Black Holes

Escape Velocity The minimum velocity needed to leave the vicinity of a body without ever being pulled back by the body’s gravity is the escape velocity.

Escape Velocity The escape velocity from a body depends on its mass and on the distance from its center. It is faster for larger mass and smaller distance (i.e., when the body’s gravity is stronger). Escape velocity = R R

Escape Velocity At the surface of the Earth, the escape velocity is 11 km/s.

Definition of a Black Hole If the Earth was compressed to a radius of 1 cm, the escape velocity at its surface would be the speed of light (300,000 km/s). If the Earth was compressed any more, the escape velocity would be greater than the speed of light. Nothing could escape its surface, not even light. This is the definition of a black hole. Theoretically, anything could become a black hole if it is compressed enough so that = speed of light.

The Event Horizon and Singularity The radius from the center of a black hole at which the escape velocity equals the speed of light is the event horizon. This is the point of no return. All matter in a black hole is crushed into a single point at the center, which is called the singularity. It has zero volume and infinite density. V esc >V light V esc <V light

Surface Gravities of Different Types of Stars Red giants M  Earth’s orbit (1000 R  ) Among the various types of stars, the radii span a much larger range than the masses. As a result, it is mostly the differences in radii that determine the differences in surface gravities so that the stars with smaller radii tend to have stronger surface gravities (higher escape velocities). MassRadius Main sequence M  R  White dwarfs<1.4 M  Earth (0.01 R  ) Neutron stars1.4-3 M  city ( R  ) Black holes>3 M  small town ( R  ) Escape velocity = Higher escape velocity Stronger surface gravity

Black Holes Don’t Suck Black holes obey the law of gravity like all other objects. The force of gravity from a black hole is the same as from any other object with the same mass at the same distance.

Black Holes Don’t Suck For instance, the orbit of the Earth would not change if the Sun was replaced with a black hole with the same mass as the Sun.

Force on the rocket: But black holes do have extremely strong gravity near them because their mass is concentrated in a very small volume

Force on the rocket: But black holes do have extremely strong gravity near them because their mass is concentrated in a very small volume

Force on the rocket: But black holes do have extremely strong gravity near them because their mass is concentrated in a very small volume

Force on the rocket: But black holes do have extremely strong gravity near them because their mass is concentrated in a very small volume

Same gravity

Different gravity

Black Hole Sizes The radius of the event horizon is the “size” of a black hole. It depends only on the mass of the black hole. 2 x cm 1 cm3 km black holes with masses equal to: have sizes of: Black holes are very compact. The black holes produced by the deaths of massive stars have masses of 3-20 M , corresponding to radii of km.

Einstein’s theory of relativity says that a body’s gravity distorts space and time near it. Orbits can be explained as a consequence of this distortion. Effect of Gravity on Space and Time

The distortion of space-time near a black hole is large because of its intense gravity. The black hole itself can be thought of as a hole in the space-time continuum. Effect of Gravity on Space and Time

A clock near an event horizon ticks more slowly than a clock far from it. In fact, from the point of view of a distant observer, the clock will stop as it reaches the event horizon, and the observer will never see the clock cross the horizon. This is because light is not able to escape the event horizon and reach the observer. A person near the horizon would not notice anything unusual about time as they approach and cross the event horizon. Gravity distorts not just space, but time as well. Time passes more slowly in the presence of strong gravity compared to a location where gravity is weaker. This is called time dilation. Effect of Gravity on Space and Time black hole

A clock near an event horizon ticks more slowly than a clock far from it. In fact, from the point of view of a distant observer, the clock will stop as it reaches the event horizon, and the observer will never see the clock cross the horizon. This is because light is not able to escape the event horizon and reach the observer. A person near the horizon would not notice anything unusual about time as they approach and cross the event horizon. Gravity distorts not just space, but time as well. Time passes more slowly in the presence of strong gravity compared to a location where gravity is weaker. This is called time dilation. Effect of Gravity on Space and Time black hole

Effect of Gravity on Space and Time The frequency of light is the number of waves that pass by per second. Because of time dilation, this frequency becomes lower in the presence of gravity, corresponding to longer wavelengths. Thus, light emitted from the vicinity of a black hole will appear redder to an observer far away. This is gravitational redshift. Gravitational redshift can also be explained in a different way: As light leaves the vicinity of a black hole (or anything with gravity), it loses energy (and hence is redshifted) as it climbs out of the gravity well.

Tidal Forces near Black Holes Because gravity becomes very intense near a black hole, tidal forces are also very strong, stretching any nearby object so much that it will be torn into individual atoms.

Detecting Black Holes Although we cannot detect light from a black hole, it is possible to detect its presence based on how it affects its surroundings. For instance, matter attracted to a black hole forms an accretion disk, which is very hot, and hence very bright in X-rays. In 1964, X-ray emission was detected near a blue supergiant. In the 1970’s, the motion of the supergiant was measured, which indicated that it is orbiting with an unseen 15 M  companion. The companion is too massive to be a white dwarf or neutron star, and is probably a black hole that is pulling matter off the supergiant. This was the first strong candidate for a black hole to be found. Cygnus-X1

Making Black Holes Anything can become a black hole if it is compressed enough. But the only way that nature currently makes black holes is through the supernovae of massive stars. These black holes have masses 3-20 M .

Making Black Holes Black holes can sink to the center of galaxies, where they merge together to form one supermassive black hole.

These black holes have masses of >1,000,000 M  Making Black Holes

The Milky Way’s Sleeping Monster There’s even a 4,000,000 M  black hole at the center of the Milky Way. We can measure its mass using the motions of stars that orbit it.

Gravitational Waves Because gravity distorts space, the acceleration of an object should produce ripples in space called gravitational waves. The strongest waves should be produced by objects with the most intense gravity like supernovae explosions, orbiting or merging white dwarfs, neutron stars, and black holes, and the Big Bang.

Gravitational Waves The detection of gravitation waves would provide support for Einstein’s theory of relativity. The waves should compress space in one direction and stretch space in another direction. The Laser Interferometer Gravitational Wave Observatory is attempting to detect gravitational waves by monitoring for changes in the lengths of 2 vacuum tubes that are 4 km long. The signal from a wave is extremely tiny and difficult to detect -- the lengths should change by less than the width of an atom. But they were finally detected the first time in 2015! They originated from the merger of 2 black holes.

Evaporation of Black Holes vacuum

Evaporation of Black Holes -  “virtual” particles Pairs of virtual particles and anti-particles can spontaneously pop into existence.

Evaporation of Black Holes Normally, they very quickly re-combine and annihilate each other. poof

Evaporation of Black Holes -  “virtual” particles If a virtual pair appear near the event horizon of a black hole, and one particle enters the black hole while the other one travels away from the black hole, then the first particle carries negative energy into the black hole, reducing its energy, and hence its mass. Because of the escaping particle, it appears as if the black hole is producing particles, or radiation. This is called Hawking radiation.

Evaporation of Black Holes Because of Hawking radiation, black holes slowly lose mass and eventually evaporate. The rate of this mass loss is slower for more massive black holes. Tiny black holes produced during the Big Bang evaporated quickly, but the more massive black holes produced by supernova explosions require more than years to fully evaporate!