Homework 7: Research and Investigate a Metric Form

You may work alone or in a group of up to 3 people. Metric forms will be assigned on a first come-first-served topics assigned as a message on ASULearn - be sure to message me your proposed topic (or a ranked list of a few of them) as well as your group member's names. I will post who has what topic approved to the main page at least once a day.
  • anti-de Sitter metric
  • de Sitter metric for special relativity
  • Eddington-Finkelstein metric
  • Godel metric
  • Kerr metric
  • Kerr-Newman rotating charged black hole metric
  • Friedmann-Lemaitre-Robertson-Walker (FLRW) metric
  • Reissner-Nordstrom metric
  • Schwarzschild metric
  • Taub-NUT metric
  • Wormhole metric
  • Alcubierre metric or warp drive metric
  • Other intersting metrix forms may be approved
  • Explore the following via researching and (keep track of your references). Write it up in your own words but you may use pictures from elsewhere (with proper reference). You will turn this in and share some portions with your classmates (see #8).

    1. Find one or more pictures that relates to your topic. Google images is a good place to search, but be sure to reference the original site (google images is a database - it does not contain the images)
    2. Write down a metric form (like ds2=...) for your topic
    3. In bullet point format, summarize the historical significance and history of when the related people discovered or investigated it (include full names as well as dates), including at least one mathematician from a country outside of the U.S. when possible (it could be someone who laid groundwork on the surface, or peripheral but connected work). If your metric is named after someone, you should look up that person.
    4. In bullet point format, summarize (in your own words) physically interesting features
    5. In bullet point format, summarize information (in your own words) about geodesics and/or curvature [try to find information that you can understand on both if possible]
    6. Search MathSciNet for journal articles related to your metric. Note that if Godel metric is your topic, you'll want to include "metric" in the title, but for the others you'll have better luck by searching with only the names(s), like anti-de Sitter instead of anti-de Sitter metric. Choose one article you find interesting and write down the full bibliographic reference from the MathSciNet database.

      What is MathSciNet? Historically, mathematicians communicated by letters, during visits, or by reading each other's published articles or books once such means became available. For example, Marin Mersenne had approximately 200 correspondents. Some mathematical concepts were developed in parallel by mathematicians working in different areas of the world who were not aware of each others progress. In an effort to increase the accessibility of mathematics research articles, reviews began appearing in print journals like Zentralblatt fur Mathematik, which originated in 1931, and Mathematical Reviews, which originated in 1940. Since the 1980s, electronic versions of these reviews have allowed researchers to search for publications. In October 2015 MathSciNet, the electronic version of Mathematical Reviews, listed over 3.2 million items.
    7. Give proper credit to your references for pictures and content
    8. You will turn in all of the above. In addition, prepare a short presentation for your classmates based on the following components:
      1. at least one picture from #1
      2. 2
      3. one mathematician from #3
      4. one item from #4
      5. one item from #5
      6. 6
      7. 7