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2d
comment Green function integration problem
Do the integral in spherical coordinates then do a coordinate transformation to Cartesian coordinates.
2d
comment On which basis we think there is something more than just super dense matter in black holes?
Peter should also be aware the Schwarzschild coordinate $r$ does not actually correspond to "distance from the center." The distance between two values of $r$ is determined by an integral over the line element.
Nov
25
comment Gravity at event horizon
Except the quantity you've defined as "g" is not particularly meaningful. It does not correspond to any type of measurable acceleration. The proper acceleration required to hover near the event horizon asymptotically approaches infinity as $r \to 2GM/c^2$.
Nov
24
comment Time derivative of Magnetic Field as Source for Electric Field
It's not exactly clear what you're trying to do. Could you elaborate on the actual problem you're trying to solve?
Nov
24
comment Gravitational Time Dilation Formula?
@Hypnosifl Indeed. I'll edit my post accordingly.
Nov
24
comment What does this depiction of a black hole in the movie Interstellar mean?
I remember reading somewhere that Chris Nolan decided to cut out Doppler effects, and he also had them drop the angular momentum well below what would be required for the extreme time dilation the crew experiences. He apparently thought that these would confuse the audience too much.
Nov
24
comment Movie Interstellar - Question about Escape Velocity
@ChristianRau I replied to the post :).
Nov
23
comment Deriving a Useful Solution of the Schrödinger Equation
@Ruslan "Schrodinger" is a common spelling, whether originally correct or not, and is listed as one of the spellings on Erwin's wiki page.
Nov
23
comment Can we explain Newton's first law mathematically?
You might be interested in the answers here: physics.stackexchange.com/q/66057
Nov
22
comment Is there an equivalent force to magnetism for gravity?
Yes. The effect is called "frame dragging." It is an effect that appears in general relativity. Note that Brandon's link is the weak field limit of GR, where the gravitational field is weak and everything is moving slowly compared to light.
Nov
22
comment Confused about equations for the Big Bang in general relativity ad loop quantum gravity?
@21joanna12 $H^2 \to \infty$ means that space is either expanding or contracting at an infinite rate.
Nov
21
comment Derivation of the Riemann tensor confusion
Indeed. As ACuriousMind mentioned, this is the whole point of defining the covariant derivative: so that things remain covariant. I.e. tensors go to tensors under the operation.
Nov
21
comment Derivation of the Riemann tensor confusion
$\lambda_{a;b}$ is a rank-2 tensor. If you take its covariant derivative you'll get two connection terms by definition of the covariant derivative.
Nov
20
comment Why is the value of the action integral in general relativity the same on all regions that are homologous?
He's just using the residue theorem: en.wikipedia.org/wiki/Residue_theorem
Nov
20
comment “Falling upward” - how far you have to be from Earth to start falling to the Moon?
To add to what the others are saying, ~300,000 km is about 85%, or 17/20, of the distance from Earth to the Moon. Just to put that big number into perspective :).
Nov
20
comment Root of $i$, which one to take?
@Jiang-minZhang He means that, by convention, the $\sqrt{}$ symbol means only the positive root. Even though there is a positive and negative solution to $z^2=i$, just as there is with $z^2=n$, by definition we take $\sqrt{i}$ to mean the positive root, just like $\sqrt{n}$ is the positive root.
Nov
20
comment Abstract concept of wave propagating on a string
You've actually come very close to recognizing the Heisenberg uncertainty principle. If a wave packet is very localized (i.e. near definite position) then properties like frequency and wavelength don't make much sense. In the reverse case, when the wave packet is very spread out over space, the wave will have a well-defined wavelength but undefined position. In quantum mechanics the momentum of a particle is inversely proportional to its wavelength, which is only defined if the packet is spread out over space. (I.e. the more you know about momentum, the less you know about position.)
Nov
20
comment Energy of a charge inside spherical conducting shell
The potential energy while it's inside the sphere is $qV_0$. At infinity the potential vanishes. By conservation of energy the work done in bringing the charge to infinity must be $W=qV_0$. (Otherwise where did the energy go?)
Nov
20
comment Problem in deducing the equations of motion using indefinite integral
As for the first part of your question, $f = \int df$ for the same reason that $x = \int dx$.
Nov
20
comment Why we don't integrate intital velocity in body cast equation?
$\int V_0 sin(\alpha) dt = V_0 sin(\alpha) t$