AstoundingJB
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Ok, I think there is a mistake here: A general tensor $\varphi^i$ transforms as: $$\varphi^i\rightarrow U^i_{\phantom{1}j}\varphi^j$$ whereas $\varphi_i$ transforms as: $$\varphi_i\rightarrow (U^... View answer Accepted answer 3 votes In vacuum, that is, in absence of matter and electromagnetic interactions, photons and gravity waves follow the same geodesics (if gravitons are actually massless... Let us assume it for we have no ... View answer Accepted answer 2 votes The equation you wrote is a Poisson-like equation. To put it in a - hopefully - more familiar way, let's rewrite it as:$$ \nabla^2 \phi = \left( \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\...

All the previous answers are correct. Let me add just some mathematics. Take a look at the equation for Fermi normal coordinates, for example in the original article by Misner and Manasse [1] or here. ...

An electric field is said to be static if it does not change with time, i.e. the the charges that produced that field are stationary. This doesn't imply any constriction on its spatial dependence. In ...

This is a 1 million dollar question! When I studied Celestial Mechanics, I learnt that celestial bodies taken together mainly by gravitational forces must be spheroidal or, at most, ellipsoidal, if ...

As a matter of fact, the space is almost empty; usually the problem with observing a far star are not the gas clouds between us and that star, but any possible brighter source of light in the ...

All you need for solve this problem is the equation for an uniformly accelerated motion: $$x(t)=\frac{1}{2}at^2+v_0\cdot t+x_0$$ where the motion takes place on a straight line if the acceleration and ...

As Bubble said, the ship in your experiment can't travel at the speed of light. More precisely, the ship could travel at the speed of light if it would be massless. But in that circumstance the ship ...

According to our current scientific knowledge we know that we don't know what the 70% of the energy of the Universe is. Also, a comprehensive description of the thermodynamics of the Universe is ...

The angular momentum of a massive sun may cause the freely falling spaceship to start spinning in the direction of the sun's angular momentum for an effect of frame dragging. You can take a look at ...

I believe the milestone about the introduction of Yang-Mills theory from gauge invariance is the 1973 article by Ernest Abers and Benjamin Lee. You can easily find the original article on the web ...

Since the turbulence acts like an upward vertical acceleration, the bolt will experiment an additional force of $2.6\times m$ N downward. That is, the engine wants to move, by inertia, in a linear ...

You have to do some work on the object to keep it moving at a constant speed! Friction against the floor would stop it dissipating its kinetic energy as heat. You need to push the object applying to ...

I think that this problem doesn't have an exact answer. Some time ago, I talked about this with the astrophysicist Paolicchi (this is the asteroid named after him) who works on the field. The ...

Well, this is an easy problem in kinematics. "The rule" for solving it is drawing a graphic of the (differences of) time versus the speed. You will get some points. Join these points to obtain a ...

Well, in brief, the Passive gravitational mass $m_P$, as named by H. Bondi in the 1957 (see C.Will, Theory and experiments in gravitational Physics), is the one that enters the definition of ...
In fact, it is not always true that, say, horizontal and vertical components, or $x$ and $y$ components, are independent! Consider for example a skater riding a half-pipe! But it is certainly true in ...