Kinematics has a strong connection to geometry in the vicinity of a
black hole, because General Relativity connects trajectories with the
shape of space itself. Space-time diagrams are close relatives of
kinematic diagrams, and might help students get the idea of how to
represent motion using algebra and basic calculus and a little geometry.
*Maybe* looking at how light or other objects travel around black holes
might help convince students that algebra and geometry are useful tools.
Interpreting slope as a speed might be helped by seeing world lines on
space-time diagrams with "maximum slope" of 45° being the speed of
light. On the other hand, for traditional classes with rigid schedules,
adding the concept of reference frames and falling through space will
likely overcomplicate the introductory discussion of kinematics. A Power
Point file accompanying these notes explores a few of these concepts.

**Paths through space around a black hole. How it looks...**

You can see behind a black hole! The view near a black hole...

<http://rocinante.colorado.edu/~pja/plunge_i80l.mpg>

Nice cartoon at: <http://luth2.obspm.fr/~luminet/chap10.html>

-   Step by Step into a Black Hole by Ute Kraus

> <http://www.spacetimetravel.org/expeditionsl/expeditionsl.html>
>
> <http://www.spacetimetravel.org/interaktives_schwarzes_loch/interaktives_schwarzes_loch.html>

-   Light bending movies

> <http://archive.ncsa.uiuc.edu/Cyberia/NumRel/BlackHoleBend.html>

-   Apparent positions

> <http://www.astronomynotes.com/relativity/s4.htm>

-   Gravitational arcs seen in Hubble Images

> <http://en.wikipedia.org/wiki/Image:Abell.lensing.arp.750pix.jpg>
>
> <http://astro.ago.uni-lj.si/bh/pmwiki.php?n=Main.Lensing>

-   Baez's site: <http://math.ucr.edu/home/baez/> (for reference, see
    the next...)

> http://en.wikipedia.org/wiki/Einstein_ring

-   Orbits in strongly curved spacetime

> <http://www.fourmilab.ch/gravitation/orbits/>

Why those motions? Equivalence Principle

-   <http://en.wikipedia.org/wiki/Equivalence_principle>

-   <http://www.astronomynotes.com/relativity/s3.htm>

    -   "Curved spacetime"

    -   See the zero motion, constant motion, acceleration scenarios for
        path of a light beam in the elevator

-   Nice video
    <http://www.phy.syr.edu/courses/modules/LIGHTCONE/equivalence.html>

**Black hole structure**

Conic sections for orbits...

-   Circular...

    -   Uniform circular... balance centripetal and gravitational force

Event horizon

-   Classical (wrong) l set escape velocity to c

    -   The right answer, the wrong calculation...

Gravity: Newtonian vs. Einsteinian

-   Newtonian: 1/r^2^ force at a distance

-   Einsteinian: accelerations away from the "free fall"

    -   Geodesics & kinematics

        -   Accelerometer: Candle in a glass

Black hole formation

-   Nice "kinematic" diagram:
    <http://www.astro.ucla.edu/~wright/bh-st.html>

Nice little visuals

-   <http://casa.colorado.edu/~ajsh/>

-   <http://casa.colorado.edu/~ajsh/kitp06/>

Diagrams

-   Penrose Diagrams

-   Space-time Diagrams:

```{=html}
<!-- -->
```
-   <http://dnausers.d-n-a.net/dnetGOjg/Black/holem.htm>

-   <http://www.upscale.utoronto.ca/PVB/Key/relgen.htm#TOP>

-   
    <http://www.phy.syr.edu/courses/modules/LIGHTCONE/schwarzschild.html>

-   Kinematics: <http://www.astro.ucla.edu/~wright/st_diags.htm>

-   <http://nrumiano.free.fr/Estars/int_bh.html>

-   <http://casa.colorado.edu/~ajsh/schwp.html>

**Notes & Background**

Intro astronomy notes

-   Nick Strobel's notes: <http://www.astronomynotes.com/>

-   <http://www.astronomy.ohio-state.edu/~pogge/TeachRes/Artwork/All162/index.html>

GR Tutorial: <http://math.ucr.edu/home/baez/gr/>

Relativity: <http://www.astro.ucla.edu/~wright/relatvty.htm>

Lectures & Tutorials

-   <http://heseweb.nrl.navy.mil/gamma/~dermer/Book/index.htm>

-   High School

    -   Tutorial website <http://www.physicsclassroom.com/Default2.html>

**Hyperphysics, an ontology or Encyclopedia**:

<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relcon.html>

> Grav detection of light:
> <http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/grel.html#c4>
>
> Trajectory ideas:
> <http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tracon>
>
> Motion: <http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#motcon>

Physics Resources

-   <http://jersey.uoregon.edu/vlab/>

-   Hypertext book <http://zebu.uoregon.edu/text.html>

-   <http://www.astrosociety.org/education/resources/educsites02.html>

-   Aside: Physics Virtual Bookshelf

> <http://www.upscale.utoronto.ca/PVB/PVB.html>
>
> <http://www.upscale.utoronto.ca/>
>
> Nice GR side: <http://www.upscale.utoronto.ca/PVB/Key/relgen.htm#TOP>

Gas kinematics: specify the motion of gas falling into a black hole.
What forces does the gas feel? Where does the energy go? Where does the
angular momentum go? If the orbital kinetic energy goes into thermal
energy, how hot does the gas get?

Clip art

A ruler:
<http://school.discoveryeducation.com/clipart/clip/inchworm.html>