What is a Black Hole? - PDF Free Download

What is a Black Hole? Robert H. Gowdy Virginia Commonwealth University December 2016 Bob G (VCU) Black Holes December 2016 1 / 29

Black Holes Bob G (VCU) Black Holes December 2016 2 / 29

Overview Spacetime near a normal star No problem. Bob G (VCU) Black Holes December 2016 3 / 29

Overview Spacetime near a normal star No problem. Spacetime outside any arbitrary star a little problem if you push it too far. Bob G (VCU) Black Holes December 2016 3 / 29

Overview Spacetime near a normal star No problem. Spacetime outside any arbitrary star a little problem if you push it too far. The spacetime of a wormhole solves the problem (in theory). The "event horizon" The spacetime of a collapsing star shows what could actually happen. Bob G (VCU) Black Holes December 2016 3 / 29

Spacetime Near a Normal Star Here, r is the distance from the center of the star and t is clock time synchronized with a distant observer. Choose units so that light travels one distance unit per time unit. Bob G (VCU) Black Holes December 2016 4 / 29

Some thing very bad happens where r = 2m, the Schwarzschild Radius. Bob G (VCU) Black Holes December 2016 5 / 29 General Relativity Spacetime Outside a Star of Mass m Here, r is the radius that corresponds to the area A = 4πr 2 and t is the time synchronized with a distant observer s clock. Use units with c = G = 1.

Why Worry? Switch to ordinary units to see if the problem at the Schwarzschild radius is worth worrying about. For m the mass of the Earth, the Schwarzschild radius is about a centimeter. That is certainly not "outside" the Earth, so our "outside" spacetime is just fine. For m the mass of the Sun, the radius where bad things happen is about 3 kilometers, certainly not "outside" the Sun, so we are still OK. But wait! There are hundreds of neutron stars with masses similar to the mass of our Sun and they are only a few kilometers in radius. Add just a little mass to a neutron star and its Schwartzschild radius would be outside of it. That s a problem. Bob G (VCU) Black Holes December 2016 6 / 29

Bad Coordinates In a curved geometry, coordinates can easily go bad where the geometry is still OK. For example, on the spherical Earth, longitude and latitude are bad coordinates to use at the north and south pole. We are using time t synchronized with the clock of an observer at infinity. One problem with that is that the clock time of an observer sitting at the Schwarzschild radius stops advancing when our coordinate t increases. Perhaps the lines of constant t are doing something like this? Bob G (VCU) Black Holes December 2016 7 / 29

Good Coordinates 1958 - David Finklestein finds an example of an event horizon and recognizes the one in the Schwarzschild solution. 1960-61 - Szekeres and Kruskal separately find a good coordinate system that reveals what happens near r=2m. In these coordinates, the path of a light ray is always at 45 to the v axis. Bob G (VCU) Black Holes December 2016 8 / 29

Extending the Vacuum Solution The exterior part of the Schwarzschild solution occupies just a wedge of the u v plane. The geometry is regular at the boundary of the wedge, so the solution can be extended. Bob G (VCU) Black Holes December 2016 9 / 29

The Extended Solution Here is a nice diagram of the fully extended solution (with T and X instead of v and u and r in units of 2m) This fully extended solution is called a wormhole because it connects two "outside" regions, region I and region III. There is an infinite curvature singularity at r = 0, so no further extension is possible. Bob G (VCU) Black Holes December 2016 10 / 29

Picture of a Wormhole A constant-t or v slice through the solution shows r going from infinity to a minimum of 2m and then increasing to infinity again. The equatorial plane of the wormhole looks like this Bob G (VCU) Black Holes December 2016 11 / 29

Travel Through the Wormhole The red curve is the history of someone traveling slower than light. hit the singularity and space collapses around them. They The blue line is the history of someone moving faster than light. They make it through OK. Bob G (VCU) Black Holes December 2016 12 / 29

The Event Horizon An observer falling through the r = 2m surface notices nothing unusual. However, a distant observer will not see any signals from the falling observer after that. Light can go in through the r = 2m surface, but it cannot come out. Bob G (VCU) Black Holes December 2016 13 / 29

Spacetime Near a Collapsing Star Only part of the fully extended vacuum solution is needed to describe the spacetime near a collapsing star. Once the surface of the star collapses past the event horizon at r = 2m the star is doomed to collapse to zero size. Bob G (VCU) Black Holes December 2016 14 / 29

Black or Frozen In this picture, the history of an outside observer hovering at a constant distance from the event horizon is a hyperbola. The last light signal from the surface of the star never reaches them and the last few light signals take longer and longer. To the outside observer, the star appears to be "frozen" at the event horizon and is never seen to cross it. Bob G (VCU) Black Holes December 2016 15 / 29

Why that is a Black Hole!! In the late 1950s, John Archibald Wheeler turned his attention from nuclear physics to gravity. He was fascinated by the concept of an "event horizon" and gave many talks about it. While he was lecturing about this surface that could only absorb all light and from which nothing could escape, a member of the audience (thought to be Robert Dicke) spoke up and said "Why that is a black hole!!" The name stuck. Bob G (VCU) Black Holes December 2016 16 / 29

Collapsed Objects: White Dwarfs When a star similar in size to our Sun runs out of nuclear fuel, its outer atmosphere blows away, leaving behind a dense core about the size of the Earth. For a few thousand years afterward, we see a planetary nebula with the newborn white dwarf star at its center. Bob G (VCU) Black Holes December 2016 17 / 29

Collapsed Objects: Neutron Stars When a very massive star runs out of nuclear fuel, its core collapses, causing a supernova explosion, and leaves behind a neutron star. The Crab Nebula is the aftermath of a supernova explosion that was seen on Earth in AD 1054. Radio pulses from a spinning neutron star at the center of the nebula were observed in 1968. Bob G (VCU) Black Holes December 2016 18 / 29

Collapsed Objects: Sizes Here is a rough comparison of the sizes of different collapsed objects Black Holes can actually be any size. Here we show a black hole that might form from the collapse of a massive star. Bob G (VCU) Black Holes December 2016 19 / 29

Collapsed Objects: X-rays from Neutron Stars About half of all stars are member of binary or multiple star systems. When one member of such a system collapses, material from a partner star can fall onto it, generating X-rays. If the collapsed object has a visible surface, the result is a steady stream of X-rays. Bob G (VCU) Black Holes December 2016 20 / 29

Collapsed Objects: X-rays from Black Holes Shortly after the idea of an event horizon was understood, Ya B. Zeldovich realized that the X-rays emitted when material falls on it would be very different from the X-rays emitted by material falling on a neutron star. There will be a "traffi c jam" of material orbiting close to the event horizon and the falling material will hit those orbiting clouds instead of hitting a surface. Instead of steady X-rays, the X-rays will fluctuate on a timescale of one orbit time about a millisecond. Bob G (VCU) Black Holes December 2016 21 / 29

Collapsed Objects: Cygnus X-1 In 1964 the first X-ray survey of the sky was done by a sounding rocket with an X-ray detector. Bob G (VCU) Black Holes December 2016 22 / 29

Collapsed Objects: Cygnus X-1 In 1964 the first X-ray survey of the sky was done by a sounding rocket with an X-ray detector. A very strong signal was coming from somewhere in the constellation Cygnus and it was fluctuating exactly as Zeldovich had predicted. The signal was turning on and off. When it was off, a strong radio signal came from the same part of the sky. When optical telescopes looked at the radio source location, they found a star with its spectrum shifting back and forth a star being pulled back and forth by an invisible partner. The minimum mass of the invisible partner is now estimated to be 14 times the mass of our Sun. Bob G (VCU) Black Holes December 2016 22 / 29

Galactic Black Holes: The Milky Way Here we are in the Milky Way Galaxy: As you can see, it is a barred spiral galaxy. Bob G (VCU) Black Holes December 2016 23 / 29

Galactic Black Holes: Sgr A* A powerful source of radio waves, infra-red light, and X-rays is at the center of our Galaxy. Here is a picture from the Chandra X-ray Space Observatory: It has been a suspected black hole since its discovery in 1974. Martin Rees had predicted it in 1971. Bob G (VCU) Black Holes December 2016 24 / 29

Galactic Black Holes: The Theory It was predicted that material falling in to the black hole should form an accretion disk like this: That looks a lot like Sgr A*. Bob G (VCU) Black Holes December 2016 25 / 29

Galactic Black Holes: The Evidence for Sgr A* The stars near Sgr A* are moving fast enough that we can track them from 30,000 light years away. Several are in tight orbits around Sgr A* The mass of the attracting object is almost 3 million times the mass of our Sun. Bob G (VCU) Black Holes December 2016 26 / 29

Galactic Black Holes: Jets In Other Galaxies Jets such as the one streaming out of the galaxy M87 are common. They are evidence of supermassive black holes with accretion disks. Bob G (VCU) Black Holes December 2016 27 / 29

Galactic Black Holes: Lots of Them Many, if not most, galaxies appear to have supermassive black holes. A recent example is NGC 4845. The Hubble Space Telescope tracked the motion of stars near its center. The hole is small as supermassive black holes go: Only 300,000 solar masses. Bob G (VCU) Black Holes December 2016 28 / 29

Problems Our telescopes basically just show objects in orbit around black holes and the results of things falling in. They do not show the event horizons. Are event horizons real? An event horizon destroys information. Quantum theory says that is impossible. Are event horizons real or is there a "firewall" instead? Which came first, the supermassive black hole or the galaxy that it is in? Bob G (VCU) Black Holes December 2016 29 / 29