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Black Holes & Curved Spacetime 15 August 2005 AST 2010: Chapter 23 1 Questions about Black Holes What are black holes? Do they really exist? How do they form? Will the Earth someday be sucked into a black hole? 15 August 2005 AST 2010: Chapter 23 2 Introduction to Black Holes At the end of a massive star’s life, its outer layers are blown off in a (Type II) supernova explosion If the core remnant has a mass greater than 3 MSun, then not even the super-compressed degenerate neutrons can support the core against its own weight Consequently, according to theories, gravity overwhelms all other forces and crushes the core until it is infinitely small The resulting point-like object is a black hole Only the most massive, very rare stars (with initial masses greater than 40 MSun) will form black holes when they die 15 August 2005 AST 2010: Chapter 23 3 General Relativity Under the extreme circumstances of a black hole, Newton’s theory of gravity is inadequate Newton’s theory works well in ordinary situations (motions in everyday life, planetary orbits, etc), but it fails when gravity becomes extremely strong large masses move very rapidly light is affected by a huge mass To understand what black holes are, we begin with an introduction to Einstein’s theory of general relativity It improves on Newton’s theory of gravity 15 August 2005 AST 2010: Chapter 23 4 The Equivalence Principle (1) The equivalence principle says that life in a freely falling laboratory is indistinguishable from, and hence equivalent to, life with no gravity No experiment can be done inside a sealed laboratory to determine whether it is floating in space without gravity or falling freely in a gravitational field In other words, the two situations are equivalent In the absence of air friction, the boy and girl on the right fall downward at the same rate (their speeds increase by the same amount each second), and so does the ball if they aim it straight at each other Consequence of the equivalence principle: if the three are isolated in a box that is falling with them, no one inside it will will be aware of any gravity 15 August 2005 AST 2010: Chapter 23 5 The Equivalence Principle (2) When a space shuttle is in free-fall orbit around the Earth, everything inside the shuttle either stays put or moves along a straight line because gravity appears to be absent inside the shuttle To the astronauts inside it, falling freely around the Earth creates the same effects as being far off in space, remote from all gravitational influences In other words, the astronauts feel weightless in such orbit Thus the effects of gravity can be compensated by the right acceleration 15 August 2005 AST 2010: Chapter 23 6 Here’s the Rub If a laser beam is sent from the back of a shuttle to the front, in zero gravity the laser will hit the front center of the shuttle in free fall around the Earth the laser must also hit the front center, according to the equivalence principle but from the time the light left the rear wall until it reaches the front the shuttle has moved! Thus the equivalence principle would seem to imply that light is bent by gravity! Since light has no mass, this would contradict the expectation that only objects with mass are influenced by gravity 15 August 2005 AST 2010: Chapter 23 7 Einstein’s Radical Idea He suggested that the light curves down to meet the front of the shuttle because the Earth’s gravity bends the fabric of space and time Any event in the universe can be pinpointed using the three dimensions of space (where?) and the one dimension of time (when?) Einstein showed that there is an intimate connection between space and time we can build a correct picture of the physical world by considering the two together, in what is called spacetime According to his theory, called general relativity, the presence of mass (gravity) curves or warps the fabric of spacetime the stronger the gravity (the larger the mass) is, the more spacetime is curved or warped 15 August 2005 AST 2010: Chapter 23 8 Gravity Bends Spacetime (1) When an object (an electron, a space shuttle, or a light beam) enters a region of spacetime distorted by the presence of another object’s mass, the path of the first object will be different from what it would have been in the absence of the second’s mass In summary, matter tells spacetime how to curve, and the curvature of spacetime tells other matter how to move Three-dimensional analogy of spacetime: 15 August 2005 AST 2010: Chapter 23 9 Gravity Bends Spacetime (2) 15 August 2005 AST 2010: Chapter 23 10 Gravity Bends Light’s Path 15 August 2005 AST 2010: Chapter 23 11 Tests of Einstein’s Theory of General Relativity (1) Since Newton’s theory is inadequate when gravity is very strong, Einstein’s theory can be tested where Newton’s fails The motion of Mercury about the Sun provides a “laboratory” to test Einstein’s theory Mercury’s orbit undergoes very slow, but detectable, rotation in space This rotation cannot be fully explained by Newton’s theory Einstein’s prediction was remarkably close to the data, giving him much confidence in his theory 15 August 2005 AST 2010: Chapter 23 12 Tests of Einstein’s Theory of General Relativity (2) Einstein’s theory also predicts that starlight is deflected when it passes near the Sun If a star’s position is known when the Sun is not in the way, then an observation of a shift in the star’s position when the Sun is in the way will confirm the theory Such an observation could be done during a total solar eclipse so that much of the Sun’s bright light is blocked out The confirmation was made first in 1919 by British astronomers and later by others! 15 August 2005 AST 2010: Chapter 23 13 Bending of Light 15 August 2005 AST 2010: Chapter 23 14 Tests of Einstein’s Theory of General Relativity (3) Einstein’s theory further predicts that the stronger the gravity, the slower the pace of time In 1959, a comparison of time measurements on the ground and top floors of the physics building at Harvard University showed that the clock on the ground floor ran more slowly than the one on the top floor confirming Einstein’s prediction It was further confirmed in 1976 by the measurements of time delays experienced by radio signals sent by the Viking lander on Mars as they passed near the Sun The delays were also caused by the curving of spacetime near the Sun 15 August 2005 AST 2010: Chapter 23 15 Summary of Black-Hole Formation 15 August 2005 AST 2010: Chapter 23 16 Ultra-strong Gravity As a massive star collapses, the gravity on its surface increases and therefore, according to general relativity, the spacetime around the star becomes more and more curved In other words, the curvature of the spacetime increases As a result, when the star has shrunk down to a sufficiently small size (just a little larger than a black-hole), only light beams sent out perpendicularly to its surface could escape Other light beams and objects sent outward could no longer escape, following paths that curve back to the surface If the collapsing star shrinks just a little more, nothing will be able to escape and the star will become a black hole Since not even light can escape, the object appears black The black hole’s size defines its event horizon 15 August 2005 AST 2010: Chapter 23 17 “Event Horizon” 15 August 2005 AST 2010: Chapter 23 18 Escape Velocity: Rocket Analogy 15 August 2005 AST 2010: Chapter 23 19 Escape Velocities White dwarfs and neutron stars have huge surface escape-velocities because they have roughly the mass of the Sun packed into an incredibly small volume A solar-mass white dwarf has a radius of only 10,000 kilometers, and its surface escapevelocity is about 5,000 km/s A 2-solar-mass neutron star would have a radius of just 8 km, and its surface escapevelocity would be an incredible 250,000 km/s! Real neutron stars have masses above 1.4 solar masses and smaller radii, and so their escape velocities are even larger! 15 August 2005 AST 2010: Chapter 23 20 Event Horizon A black hole probably has no surface Astronomers use the distance at which the escape velocity equals the speed of light for the size of the black hole This distance defines a surface called the event horizon because no messages (via electromagnetic radiation or anything else) of events happening within that distance of the point mass can make it to the outside The region within the event horizon thus appears black 15 August 2005 AST 2010: Chapter 23 21 Schwarzschild Radius Within the event horizon space is so curved that any light emitted is bent back to the point mass Karl Schwarzschild was the physicist who derived the first exact solution to Einstein’s equations of general relativity Schwarzschild found that the light rays within a certain distance of the point mass would be bent back to the point mass This distance is the same as the radius of the event horizon, and is sometimes called the Schwarzschild radius 15 August 2005 AST 2010: Chapter 23 22 What Would It Feel to Fall into a Black Hole? Falling into a Black Hole (1) According to theory, falling toward a black hole would not be a pleasant experience… Falling feet-first, your body would be scrunched sideways and stretched along the length of your body by the tidal forces of the black hole Your body would look like a spaghetti noodle! Stretching happens because your feet would be pulled much more strongly than your head Sideways scrunching happens because all points of your body would be pulled toward the center of the black hole Your shoulders would be squeezed closer together as you fell closer to the center of the black hole Tidal stretching/squeezing of anything falling into a black hole is conveniently forgotten in Hollywood movies 15 August 2005 AST 2010: Chapter 23 24 Falling into a Black Hole (2) A friend watching you as you enter a black hole would see your clock run slower and slower (than his) as you approached the event horizon This is the effect of time dilation Your friend would see you take an infinite amount of time to cross the event horizon Time would appear to him to stand still However, in your reference frame your clock would run forward normally and you would reach the center very soon… …a truly once-in-a-lifetime experience 15 August 2005 AST 2010: Chapter 23 25 Falling into a Black Hole (3) If you reported back the progress of your journey into the black hole using photons with very short wavelengths (very high frequencies), your friend would have to tune to progressively longer wavelengths (lower frequencies) as you approached the event horizon This is the effect of gravitational redshift Animation Eventually, the photons would be stretched to infinitely long wavelengths 15 August 2005 AST 2010: Chapter 23 26 Detecting Black Holes (1) Since, according to theory, black holes (their event horizons) are only several miles across and completely black, how do we go about finding them? Indirect methods must be used! Their presence may be detected from their effects on surrounding material and stars A binary-star system may have a black hole as one of its members The behavior of the visible companion may reveal whether or not the other is a black hole If sufficient data about the system is collected, Kepler’s laws can be used to deduce the invisible object’s mass If it is too big for a neutron star or a white dwarf, then it is likely a black hole! 15 August 2005 AST 2010: Chapter 23 27 Views of a Possible Black Hole far away 15 August 2005 up close AST 2010: Chapter 23 28 Detecting Black Holes (2) Measuring the masses of all of the binary-star systems in the Milky Way Galaxy would take much too long a time It is estimated that there are over a 100 billion binary systems in the Galaxy! Even if it took you just one second to somehow measure a binary's total mass and subtract out one star's mass, it would take you over 3,000 years to complete your survey How could you quickly hone on the binary systems that might have black holes? Fortunately, black holes can advertise their presence loud and clear with the X-ray emission associated with them 15 August 2005 AST 2010: Chapter 23 29 X-Ray Emission A visible star in a binary system loses some of its gas to its black-hole companion The gas material forms an accretion disk as it spirals onto the black hole Gas particles in the disk rub against each other and heat up from friction As the particles whirl closer to the event horizon, the friction can heat them to about 100 million kelvins, which is hot enough for the emission of X-rays Since X-ray sources in the Galaxy are rare, if you find an X-ray source, then you know something strange is happening with the object If the unseen companion is very small, then the X-ray brightness of the disk will be able to change rapidly 15 August 2005 AST 2010: Chapter 23 30 Accretion from a Binary Partner 15 August 2005 AST 2010: Chapter 23 31 X-Ray Emission Visible Star black hole accretion disk Gas pulled off Animation of black hole in binary star system 15 August 2005 AST 2010: Chapter 23 Gas temperature increases closer to BH. Gas near BH emits x-rays. 32 Chandra X-Ray Observatory It is one of NASA's great observatories launched by the space shuttle Columbia on July 23, 1999 It detects/images X-ray sources that are billions of LY away Chandra’s mirrors are the largest, most precisely shaped and aligned, and smoothest mirrors ever constructed It produces images 25 times sharper than the best previous X-ray telescope Chandra's improved sensitivity is making possible more detailed studies of black holes, supernovae, and other exotic objects 15 August 2005 AST 2010: Chapter 23 33 Black-Hole Candidates Several black-hole candidates have been found Examples include Cygnus X-1 and V404 Cygni in the constellation of Cygnus LMC X-3 in the constellation Dorado V616 Mon in the Monocerotis constellation J1655-40 in Scorpius and the closest, V4641 Sgr in Sagittarius, is about 1600 light years away 15 August 2005 AST 2010: Chapter 23 34 Some Black-Hole Candidates in Binary Star Systems 15 August 2005 AST 2010: Chapter 23 35 Chandra's X-Ray Images of Black Holes This movie is a sequence of X-ray images of deep space taken by Chandra The black holes are first marked, and then the view zooms onto one pair of particularly close black holes, known as SMG 123616.1+621513 Astronomers believe that these black holes and their galaxies are orbiting each other and will eventually merge The movie ends by showing an animation of this scenario 15 August 2005 AST 2010: Chapter 23 36 Black Hole in Center of Milky Way Astronomers believe that super-massive black-holes may lie in the central regions of large galaxies These regions may serve as “feeding grounds” for black holes that form therein A black hole can grow in mass and size by “eating” the surrounding matter, such as dust, asteroids, other stars, or even other black holes The central region of our Galaxy is thought to harbor a super-massive black-hole with a mass of around 3.6 million MSun 15 August 2005 AST 2010: Chapter 23 37 Stellar Question What would happen to the Earth’s orbit if the Sun were suddenly replaced by a black hole with the same mass as the Sun? 15 August 2005 AST 2010: Chapter 23 38 Hollywood and Reality Black holes are portrayed in TV and films as cosmic vacuum cleaners, sucking up everything around them or as tunnels from one universe to another Black holes are dangerous only if something gets too close to them Because all of their mass is compressed to a point, it is possible to get very close where the gravity gets very large Objects far enough away will not sense anything unusual If the Sun were replaced by a black hole of the same mass, the orbits of the planets would remain unchanged It would, however, be darker and colder 15 August 2005 AST 2010: Chapter 23 39