Supernova remnant stars and galaxy centers {black hole}| have high-enough mass-energy density to cause high-enough gravity so that object escape velocity is higher than light speed, so matter and radiation cannot leave the black hole. Outside observers receive no radiation, so black holes are not visible. Gravity is so strong that space curvature is so high that it curves moving matter and radiation back into the black hole or into orbit around the black hole.
stars
Some stars with more than 2.25 Sun mass become supernovas. After supernova, remaining neutron star has mass two times Sun mass and diameter 2000 meters. When neutron-star nuclear fusion slows, black holes form in one second, with no measurable diameter but with close event horizon. Galaxies average 10^6 star black holes.
galaxies
Galactic centers, including Milky Way and Cygnus X-1, have one large black hole. Galactic centers have high star concentrations and stars collide and merge to make larger mass, until mass is so high, black hole forms. Then black hole attracts more mass and grows larger. Galactic-center black holes contain mass from 10 million stars and have no measurable diameter but distant event horizon.
mass
Black holes can have unlimited mass and gravity.
density
High-enough gravity can overcome neutron-degeneracy pressure, so neutrons compress into each other, making density greater than in atomic nuclei.
diameter
Black holes are space-time singularities. Black holes have no measurable diameter. Black holes are outside space and so are one point in time.
rotation
Non-rotating black holes far from matter have a point singularity. Space around non-rotating black holes far from matter has Kerr metric.
Black holes probably rotate with angular momentum equal to mass. Rotating black holes have ring-shaped singularity, perpendicular to rotation axis. Perhaps, objects can go through ring center and come out into negative or antigravity space. Spinning black holes produce long gamma-ray bursts.
electric charge
Black holes can have positive or negative electric charge. Black holes can have only small charge {no hair}, because they rapidly attract or repel nearby charges and become neutral.
sizes and lives
Early universe probably had enough radiation pressure to create tiny black holes. Planck-size black holes have mass 10^-8 kilograms, density 10^97 kg/m^3, and radius 10^-35 meters. Smaller black holes compress neutrons more, as inverse square of mass. Hawking radiation evaporates them quickly.
Ball-size black holes are hotter than the hottest star center.
Mountain-mass black holes have mass 10^12 kilograms and proton-sized radius. Hawking radiation evaporates them in 10^12 years at 10^12 K.
Sun-mass black holes have mass 10^30 kilograms, density 10^19 kg/m^3, and radius 3000 meters. Hawking radiation evaporates them in 10^64 years at temperature 10^-6 K.
radiation
Black-hole event horizons have high space curvature and high tidal forces, and so form virtual-particle pairs. Sometimes, one virtual particle enters black hole, and the other escapes and becomes a real particle (Hawking radiation). It is like quantum tunneling. In-falling and escaping particles carry energy. Negative energy flows into black hole, reducing mass-energy density, and positive energy escapes, reducing mass-energy, so energy conservation energy holds overall, but black-hole mass and energy decrease. Hawking radiation decreases black-hole mass and energy, so event horizon has shorter radius and smaller surface area.
Spatial-surface gravity determines particle-creation amount. Mass-energy-loss rate varies inversely with mass squared, so smaller black holes radiate more rapidly and lose mass faster. Smallest ones can explode. Smallest ones radiate particles with no spin. Small ones radiate neutrons and other neutral particles with spin in equatorial plane. Large ones radiate protons, electrons, and other charged particles. Largest ones radiate photons and gravitons. Equal numbers of baryons and anti-baryons leave black holes.
However, outside space also creates virtual photons, and some enter black holes, so typical black holes probably are in thermal equilibrium with surrounding space and do not evaporate.
temperature
Hot objects radiate to cooler objects. Warm objects radiate infrared light. Light-frequency distribution depends on object temperature. Black holes radiate Hawking radiation, and event-horizon temperature determines frequency distribution. Event-horizon temperature varies inversely with black-hole surface area and mass. Smaller black holes have higher energy-to-mass ratio and so higher temperature. Large black holes have event-horizon temperatures near absolute zero. Tiny-black-hole event-horizon temperatures are 10^21 K.
Black holes have high gravity and attract outside particles. In-falling particles add heat and increase event-horizon temperature.
Hawking radiation reduces black-hole mass more than it reduces energy, so energy-to-mass ratio increases, and so event-horizon temperature rises.
Black-hole event-horizon temperature results from quark and gluon motions. Black holes have strongly interacting quarks and gluons, which have low shear viscosity. Temperature T varies directly with acceleration a: T = (h / (2 * pi * c)) * a, where c is light speed, and h is Planck constant. T = kappa / (2 * pi), where kappa = (h/c) * a. Particles have high acceleration at event horizon. Larger black holes have smaller particle accelerations, and so lower event-horizon temperatures. Temperature represents quantum-fluctuation strength.
Classically, emitting thermal radiation from hot bodies removes energy and makes surface have lower temperature, because hotter-than-average particles preferentially leave. Does only cooler-than-average radiation leave black holes, so they get hotter? Is virtual radiation thermal emission or another radiation kind?
entropy
Black holes have entropy proportional to star information that becomes lost when star collapses. From outside, only black-hole event horizons are observable, so event horizons carry all information. Black-hole entropy S depends on event-horizon surface area A: S = A * k * c^(3/4) * h * G, where k is Boltzmann constant, c is light speed, h is Planck constant, and G is gravitational constant.
In cosmological units, entropy S varies directly with event-horizon surface area A divided by four: S = A / (4 * h * G), where h is Planck constant and G is gravitational constant in Planck units. Partition-function P logarithm is negative of free energy FE divided by temperature T: ln(P) = - FE / T. Free energy FE is energy E plus temperature T times entropy S: FE = E + T*S.
Because things can only go into black holes, and nothing can come out except Hawking radiation, event-horizon surface area and entropy typically increase. If black hole and space are in thermal equilibrium, surface area and entropy stay constant. If Hawking radiation is more than photon and particle entry from space, surface area and entropy decrease. Black-hole entropy relates thermodynamics and quantum gravity.
entropy: information
When black holes form, where does information about matter type and distribution {multipole moment} go? Information can be at event horizon, below event horizon, in black hole, or at singularity. Outside observers never see information loss, because they see time slow and light red-shift but never see black hole form.
Information has quantum-mechanical limits.
By string theory, black holes seem to destroy information but actually just transfer it {AdS/CFT correspondence}.
gravity
Gravity strength is the same at all event-horizon points {zeroth law of black-hole mechanics}. The zeroth thermodynamics law says all points in contact are at same temperature (thermal equilibrium).
energy
Mass or energy change dE is event-horizon spatial-area change dA times constant kappa / (8 * pi), plus angular-momentum change dJ times omega constant, plus charge change dQ times psi constant {first law of black hole mechanics}: dE = (kappa / (8 * pi)) * dA + omega * dJ + psi * dQ, where kappa is event-horizon gravity strength. The first thermodynamics law says total energy is constant.
temperature
Event-horizon gravity strength is like thermodynamic temperature. Event-horizon spatial area is like thermodynamic entropy. Because null geodesics have no observable future and can never converge, event-horizon spatial-area change dA never decreases over time {second law of black hole mechanics}: dA >= 0. The second thermodynamics law says entropy never decreases.
Physical Sciences>Astronomy>Universe>Cosmology>Singularity>Black Hole
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Date Modified: 2022.0224