Wednesday, July 29, 2015

CQW holiday project: gravitational field of a cube

show that the lowest two non-vanishing multipole components of the gravitational field of a cubical planet are the monopole and the octupole. what's the next-lowest non-vanishing multipole?

(a solution without a multipole expansion and the added bonus question on the shape of the surface of a lake on such a planet is discussed in http://arxiv.org/pdf/1206.3857v1.pdf)

with that, we wish all readers of CQW a nice summer vacation and hope to see you again in october. if you came across an interesting question that would fit our blog, you're invited to appear as a guest author: please contact us for that purpose under cosmologyquestionoftheweek"[AT]"gmail"[DOT]"com.

Wednesday, July 22, 2015

temperature measurement

imagine a device which is able to measure the thermal radiation power $S(\nu)$ at a given frequency $\nu$. would it be possible to determine unambiguously the temperature of a blackbody by carrying out measurements at two frequencies $\nu_1$ and $\nu_2$?

Wednesday, July 15, 2015

wrong sign in the induction equation

imagine that the induction equation would read $\mathrm{rot}E = +\partial_{ct}B$ instead of $\mathrm{rot}E = -\partial_{ct}E$. can you think of as many consequences as possible this would have?

Wednesday, July 8, 2015

magnetic charges and energy conservation

imagine to extend Maxwell electrodynamics with a magnetic charge density $\rho_m$. would the resulting set of equations still obey energy-momentum conservation? what changes would this yield in the Poynting-law?

Wednesday, July 1, 2015

too many Maxwell equations?

why are there 2 scalar and 2 vectorial Maxwell equations in electrodynamics, which provide 8 relations in total for only two vector fields, i.e. 6 field components? is the system of equations overdetermined?

Wednesday, June 24, 2015

critical density in stationary universes

imagine that the scale factor does not change, because we're at the point of maximum extend of a recollapsing universe. would it be possible to define a critical density?

Wednesday, June 17, 2015

conservation laws in relativity

why can you formulate energy-momentum conservation in general relativity in a differential form but not in all cases in integral form?