Potpourri: Gravity

by Robert NemiroffMichigan Technological University

Physics X: About This Course

• Officially "Extraordinary Concepts in Physics"• Being taught for credit at Michigan Tech

o Light on math, heavy on concepts o Anyone anywhere is welcome

• No textbook requiredo Wikipedia, web links, and lectures onlyo Find all the lectures with Google at:

"Starship Asterisk" then "Physics X"  o http://bb.nightskylive.net/asterisk/viewforum.php?f=39

Birkhoff's Theorem

A very useful theorem that leverages spherical symmetry in General Relativity.  Two common applications: • Outside a spherically symmetric mass distribution (hence not

rotating), the solution is always the Schwarzschild metric. o useful for ignoring stellar pulsations

• Inside a spherically symmetric mass shell, the gravitational "field" will vanish. o useful for ignoring the outside universe

Virial Theorem

A relation between the average total kinetic energy of a system of particles (Ktot) and the average potential energy of the particles (Vtot).  For Newtonian gravity:

2 * Ktot = - Vtot

Useful for determining the amount of dark matter in clusters of galaxies (for example).  Theorem can apply to even one particle.

Gravothermal Catastrophe

The center of a gravitationally bound system of particles will heat up at it gravitationally collapses.  For those particles, the increase in energy comes from a conversion of potential energy to kinetic energy.

However, some other particles will be thrown out from the center and will "cool down".

Runaway: For sufficiently condensed systems of particles acting gravitationally, the center will be unstable to becoming increasingly dense and hot, since that will decrease system entropy.  A single temperature will no longer describe the system.

Gravitomagnetism

• A gravitational force that complements standard gravity like magnetism complements standard electric force.

• Predicted by General Relativity (and even other gravitational theories that predate GR).

• A small effect -- it is being tested by Gravity Probe B, although these results have not yet been announced.  

Gravitomagnetism

• Typically a very small effect.

• If two wheels are spun on a common axis, their mutual gravitational attraction will be (slightly) greater if they spin in opposite directions.

• A ring rotating about its minor axis (a circle inside the ring) will accelerate matter through the ring while that matter feels no acceleration. 

• Earth's gravitomagnetic acceleration at the Equator is about 10-7 g.

• Cannot be used to create a perpetual motion machine.

Frame Dragging

The General Relativity expected effect that rotating objects drag spacetime around with them. • A gravitomagnetic effect.• Also known as the Lens-Thirring Effect• When near a massive rotating object, you may feel that you are not

rotating with respect to the universe, even though you can see that you are.

• Typically a small effect.

Frame Dragging

• FD has never been measured in the laboratoryo very difficult to do

 • Would rotating a bucket create the same effect as rotating the entire

universe? • Might be relevant to jets emitted from active galaxies.

Gravitational Radiation

• Emitted by accelerating masses in GR, in analogy to electromagnetic radiation emitted by accelerating charges.

• Acceleration must be non-spherically symmetric.

• Very weak compared to common photon energies.

• Not yet directly detected on Earth.o Ongoing searches include LIGO

Gravitational Radiation

• Strongly emitted by massive and rapidly changing astronomical objects.o Supernovas (we know)o Gamma ray bursts (we think)

• Steadily emitted by decaying binary star systemso binary pulsar's orbital decay can be attributed to gravitational

radiation to high accuracy

Gravitational Radiation

• moves at the speed of light.

• has wavelength and frequency like light: lambda = c f.

• A passing polarized gravitational wave would have this effect on a ring of particles: