1. To look for black holes formed by the death of high-mass stars, we look for binary systems that allows us to determine the mass of the objects. If we can find an object with mass exceeding 3 M ⊙, but is neither a regular star, nor a neutron star, then we can argue that it may well be a black hole. The Case of Cygnus X-1 Cygnus X-1 is a X-ray binary system with a bright star of 18 M ⊙, and an unseen (invisible in the visible) companion of about 10 M ⊙. If the mass estimate of the X-ray source is correct, than it certainly exceeds the upper mass limit of neutron star (~ 3 M ⊙ ), making it a prime stellar black hole candidate. Black Holes: Do They Really Exist? W e cannot see black holes directly, so we have to look for indirect evidences…What would you look for to find a stellar-mass black hole, like those formed after the death of high mass stars?

2. Can We Tell if it is a Black Hole? I f our X-ray telescope have high-enough resolution and can resolve the structure around neutron stars and (stellar-mass) black holes, then these are what we might be able to see…Illustration of the X-ray emissions from the accretion disks around black hole and neutron star…but this is beyond our current capability! http://antwrp.gsfc.nasa.gov/apod/ap010119.html

3. Black Hole at the Center of the Milky Way Galaxy! http://www.eso.org/outreach/press-rel/pr-2002/pr-17-02.html http://www.eso.org/outreach/press-rel/pr-2002/pr-17-02.html Star Orbiting Massive Milky Way Centre Approaches to within 17 Light-Hours An international team of astronomers [2], lead by researchers at the Max-Planck Institute for Extraterrestrial Physics (MPE), has directly observed an otherwise normal star orbiting the supermassive black hole at the center of the Milky Way Galaxy. Ten years of painstaking measurements have been crowned by a series of unique images obtained by the Adaptive Optics (AO) NAOS-CONICA (NACO) instrument [3] on the 8.2-m VLT YEPUN telescope at the ESO Paranal Observatory. It turns out that earlier this year the star approached the central Black Hole to within 17 light-hours - only three times the distance between the Sun and planet Pluto - while traveling at no less than 5000 km/sec…. S imilar to the method used to measure the mass of the unseen companion in Cygnus binary system, we can observe the orbits (period of size of the orbits) of stars near the center of the galaxy to measure the mass of the galactic center…

4. Is it a Black Hole? H ow do we know the concentration of masses at the center of our galaxy is a blackhole or not? The mass at the center of the galaxy is estimated to be about 3 million M ⊙. However, possessing a high mass does not make you qualify for a black hole… You need to pack this mass into a space smaller than the Schwarzchild radius of that mass… If the black hole at the center of the Milky Galaxy is about 3 million solar masses, then its size must be smaller than 3 million km, or 10 light seconds. This is only a tiny spot near Sagittarius A* in the picture on the left, about 1/200,000 of the length of the scale-bar in the picture… You can watch the recent NOVA program about the black hole at the center of the Milkyway Galaxy at http://www.pbs.org/wgbh/nova/blackhole/program.html http://www.pbs.org/wgbh/nova/blackhole/program.html

5. Gamma Ray Bursts G amma Ray Bursts are high energy radiations from cosmological sources discovered accidentally in the 1960s by military satellites designed to monitor nuclear weapon tests on Earth. The are found to be distributed uniformly in space, and not correlated to the strong X-ray sources that are more concentrated in our own galaxy. Because of the tremendous distances of these objects, the energy released by the GRBs exceeds the luminosity of millions of galaxies like our own Milky Way. It is still not clear today what are causing these high energy events… –At least some of the GRBs seem to come from unusally powerful supernovae. But we don’t know how the Gamma Ray are produced. –Collision of neutron stars?

6. Einstein’s Special and General Theory of Relativity E instein’s Special and General Theory of Relativity are one of the most important development of Science in the 20 th century…these theories fundamentally changed our perception of space and time. The Special Theory of Relativity deals with the law of motion without the influence of gravity. Newton’s law of motion is correct only when the speed of motions are low compared to the speed of light. Special Relativity gives us the correct description of the law of motion for all speed range, even when it is close to the speed of light. The General Theory of Relativity includes the effect of gravity and acceleration. Equivalence Principle: the effect of gravity and the effects of acceleration are identical.

7. Development of Special Theory of Relativity

8. Special Theory of Relativity T he basis of Special Relativity is two concepts in physics: 1.All physical laws are the same in the inertia frames (The laws of nature are the same for every one, Page 331 of Text book). For two persons moving with respect to each other with constant speed, they must observe the same physical laws. All motion are relative. We cannot distinguish who is in motion and who is at rest.. Inertia Frames – A coordinate system in which Newton’s first and second law of motion are valid. 2.The speed of light is constant for all inertia observers (The speed of light is the same for every one, Page 331, Text Book). The speed of light we would measure from the light emitted by a moving source is the same as that from a source at rest! However, the color of light emitted from the moving source will change with the speed of the source (with respect to the observer).

9. Speed of Light T he speed of light, commonly denoted by c, was experimentally measured to be 2,999,792,458 meter/sec. In the 19 th century, it was thought that like sound wave must be transmitted through a medium, light must be transmitted by a yet-unknown medium called ether. Ether was thought to permeates the universe. Knowing Earth’s relative motion with respect to the ether was important for our understanding of our place in the universe. In 1887, Michelson and Morley at Case Western University performed a measurement to determine the flow of ether as the Earth moves in space. A talented baseball pitcher can throw the ball with speed approaching 100 miles per hour. If the pitcher throws the ball at you from a car traveling at a speed of 100 mph toward (or away from) you, you would measure the speed of the baseball to be 200 mph (or 0 mph). Like the baseball thrown toward you by a pitcher standing on the car driving toward you, the speed of light in the ether should be different depending on how fast the Earth is moving in the ether. Michelson and Morley’s measured speed of light in the direction perpendicular and parallel to the direction of Earth’s motion in space. Their experiment showed that the speed of light is the same independent of the direction it travels.

10. The Constancy of the Speed of Light M ichelson and Morley’s results on the speed of light were completely against our intuition and every-day experience about relative motion. Either 1.the measurement was wrong, or 2.the rules concerning how physical laws should change (or not change, invariant) when viewed by two observers moving with constant speed with respect to each other (called a transformation from one reference frame to another) are different for light and matter, 3.our understanding of the law of physics was wrong… Einstein postulated that the speed of light is independent of the motion of its source. He search for a new transformation rule that apply to both matter and light, and developed The Theory of Special Relativity, which forced us to rethink our idea about space and time. It was a revolutionary idea when it was first introduced, and faced very strong resistance for many years. However, it was accepted gradually only after experimental verification of its predictions were provided. Today, the constancy of the speed of light (that the speed of light is constant regardless of the relative motion between the light source and the observer) is accepted as one of the Laws of Physics, like the universal law of gravity that says there is a gravitational field associated with every object with mass.

11. Important Results of Special Relativity S ome important results of special relativity… Time Dilation* Length Contraction* Increase of Mass* Relativistic Red Shift Equivalence of Mass and Energy: E = mc 2 Note that the effects of special relativity are significant only when the speed of the object under study is very high, close to the speed of light! The speed of motion we experience daily, or we are familiar with, such as the speed of cars, airplane, or even rockets and spaceship traveling to the Moon, are too slow compared with the speed of light, and the special relativistic effect of these motion are very small and cannot be measured easily.

12. Space Travel: A Trip to Alpha Centauri A lpha Centauri, the closest star to the Sun, is about 4.5 light years away. Assuming we have the technology to build a spaceship that can travel at a speed of 86% that of the speed of light, or about 150,000 times faster than the spaceship we used to go to the Moon in the 1970s, and that Alpha Centauri is not moving with respect to Earth. Then, after launch, the mission control will have to wait for 9.7 years to hear the report from the astronauts on the spaceship that they have just arrived to a planet orbiting Alpha Centauri, because it takes the spaceship 5.2 years (=4.5/0.86 ) to travel to Alpha Centauri, and another 4.5 years for the report sent from Alpha Centauri (traveling at speed of light!) to travel back to the Earth. However, the astronauts reported that the trip wasn’t too bad after all, because it only took them 2.5 years to get there, according to the clock in their spaceship… This is the result of Time dilation and Length Contraction in Special Theory of Relativity… (Chapter 18, Section 5)

13. Time Dilation Moving clock runs slower! G iven two identical ‘clocks’, if one were traveling with a constant speed v with respect to the other, then the traveling clock would run slower. Imagine a ‘clock’ which works by counting the time it takes for light to travel from a light source F to a mirror and bounce back to the receiver D … If this clock is traveling with a constant velocity u with respect to an observer (the observer at rest), it would appear to the observer at rest that the traveling clock is running slower compared to his identical reference clock at rest, because of the extra distance (L is larger than L0) that light needs to travel according to the observer at rest…

14. Time Dilation Y ou can see the moving clock slows down only when the speed of the moving clock (with respect to you) is very high… For v = 1,000 miles per hour (supersonic jets)… v/c ~ 0.000001, t ~ 0.999999999 t 0. The effect is not appreciable at all! For v=0.86c, t ~ 2.0 t 0, or the traveling clock runs 2 times slower than the clock at rest with respect to you! t 0 is the time measured by the observer at rest. v is the speed of the moving clock. t is the time measured by the traveling clock…

15. In Mission Control… B ecause of time dilation, to people in mission control, the clock on the spaceship appears to run slower than the clock in mission control, and the astronaut aged slower…But it takes the astronaut 5.2 years (Earth Clock time) to get to Alpha Centauri.

16. Length Contraction A standard ruler would appear shorter measured by an observer traveling with speed v with respect to this ruler (This is also referred to as the Lorenz Contraction, first derived by Lorenz, before Einstein). Assuming that the distance between the Earth and Alpha Centauri is not changing, then we can consider this distance as a ‘ruler’ For the astronaut, the Earth and Alpha Centauri are moving at a speed of 0.86 c with respect to their spaceship. Therefore, the distance between Earth and Alpha Centauri is only 2.25 light years. v = 0.86c Alpha Centauri Earth L=L 0 / 2 Alpha CentauriEarth L0L0 v = 0.0

17. For the Astronauts… A lthough the clock in the spaceship would appear to run perfectly normal to the astronaut, the distance between the Earth and Alpha Centauri is shorter because of the effect of length contraction. Therefore, it takes them only half the time (compared to Earth’s point of view) to get there. Length of ‘ruler’ that is moving at a speed of v Length of stationary ‘ruler’

18. A ccording to special relativity, the mass of an object (as measured by a person at rest) increases as its speed is increased. When it achieves the speed of light, the mass of the object becomes infinitely large. Newton’s second law of motion says that the acceleration of an object times its mass is equal to the force applied. F = m  a or, Thus, with an infinite mass, a = 0. In other words, as the speed of a mass approaches that of the speed of light, its mass approaches infinity, and we cannot accelerate it any further, no matter how hard we try… Therefore, nothing can move faster than the speed of light! Mass Increases

19. The Twin Paradox I f you are convinced about the effect of time dilation and length contraction, then think about this… Imagine we have a pair of twin, one man, one woman. If the brother stays on Earth at mission control, while the sister takes the trip to Alpha Centauri, then when the trip is over and the sister returns to the earth, she would be younger than her twin brother because, according to special relativity, her clock (the moving clock) runs slower. But… From the perspective of the sister, her clock runs perfectly normal. Her heart beat is still about 50 pulses per minute. It was her brother and the Earth and Alpha Centauri that went for a trip with a speed of 0.86c. It was the clock of her brother that’s running slow! What is wrong here?

20. The Twin Paradox – The Resolution T he resolution of the twin paradox comes from the realization that in the coordinates system of the brother, it was the sister who actually traveled! In her trip to Alpha Centauri and back, the sister went through a series of events: 1.Accelerate from rest (with respect to Earth) to 0.86 c, 2.Traveling at 0.86 c for 2.7 years 3.Making the turn around, which can be achieved by many different methods, for example, Decelerates to a stop (with respect to Earth-Alpha Centauri system), then accelerate toward earth to 0.86 c again, Making the turn (changing direction, accelerating) at the speed of 0.86 c 4.Traveling at 0.86 c for another 2.7 years… 5.Decelerates to a stop on Earth The sister went through many different inertia frames during the trip. Meanwhile, the brother remains stationary (with respect to Earth), and felt only a constant gravitational field all the time. The twin do not experience the same thing. So, the argument that the brother, the Earth, and Alpha Centauri went for a trip went for a trip equivalent to the trip the sister experienced is not valid.

21. General Theory of Relativity T he core of general relativity is the Principle of Equivalence, which describes gravitation and acceleration as different perspectives of the same thing, and which was originally stated by Einstein in 1907 as: We shall therefore assume the complete physical equivalence of a gravitational field and the corresponding acceleration of the reference frame. This assumption extends the principle of relativity to the case of uniformly accelerated motion of the reference frame. In other words, he postulated that no experiment can locally distinguish between a uniform gravitational field and a uniform acceleration. For example, a person in a sealed elevator (and cannot see outside) accelerating at 9.8 m/sec 2 (the gravitational acceleration on the surface of the Earth) cannot tell if he is sitting on the surface of the Earth, or if he is in a place far away from any stars and planets but is been accelerated…

22. Effects of Very Strong Gravity S ome important results of General Relativity of relevance to Astronomy… 1.Gravitational Redshift A blue photon emitted from a star with a strong gravitational field would appear red after it reaches us at a distance away 2.Gravitational Lensing Effect Distortion of spacetime causes the light to travel a different path… This effect is be used to measure mass of distance galaxies. 3.Gravitational Time Dilation Time appears to run slower in strong gravitational field to an observer located at a distance away in a weaker gravitational field.

23. Experimental Verification of Time Delay Hafele and Keating Experiment D uring October, 1971, four cesium atomic beam clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward, to test Einstein's theory of relativity with macroscopic clocks. From the actual flight paths of each trip, the theory predicted that the flying clocks, compared with reference clocks at the U.S. Naval Observatory, should have lost 40+/-23 nanoseconds during the eastward trip. They should have gained 275+/-21 nanoseconds during the westward trip. The flying clocks lost 59+/-10 nanoseconds during the eastward trip and gained 273+/-7 nanosecond during the westward trip. These results provide an unambiguous empirical resolution of the famous clock "paradox" with macroscopic clocks. J.C. Hafele and R. E. Keating, Science 177, 166 (1972) Nanosecond = 1 billionths of a second! 275 nanosecond is about ¼ of a millionths of a second.

24. Effects of Very Strong Gravity S ome important results of General Relativity of relevance to Astronomy… 1.Gravitational Redshift A blue photon emitted from a star with a strong gravitational field would appear red after it reaches us at a distance away 2.Gravitational Distortion Spacetime Distortion of spacetime causes the light to travel a different path… Gravitational Lensing Effect This effect is be used to measure mass of distance galaxies. 3.Gravitational Time Dilation Time appears to run slower in strong gravitational field to an observer located at a distance away in a weaker gravitational field.

25. Gravitational Redshift Explanation#1 It takes energy to move away from an object with strong gravity (e.g., going up stair, sending a satellite into orbit, or sending the astronauts to the Moon). The same can be said about a photon trying to travel from the surface of a star to a distant location where the gravitational pull of that star is almost zero. The photon need to spend energy to get to the far-away destination. So, the photon has less energy when it reaches its far-away destination. A photon with lower energy means it has longer wavelength, or, it appears redder. Throw a ball upward with initial velocity V: High kinetic energy The speed is decreased at higher height: Lower kinetic energy The ball stopped going up: zero kinetic energy For photons, think in terms of energy. Zero energy photon: Infinitely long wavelength, DARK, Can’t see it. Lower (than initial) energy photon: Long wavelength, appears REDDER Initial energy of photon depending on the wavelength

26. Gravitational Redshift: Stretching of Spacetime Explanation#2 Gravity stretches the spacetime continuum. The photons are stretches with it. Zero gravity, flat spacetime Strong gravity, curved spacetime A B DC CD The distance between C and D is stretched longer by gravity. Black hole Photons are stretched so much that it is no longer detectable.

27. Effects of Very Strong Gravity S ome important results of General Relativity of relevance to Astronomy… 1.Gravitational Redshift A blue photon emitted from a star with a strong gravitational field would appear red after it reaches us at a distance away 2.Gravitational Distortion Spacetime Distortion of spacetime causes the light to travel a different path… Gravitational Lensing Effect This effect is be used to measure mass of distance galaxies. 2.Gravitational Time Dilation Time appears to run slower in strong gravitational field to an observer located at a distance away in a weaker gravitational field.

28. Two dimensional model of the curvature of spacetime… Without gravityWith gravity Gravitational Distortion of Spacetime I n classical physics, the universe is composed of a three- dimensional space, and a one dimensional time. Space and time as separate and independent dimensions. The three-dimensional space moves in the time dimension. In Einstein’s General Theory of Relativity, space and time are considered inseparable…and gravity arises from the curvature of the spacetime continuum. Both light and matter follow the same path in spacetime… Therefore, in region of very strong gravity, the distortion of spacetime is so great that the path of both light and matter curves back inside…

29. Bending of Light Path Around Black Holes A t a distance of about 1.5 R sch of a black hole, spacetime is distorted so much that photons emitted from the back of your head actually go around the black hole and come back to you.

30. Experimental Verification of Gravitational Distortion of Spacetime E ven without a black hole, we can verify Einstein’s prediction of the gravitational distortion of spacetime… According to GR, the spacetime near a heavy object like the Sun is distorted, causing the position of stars passing near the edge of the Sun be shifted by 1.75 arcsecond… This effect was experimentally verified by Sir Eddington in 1919 during an eclipse observation: http://www.firstscience.com/site/articles/coles.asphttp://www.firstscience.com/site/articles/coles.asp Light path of star without the Sun Light path of star with the Sun Stars far away from the Sun are not affected… Star near the Sun would be affected

31. Eddington’s Eclipse Measurement of Gravitational Bending of Light The red line marks where the star should be without the gravitational bending of space time by the Sun. Eddington’s results were not accepted universally by the scientific community right away…This is actually quite normal in the scientific community. However, the results were confirmed by many other eclipse measurements later…

32. Gravitational Lensing Effect This galaxy is directly behind the cluster. Gravitational lensing produces the multiple copies of the same galaxy we see here. In general relativity, gravity causes the distortion of spacetime. Light travels along these distorted path. Thus, a large gravitational object sometime behave like a lens. It can form image or images of distant objects behind it for us to see if the alignment happens to be right. If we know the distance to the galaxy being imaged, then we can calculate the mass of the cluster.

33. What Happens if Your Neighbor is a Black Hole? I f there is a black hole in the solar neighborhood, will it pull everything – the Sun, the planets, and the asteroids and coments – in? No! as long as we stay outside of its event horizon, we are safe… – Recall that there are stable orbits around a gravitational objects – From a distance, a black hole is not different from an ordinary star or planet… If you take a trip to the black hole… If you want to know what it is like inside the black hole, the NOVA program has a simulation, but I am not so sure about it… http://www.pbs.org/wgbh/nova/blackh ole/program.html http://www.pbs.org/wgbh/nova/blackh ole/program.html

34. Concluding Remarks about the General and Special Theory of Relativity T he predictions of special and general relativity have been verified by many experiments. Today, not only physicists worry about the effects of Special and General of Relativities (SR and GR). These effects are part of our daily life also. For example, the Global Positioning Satellites (GPS) needs to take into account GR and SR time dilation effects in order to keep correct time from onboard atomic clocks.