Wednesday, July 19, 2017

horizons in relativity

an accelerated object disappears behind a horizon as well as an object at the Schwarzschild radius of a black hole: is there a difference between the two cases? is there an analogous effect in cosmology?

Wednesday, July 12, 2017

tidal shear invariants

the gravitational shear field could be quantified by the trace $\sum_{i}\partial^2_{ii}\Phi$, which is proportional to the density $\rho$ due to Poisson's equation $\Delta\Phi=4\pi G\rho$ or by the quantity $\sum_{ij}\partial^2_{ij}\Phi\partial^2_{ji}\Phi$. in what way do the two quantifiers differ? can you construct more of them? what would be their relation to the Ricci-scalar $R$ or the invariant curvature $R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}$ in general relativity?

Wednesday, July 5, 2017

clocks in acceleration

can you explain how different types of clocks (string pendulum, spring pendulum, quartz oscillator, $LC$-circuit, atomic clock, Einstein-clock) are affected by an accelerated frame of reference? how is symmetry established between acceleration of the clock and acceleration of the observer, and in what way are the situations equivalent to a gravitational field?