Wednesday, October 19, 2016

electricity and gravity

why is there a cosmological constant (even) in the classical Poisson-equation, $\Delta\Phi = 4\pi G\rho + \lambda$, but no such term in the wave-equation of electrodynamics, $\Box A^\mu = 4\pi\jmath^\mu$?

Wednesday, October 12, 2016

$CPT$ and relativity

with earlier CQWs and the idea that in relativity there's no fundamental difference between space and time coordinates (apart from the signature of the metric), could you formulate a combined $PT$-invariance of the field equation, where $\vec{x}\rightarrow-\vec{x}$ and $t\rightarrow-t$? what's the relation to charges of the gravitational field (i.e. masses) and a combined $CPT$-symmetry?

Wednesday, October 5, 2016

solutions to general relativity

is it possible to find a solution to Einstein's field equation for an arbitrary distribution of matter? in what way is the problem different from electrodynamics?

Wednesday, July 27, 2016

CQW holiday project: Oort's cloud

the solar system is encapsulated in Oorts cloud, a vast cloud of small rocks beyond the orbit of Pluto. can you set up a model for the obscuration of the Sun from this cloud? by how much would the optical magnitude of the Sun decrease?

with that, we wish all our readers a nice summer vacation and hope to see you again in october. if you happen to have an interesting question, please contact us under cosmologyquestionoftheweek"[AT]"gmail"[DOT]"com.

Wednesday, July 20, 2016

gravity from a variational principle

in classical mechanics and electrodynamics one obtains a second-order equation of motion from squares of the first derivatives, either of the position with time or of the derivatives of the potentials. gravity seems to be different: the Ricci-scalar in the Einstein-Hilbert action contains already second derivatives: can you explain this difference?

Wednesday, July 13, 2016

parity of gravitational fields

can you show parity invariance of Einstein's field equation, i.e. the invariance of the equation if $\vec{x}\rightarrow-\vec{x}$? can you think of possible implications for solutions?

Wednesday, July 6, 2016

time reversal in Einstein's field equation

can you show that Einstein's field equation is time-reversible? from that, can you say something about the existence of advanced potentials in gravity?