Chronology | Current Month | Current Thread | Current Date |
[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
At 06:22 AM 10/12/00 -0400, David Bowman wrote:
This gravitational radiation formula for the radiant power P is:
P = (1/5)*(G/c^5)* tr(d^3q_i_j/dt^3) [1]
1a) That doesn't pass the dimensional-analysis test.
1b) It doesn't express the following "product" operation:
2) I think you need to take the time derivatives before taking that product.
Here d^3q_i_j/dt^3 is the third time derivative of the traceless mass
quadrupole tensor q_i_j.
3) Uhhh, if it's traceless, why are we taking its trace in equation [1]?
How about this:
P = (1/5) (G/c^5) average([ (d/dt)^3 Itick ]^2) [2]
where Itick would be typeset as an I with an overstrike tick-mark, and
represents the "reduced quadrupole moment":
Itick_j_k := I_j_k - (1/3) delta_j_k trace(I)
and where I is just the ordinary second moment of the mass
distribution. Reference: Misner, Thorne, Wheeler equations 36.1 and 36.3.
The constants G and c are Newton's gravitational constant and the speed
limit of causation respectively.
Speed limit of causation. I like that. I wonder if it will catch on.