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.

# cosmology question of the week

CQW is an educational resource for theoretical physics and astrophysics, field theory, relativity and cosmology. we post a new question every wednesday for students to get and for teachers to stay in shape.

## Wednesday, July 29, 2015

## 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?

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