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?

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?

Wednesday, June 29, 2016

degree of symmetry

can you show that Schwarzschild black holes and FLRW-models in cosmology have the same degree of symmetry? what's the corresponding quantity in cosmology to the Schwarzschild radius $r_s=2GM/c^2$?

Wednesday, June 22, 2016

similarity in cosmology

following up on last week's question: imagine a FLRW-model with only one fluid characterised by a density parameter $\Omega$. could you find in a second model with a different $\Omega$ a time with the same expansion rate and acceleration as the first model?

Wednesday, June 15, 2016

similarity in modern physics

can you construct a similarity transform that relates the Schwarzschild-metrics of black holes with different mass to each other? what would be a sensible parameter? would it be possible to formulate an addition theorem for  masses and gravitational fields using that relation, which could replace linear superposition for a nonlinear field theory?