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?


Wednesday, June 8, 2016

local field equations and nonlocal components

the Poisson-equation of electrostatics (or Newtonian gravity) links the second derivatives of the potential $\Phi$ to the local charge (or matter) density $\rho$, by requiring $\Delta\Phi=4\pi(G)\rho$. this is nice, because $\Delta\Phi$ is the trace of the Hessian $\partial_i\partial_j\Phi$, making it invariant under rotations and therefore generates a spherically symmetric potential. but what fixes the off-diagonal components? would there be a possibility to measure them directly?

Wednesday, June 1, 2016

homogeneity of random fields

can you give an argument why the covariance $\langle\delta(k)\delta(k^\prime)^*\rangle$ of a homogeneous random field $\delta(x)$ does not change if one introduces a shift in the coordinates $x\rightarrow x+y$?