Black Hole Physical Properties

The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916.^[15] According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.^[55] This means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore only correct near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.^[56]

Solutions describing more general black holes also exist. Non-rotating charged black holesare described by the Reissner–Nordström metric, while the Kerr metric describes a non-charged rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum.^[57]

While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. In Planck units, the total electric charge Q and the total angular momentum J are expected to satisfy

${\displaystyle Q^{2}+\left({\tfrac {J}{M}}\right)^{2}\leq M^{2}\,}$

for a black hole of mass M. Black holes with the minimum possible mass satisfying this inequality are called extremal. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called naked singularities that can be observed from the outside, and hence are deemed unphysical. The cosmic censorship hypothesis rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter.^[2] This is supported by numerical simulations.^[58]

Due to the relatively large strength of the electromagnetic force, black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a universal feature of compact astrophysical objects. The black-hole candidate binary X-ray source GRS 1915+105^[59] appears to have an angular momentum near the maximum allowed value. That uncharged limit is^[60]

${\displaystyle J\leq {\frac {GM^{2}}{c}},}$

allowing definition of a dimensionless spin parameter such that^[60]

${\displaystyle {\frac {cJ}{GM^{2}}}\leq 1.}$^{[60][Note 1]}

Black hole classifications

Class	Approx. mass	Approx. size
Supermassive black hole	105–1010MSun	0.001–400 AU
Intermediate-mass black hole	103 MSun	103 km ≈ REarth
Stellar black hole	10 MSun	30 km
Micro black hole	up to MMoon	up to 0.1 mm

Black holes are commonly classified according to their mass, independent of angular momentum, J. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is roughly proportional to the mass, M, through

${\displaystyle r_{\mathrm {s} }={\frac {2GM}{c^{2}}}\approx 2.95\,{\frac {M}{M_{\mathrm {Sun} }}}~\mathrm {km,} }$

where r_s is the Schwarzschild radius and M_Sunis the mass of the Sun.^[62] For a black hole with nonzero spin and/or electric charge, the radius is smaller,^{[Note 2]} until an extremal black hole could have an event horizon close to^[63]

${\displaystyle r_{\mathrm {+} }={\frac {GM}{c^{2}}}.}$