzero spin has two radii:
r
±
=
M
±
M
2
−
(
J
/
M
)
2
.
{\displaystyle r_{\pm }=M\pm {\sqrt {M^{2}-{(J/M)}^{2}}}.}
Most observed black holes have close to maximum angular momentum that seems to be allowed:
|
J
|
≤
M
2
.
{\displaystyle |J|\leq M^{2}.}
For such black holes the radii will approach