High-enough mass-energy density makes high-enough gravity to make space curvature so high that radial matter and radiation curve back into the region and so cannot leave. Space-time singularities have a surface {event horizon} beyond which no particles or radiation can escape. Therefore, outside observers cannot detect physical processes in the space {hidden region} inside event horizon. For black holes and other spherical objects with no charge and no angular momentum, event-horizon radius is two times object mass. For such spherically symmetric singularities, space-time has Schwarzschild metric. For non-spherically-symmetric singularities, space-time has Kerr metric.
photon layer
At event horizon, gravity potential energy equals light kinetic energy, so photons orbit singularity in stable and unstable circular orbits, making a photon layer.
inside horizon
To observers inside event horizon, all matter and radiation appear to move toward singularity center. Observers inside event horizon see nothing outside horizon, because high gravity slows time so much that radiation frequency red-shifts to very low, so photons have almost no energy and are undetectable.
outside horizon
To observers outside event horizon, objects falling toward singularity appear to slow to a stop at horizon, because time slows greatly in high gravity. Because high gravity makes object part closer to singularity have much more acceleration than farther part, objects falling toward singularity elongate perpendicular to event-horizon surface. Outside event horizon, observers can measure only electric charge, mass (monopole moment), and angular momentum (dipole moment).
Outside observers cannot see universe singularities {cosmic censorship hypothesis}. Universe has no singularities without an event horizon ("naked" singularities). All singularities have an event horizon. Outside observers cannot see space-time time-like singularities (ideal points) {strong cosmic censorship hypothesis}. Universe singularities can be space-like or light-like (null) but not time-like. Outside observers far away in space-time cannot see time-like singularities {weak cosmic censorship hypothesis}.
Universe can have singularities without an event horizon. Spinning or charged black holes can lose event horizons after small charge or spin increases or small mass decreases. Exploding black holes can expose singularities. Perhaps, cosmic censorship is true only if cosmological constant is zero or negative.
Some singularities {white hole}| emit particles and/or radiation. In quantum theory, small singularities emit particles and/or radiation rapidly, while black holes emit slowly. Perhaps, universe has large white holes.
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.
If double stars have one black hole and one ordinary star, black hole can pull gas from star, making a disk {accretion disk}. Gas has fast-moving charged particles, whose magnetic interactions cause turbulence (magnetorotational instability). Gas particles closer to black hole are faster. Magnetic attractions slow near-black-hole gas particles, so they move closer to black hole. Magnetic attractions speed far particles, so they move farther from black hole. Overall potential energy decreases, and kinetic energy increases (generating heat), providing energy for accretion disk to radiate.
Black holes have maximum entropy and information. Outside observers cannot see inside event horizons, so black-hole information is in event-horizon surface area. More massive black holes have larger event-horizon surface areas. By quantum-loop theory, event-horizon surfaces have area quanta, which hold one information bit. Larger event-horizon surfaces have more area quanta, hold more bits, and represent more entropy. Event-horizon surface area varies directly with black-hole entropy. Event-horizon surfaces have maximum entropy {Bekenstein bound}. If mass-energy falls into black hole, black-hole mass-energy increases, event-horizon surface area increases, and entropy increases. regions bounded by event horizons have limited information amounts.
Rotating black holes have a region beyond event horizon but inside stationary limit {ergosphere}. Ergosphere particles appear to have negative energy to outside observers.
For charged rotating stationary black holes, angular momentum and magnetic moment are in same direction and their ratio {gyromagnetic ratio} is 2. Angular momentum is 2*m*e*w, and magnetic moment is m*e*w, where m = mass, e = charge, and w = angular velocity. (Electrons also have gyromagnetic ratio 2.)
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 {black hole evaporation}. 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. Thermal emission reduces black-hole mass and makes black hole hotter.
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?
If double stars have one black hole and one ordinary star, black hole can pull gas from star, making an accretion disk. Gas has fast-moving charged particles, whose magnetic interactions cause turbulence {magnetorotational instability} (MRI).
At a radius {Roche limit} around black holes, gravity equals electric force.
From black-hole center, the farthest distance {Schwarzschild limit} {Schwarzschild radius} from which light cannot escape is 2 * G * m / c^2, where G is gravitational constant, m is mass, and c is light speed. Larger-mass black holes have farther Schwarzschild limit.
After objects fall into black holes, outside observers cannot observe object properties, because nothing can come out except Hawking radiation, which is random and has no information. Outside observers can only measure total black-hole mass, charge, and angular momentum. All object information is lost, but there should be information conservation {black hole information paradox}. By string theory and quantum-loop theory, because strings are unitary, information is constant {unitarity} {unitary process}, and object information goes into event-horizon surface area. Perhaps, when black holes evaporate and so have no event horizon, outside observers can see all information again.
5-Astronomy-Universe-Cosmology
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Date Modified: 2022.0225