1. Homework:
To prepare for TMT discussions next week, you should read the following article critically…
Don’t forget to find me at the IfA open house on Sunday for extra credit

2. Wormholes

3. The simplest example
Has solution (the Schwarzschild metric):
The r = 2m singularity is more complicated than previously mentioned…

4. This is what the vicinity of the space-like singularity looks like (with 2 dimensions suppressed):

5. The solution actually has two parts, the black hole part in one universe where matter flows in and essentially a white hole part in another universe where matter flows out.

6. The connection is unstable and the gravitational attraction pinches off the wormhole

7. A wormhole could be kept open by filling its throat, or the region around it, with an ingredient called exotic matter. This is strange stuff which doesn’t exist in the classical physics world, but may be allowed by quantum physics.
Exotic matter is repelled, rather than attracted, by gravity and is said to have negative energy - meaning it has even less than empty space.

8. Scientists like John Wheeler and particularly Kip Thorne, realized that Einstein’s laws of gravity do not:
determine the topology of the spacetime – that is determined by the matter distribution.
give a direction to time.
What does 1) mean?

9. Topologically, a coffee cup is the same as a donut!!
Since Einstein’s equations don’t determine the topology of space time, then maybe we can fold it and do this:

11. A jet emerging from a wormhole!!!
A jet emerging from a wormhole!!! Not!!!!

12. Scientists like John Wheeler and particularly Kip Thorne, realized that Einstein’s laws of gravity:
Do not determine the topology of the spacetime – that is determined by the matter distribution.
Do not give a direction to time.
What does 2) mean?

13. We could use wormholes to travel in time!
Heres one scheme – A traveler could move from event A to B using stationary Wormholes and then back in time using a moving wormhole.

14. Critical thinking exercise – Why won’t these schemes work?
Exotic matter
Could use anything – fairy godmothers, aliens, mental telepathy, inflation, dark energy…
Direction of time
The laws of Thermodynamics give time a direction – gravity must obey thermodynamics

16. What do we mean by dark matter and dark energy?

19. Dark Stuff in the Universe
                
Dark matter
Not dark matter

20. Unseen Influences
Dark Matter: An undetected form of mass that emits little or no light but whose existence we infer from its gravitational influence
Dark Energy: An unknown form of energy that seems to be the source of a repulsive force causing the expansion of the universe to accelerate

21. For groups of stars, galaxies, clusters of galaxies,
we measure the velocities of the member objects,
then assume there has to be enough mass there for gravity to stop them from flying apart. When we measure these velocities, it turns out that more mass is needed!
So we assume there is dark stuff.
The first to observe this behavior was Fritz Zwicky in He was looking at galaxies in clusters.
No one believed him.
He was quite a character!

22. What is the evidence for dark matter in clusters of galaxies?

23. We can measure the velocities of galaxies in a cluster from their Doppler shifts

24. The mass we find from galaxy motions in a cluster is about
50 times larger than the mass in stars!

25. Clusters contain large amounts of X-ray emitting hot gas
Temperature of hot gas (particle motions) tells us cluster mass:
85% dark matter
13% hot gas
2% stars

26. Gravitational lensing, the bending of light rays by gravity, can also tell us a cluster’s mass

27. All three methods of measuring cluster mass indicate similar amounts of dark matter

28. She is still a character!
Vera Rubin detected this lack of luminous stuff in individual galaxies in the early seventies.
No one believed her!
She is still a character!
Vera graduated from Vassar College in 1948 with a bachelors degree in Astronomy and accompanied her new husband Bob Rubin, a physicist, to Cornell University. She completed her Master's degree there in At this time the big bang theory was becoming widely accepted. Vera presented her master's thesis to the American Astronomical Society\ in which she suggested that galaxies might be rotating around an unknown center, not just expanding out as described in the big bang theory. There was no scientific theory to explain this finding and as a 22 year old woman her ideas quickly earned a her negative reputation.
She completed her doctorate at Georgetown University in 1954 by taking night classes while her parents watched her 2 children and her husband waited in the car. Vera did not know how to drive. Her doctorate work showed that galaxies were not evenly distributed in the universe, but that in some areas there are more, and in some there are less. Again this went against the predictions of the big bang theory of an evenly distributed universe. ( More research gave her observations validity 15 years later.)

29. Mass within Sun’s orbit:
1.0 x 1011 MSun
Total mass:
~1012 MSun

30. Spiral galaxies all tend to have flat rotation curves indicating large amounts of dark matter

31. The visible portion of a galaxy lies deep in the heart of a large halo of dark matter

32. What is the Dark Matter?
Some Possibilities:

33. Ordinary Matter:
Dust, Gas, Planets, Jupiters, Brown Dwarfs, Faint Stars, White Dwarfs, bowling balls, black holes, MACHOs …
Current theories/observations say there just isn’t enough mass possible.
Plus the Hot Big Bang idea doesn’t produce enough “baryonic matter” (protons, neutrons, electrons etc.) to do it.
Non-Baryonic
hot dark matter (HDM) and
Baryonic
cold dark matter (CDM),
depending on their respective masses and speeds. CDM candidates travel at slow speeds (hence "cold") or have little pressure, while HDM candidates move rapidly.

34. Not-so-ordinary Matter:
Neutrinos are an example of a particle that interacts with matter through the weak nuclear force. There are so many neutrinos in the universe, however, that even a small mass would be important for dark matter; a mass of 92 eV, one five-thousandth the mass of the electron, would close the universe!

35. WIMPS
Most exotic matter candidates fall into the category of WIMPS, or Weakly Interacting Massive Particles. These are heavy particles that only interact weakly with other matter (or else they would have been discovered by now).
There are many possible – e.g., neutralinos, axions, etc.

36. Change Gravity:
Another possibility – Perhaps gravity on large scales, such as the size of galaxies, doesn't work the same way as gravity does on the small scales we can measure.
MOND – MOdified Newtonian Dynamics
Milgrom Bekenstein Sanders

37. Change Gravity:
MOND – MOdified Newtonian Dynamics

38. A word from our sponsor!!