/sci/ - Science & Math

[Anonymous No.5010494]

experimental physics 1 homework:
1 (5 credits). calculate the frequency of a pendulum
2 (7 credits). calculate the acceleration of a yoyo
3 (5 credits). how many times does a wheel spin during deceletation
4 (50 credits). - calculate the pertubation of the riemann spacetime metric of a rotating charged black hole ... quadrupol gravitational waves... binary pulsar system ...
- by this calculate quantum fluctuation amplitude .... chromodynamic quarkoszillation in gluon field

professor is a cool guy

[Anonymous No.5010507]

*oscillation

[Anonymous No.5010508]

Question 4 is a trick question: the spacetime metric of a rotaing charged black hole is the Kerr-Newman metric, which is obviously Lorentzian and not Riemannian.

[Anonymous No.5010514]

>>5010508
what is the difference between lorentzian and riemannian metrics?

[Anonymous No.5010532]

>>5010514
A Riemannian metric is positive-definite, i.e., g (v,v) >0 for v a non-zero vector. In other words, all its eigenvalues are positive. On the other hand, a Lorentzian metric has one negative eigenvalue and three positive ones (although some people insist on using the converse). Prime example is the Minkowski metric, given by g = diag (-1, +1, +1, +1).

[Anonymous No.5010534]

>>5010514
Riemannian has signature + + + +
lorentzian has signature - + + + or + - - -

[Anonymous No.5010557]

so do you usually use lorentz in GR or are riemannian metric used also?

[Anonymous No.5010560]

>>5010557
lorentz, but in some cases you can use riemannian with the time variable replaced by a imaginary time variable.

[Anonymous No.5010564]

>>5010557
Lorentz, since you want GR to generalize SR, which requires your metric to be the Minkowski metric. In Condensed Matter one usually employs Wick-rotations to work with Euclidean spacetime rather than Minkowskian, although I've seen it being used in some supersymmetric field theories as well. I'm sure there's some GR theories where people make use of this trick too.

[Anonymous No.5010568]

why is it so important that the black hole is charged? does this make any difference?

[Anonymous No.5010573]

>>5010568
It does. It gives you an extra term in your metric.

[Anonymous No.5010577]

>>5010573
how come?

[Anonymous No.5010589]

>>5010577
the energy in the electromagnetic field around the black hole also causes gravity.

[Anonymous No.5010594]

>>5010577
Not entirely sure. I believe it's because you add an electromagnetic term to the Einstein equation on the RHS in the energy-momentum tensor, then find these metrics as solution, which reduce to other known solutions when taking the limit where the electromagnetic term vanishes. Apparently, space curves differently in the presence of charged black holes vs uncharged black holes.

Dunno if that answer is helpful or requires too much technical knowledge.

[Anonymous No.5010597]

>>5010594
Yeah I know the basics up to Einsteins field equations so I know what you mean by energy momentum tensor.

[Anonymous No.5010639]

>>5010494
>1 (5 credits). calculate the frequency of a pendulum
<span class="math">\sqrt{\frac{l}{2g}}* \int_0^{\theta _0} \frac{1}{\sqrt{ \cos \theta - \cos \theta_0 }} [/spoiler]

[Anonymous No.5010658]

>quarkoszillation

[Anonymous No.5010663]

>>5010658
*quark oscillation

[Anonymous No.5010687]

> experimental physics

> calculation exercises

your school sucks.

>>5010508

So? Just do analytic continuation of the GR functions into complex values and preform Wick rotation. Totally impractical for calculating anything I can think of in this case, but certainly not impossible.

[Anonymous No.5010730]

>>5010687
what is wrong with that?
thats from a german school so I don't know about the us, but we do dumb calculations in exphys and in theoretical physics we would derive lagrangian and hamiltonian mechanics.