imagine that one measures the 40 components of the Christoffel-symbol by observing geodesic motion: in what way are the 20 components of curvature fixed? and how does that determine the 10 components of the metric?

# 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, March 22, 2017

## Wednesday, March 15, 2017

### intuition from the geodesic equation

what would be your argument why the Christoffel-symbol $\Gamma^\rho_{\mu\nu}$ needs to be symmetric in the lower two indices $\mu$ and $\nu$?

## Wednesday, March 8, 2017

### Lorentz force and acceleration

please explain why the 6 entries of the Maxwell field tensor $F_{\mu\nu}$ determine 4 components of 4-acceleration, and how it is possible to infer all 6 entries from experimenting with a charge.

## Wednesday, March 1, 2017

### Christoffel-symbols and geodesic motion

why does one need 40 entries of the Christoffel symbol to determine the 4 components of 4-acceleration? can one, from observation of geodesic motion, infer all 40 components?

## Wednesday, February 22, 2017

### charge asymmetry, part 2

if the charge of electrons was not the exact opposite of the charge of protons, the rings of Saturn would act as a current loop, resulting in a magnetic field. could you estimate the magnitude of the magnetic field (in terms of its dipole moment)?

## Wednesday, February 15, 2017

### gravitational field of the hot sun

could you estimate by how much the gravitational field of the sun is larger because of the high internal energy compared to simply the rest mass? can one write down a correction factor as a function of temperature $T$?

## Wednesday, February 8, 2017

### spin-down of the Crab-pulsar

the Crab-pulsar is a rapidly spinning magnetic neutron star, which induces very large electric fields in the surrounding Crab-nebula, where the resulting electric currents are dissipated by Ohm losses. could you estimate the time-scale of this process and judge if it's a viable model for explaining the spin-down?

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