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Black Holes. W Dietsch Ph.D. Black Hole Formation. When a star runs out of nuclear fuel, it will collapse.
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Black Holes W Dietsch Ph.D.
Black Hole Formation • When a star runs out of nuclear fuel, it will collapse. • If the core, or central region, of the star has a mass that is greater than three Suns (3 solar masses), no known nuclear forces can prevent the core from forming a deep gravitational warp in space called a black hole.
Event Horizon • A black hole does not have a surface in the usual sense of the word. There is simply a region, or boundary, in space around a black hole beyond which we cannot see. This boundary is called the event horizon.
The Accretion Disc • As this gas forms a flattened disk, it swirls toward the companion. • Frictioncaused by collisions between the particles in the gas heats them to extreme temperatures and they produce X-rays that flicker or vary in intensity within a second. • These X-rays are observed here on Earth.
X Ray Binary Systems • Many bright X-ray binary sources have been discovered in our galaxy and nearby galaxies. In about ten of these systems, the rapid orbital velocity of the visible star indicates that the unseen companion is a black hole. (The figure at left is an X-ray image of the black hole candidate XTE J1118+480.)
X Ray Jets and Stellar Winds • Not all the matter in the disk around a black hole is doomed to fall into the black hole. • In many black hole systems, some of the gas escapes as a hot wind that is blown away from the disk at high speeds. • Even more dramatic are the high-energy jets that radio and X-ray observations show exploding away from some stellar black holes. These jets can move at nearly the speed of light in tight beams and travel several light years before slowing down and fading away.
X-ray data from Chandra, the European Space Agency's XMM-Newton, and the German Roengtensatellite (ROSAT) X-ray observatories provide direct evidence for the catastrophic destruction of a star that wandered too close to a supermassive black hole (SMBH). Evidence for SMBH
Types of Black Holes • Static (a Schwarzschild black hole) • Charged (a Reissner-Nordstrøm black hole) • Rotating (a Kerr black hole)
Schwarzschild Radius • Rs = 2MG/c^2 • M stands for massG is Newton's constant coefficient of gravity, 6.67 10^-11c is the speed of light, 3.0 10^8 m/s.
The Photon Sphere • occurs at 3/2 the Schwarzschild Radius • light rays can have (very) unstable orbits • Speed you would have to go to stay in orbit is c, the speed of light, some 3 x 10^8 m/s.
The Event Horizon • Occurs at the Schwarzschild radius • The first sphere of light that does not expand (due to the extreme curvature of spacetime). • Once something passes beyond the event horizon, it can never leave.
The Singularity • At the singularity the curvature of spacetime is infinite. • Nothing is there except a lot of bent spacetime. • Space and time cease to exist. • Matter goes out of existence, but its gravity persists.
Where does matter go after it is squeezed through a Singularity? • Some physicists including Stephen Hawking believe that matter entering a black hole in our universe, will emerge as matter spewed forth from a so-called white hole in another universe. • The mathematics seem to say this, but there are many difficulties in interpreting such theories without knowing whether they are accurate representations of our physical world.
Photon Sphere • Much like the photon sphere of a static black hole. • Light rays can hold unstable orbits around the black hole. • If you leveled your eye there, you would see the back of your head.
Event horizons • Reissner-Nordstrøm solution. • if a small charge is added to a black hole, the event horizon shrinks and a second, inner horizon forms just above the singularity! (Cauchy horizon ). • Increasing charge increases outer EH and shrinks inner EH. • If the charge equals the BH mass, both event horizons disappear.
Singularity • The singularity of a charged black hole is the same as that of a static black hole • With the exception that it is possible for the singularity to exist without any protective horizons. • Physicists just don't like this, Roger Penrose included (no naked singularities).
View of a Kerr BH • A ray trace of what the emission from an accretion disk of gas would look like around a Kerr black hole viewed at an inclination of 30 degrees from face-on.
Rotation • Angular momentum is one of the three properties of a black hole (along with mass and charge). • with a speed that is 99.8% their mass • Most stars rotate, and retain their angular momentum after collapsing to form a BH. Since the radius gets very small, the radial speed becomes very large. • According to the calculations done by Kip Thorne, most black holes would rotate
Two Photon Spheres • Rotation “drags spacetime”. • Light rays can go in the direction of rotation and as a result of frame dragging, go “faster”. • Light rays going against the direction of rotation (counterrotating) go “slower”.
The Ergosphere • Not a photosphere. • Not an event horizon. • The outer boundary of the ergosphere is the static limit of the rotating black hole. • Once crossing into the ergosphere, it is impossible to stay still, even light can not remain stationary radially.
Familiar Horizons • The two event horizons of the rotating black hole are pretty much the same as a charged black hole's event horizons. • Two radii where a distant observer would say time seems to stop. • The outer horizon switches time and space around one way, and the inner horizon switches them back the other way (counterrotation).
Ring around the Singularity • Calculations using Kerr geometry describe the singularity as ring-shaped. • Some physicists like to call it 'negative space.' Others (myself included) like to call it another universe or another part of this universe.
Hawking Radiation • In a vacuum, virtual electron-positron particle pairs are always flashing in and out of existence. • They can become separated by the strong gravitational tidal forces near the horizon. • One of the particles may then escape while the other falls into the hole. • The event horizon is not black but from the viewpoint of a distant observer it is constantly emitting particles. • Over time, this 'Hawking radiation' would steadily reduce the gravitational mass of the black hole, causing it to eventually evaporate.
How can you use black holes for time travel? • Black holes can be used to travel into the future only. So far as we know, our universe prohibits traveling into the past. • According to Einstein's theory of general relativity, in the presence of a gravitational field, an external observer would see a clock in a strong gravitational field tick more slowly. • This is analogous to the famous time dilation effect in special relativity, except that in the 'gravitational redshift' effect no motion between the observer outside the gravitational field and the clock located within the field, is required.
What is the importance of black holes to cosmology? • Indirectly they tell us that our relativistic theory of gravity and space-time provided by Einstein's general relativity is fundamentally correct. • When we use these same equations to study cosmology we have some confidence that they may be correct and give us answers that make sense.
Directly, black holes tell us that the universe can hide much of its matter in a way that still contributes to the total mass of the universe, but may not contribute to the abundances of certain primordial elements such as hydrogen and helium. If enough black holes were produced soon after the big bang but before the first few minutes, this could have an impact on the relationship between how rapidly the universe is expanding and the origin of the primordial elements.
It is expected that most black holes formed long after the big bang by stellar evolution. • These black holes may contribute to the missing mass in the universe up to the maximum limit set by the primordial element abundances themselves. • Black holes are cosmologically important from many different standpoints.
