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Does cosmic inflation create potential energy?

Inflation does not quite work that way. The objects are not pinned to a point in space, so as space expands, they just move to maintain their relative potential energy. That being said, in Lagrangian ...
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Is it possible to derive the Weyl tensor from the Ricci tensor or Ricci scalar? If so, how?

To add up to the above answer, even though the Weyl tensor contribution to the Riemann curvature tensor is naturally an independent degree of freedom from the Ricci tensor, it cannot be fully ...
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Is it possible to derive the Weyl tensor from the Ricci tensor or Ricci scalar? If so, how?

No. The Weyl tensor and the Ricci tensor correspond to different "degrees of freedom" of the Riemann tensor. As an example, notice that there are many Ricci-flat solutions to the Einstein ...
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Would obliquity and precessional changes of Earth affect the accuracy of GPS-based measurement of tectonic movements?

I can't give you any precise answer, but the GPS takes some of such changes into account. Have a look at the IS-GPS-200 document, page 181 (30.3.3.5.1.1 User Algorithm for Application of the EOP). ...
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Free falling bodies in the absence of external forces

You are right that gravity pulls harder in the heavy object. You are forgetting that the heavy object is also harder to move. These two effects happen to perfectly balance each other out. An object ...
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Free falling bodies in the absence of external forces

Neglecting any kind of resistance, and assuming the height from which balls are released is not very large (the height must be very small as compared to the radius of earth), THEN the answer is simple!...
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Free falling bodies in the absence of external forces

If the balls were dropped in a vacuum, both balls would experience the same acceleration, which if near the surface of the earth would be $g$. From Newton's 2nd law $a=F/m$. Since the force of gravity ...
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Free falling bodies in the absence of external forces

Newton’s second law applied to each of the two masses yield the same acceleration $g$, them acceleration of free fall because even though the larger mass has the gravitational attractive force on it ...
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Free falling bodies in the absence of external forces

$\vec F = m\vec a$ where $\vec F $ is the applied force, $m$ the mass, and $\vec a$ the acceleration. For gravity close to the earth $\vec F = m\vec g$ where $\vec g$ is constant. So $m\vec g = m\...
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2 votes

Doubt about General relativity

You can have curvature without having a non-zero energy momentum tensor, indeed. In fact, these are special solutions to Einstein Equations, called the Vacuum solutions, where you set $T_{\mu \nu}=0$.
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Why are fields described as force divided by mass or charge?

Let me start by eliminating a possible misunderstanding. You wrote ...application of force on a body from a distance, like gravitational or electrostatic force is a two-step process, first, the field ...
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Why are fields described as force divided by mass or charge?

Why are fields described as force divided by mass or charge? Because they follow from the classical universal law of gravitation and Coulomb's law. The force that each of two masses or charges ...
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1 vote

Why are fields described as force divided by mass or charge?

The definition of field, is there to tell us about the effects of the field on an object of unity value. most force fields have the parameter of the object they effect as a multiplier, hence when you ...
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Why is it said that gravity is weaker at the equator due to centrifugal force?

The answer by @Miyase is correct. A simple discussion of the effect of being fixed in a non-inertial (rotating) frame follows. Hope this helps. Your "weight" is the force you exert on the ...
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2 votes

Why is it said that gravity is weaker at the equator due to centrifugal force?

There are two things that could give meaning to your question. First, there's the phenomena mentioned in rhomaios's answer: Earth's radius is slightly higher at the equator, so objects at the surface ...
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1 vote

Why is it said that gravity is weaker at the equator due to centrifugal force?

I have never seen anyone claim that gravity is weaker due to the centrifugal force. Gravity is (extremely slightly) weaker at the equator because the earth is not a perfect sphere, hence the distance ...
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Does solving Einstein's field equation depend on Newtonian equations?

I recently heard, that there is a derivation of the field equations not using the Newtonian limit. The one I know of uses it though. We get $g_{00}=1-\frac{2\Phi}{c^2}$ out of the Newtonian limit of ...
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12 votes
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Does solving Einstein's field equation depend on Newtonian equations?

When Einstein derived his equations the Newtonian limit (and it may be taken also in the present of sources) was an important check for the theory. It is also useful to understand the limits of the ...
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1 vote

For the Schwarzschild metric, are the values of the Ricci tensor and Ricci scalars always zero?

Yes, but only if you ignore dark energy. Considering dark energy, the field equations are given by: \begin{equation} R_{\mu\nu}-\frac{R}{2}g_{\mu\nu}+\Lambda g_{\mu\nu} =\kappa T_{\mu\nu}. \tag{1}\...
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2 votes

Does solving Einstein's field equation depend on Newtonian equations?

If, in some limit, GR didn't reduce down to $\kappa \nabla ^{2}\phi = \rho$ for some constant kappa, (where $\phi$ is a gravitational potential such that ${\vec g} = {\vec \nabla}\phi$), then it ...
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5 votes

For the Schwarzschild metric, are the values of the Ricci tensor and Ricci scalars always zero?

Yes. It follows straight from the $$ R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} = 8\pi T_{\mu\nu}$$ If there's no matter sources (spacetime outside the event horizon), $T_{\mu\nu}=0$. We're left with: $$ R_{\...
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2 votes

Gravity = Yang-Mills squared? What is the Lagrangian?

The statement $$ \text{(super) gravity} = [\text{(super) Yang-Mills]}^2 $$ is the punch line of the Bern-Carrasco-Johansson (BCJ) colour-kinematic duality conjecture that the perturbative on-shell ...
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How come gas molecules don't settle down?

"Ideal gas" If we consider an ideal gas, the molecules of which do not collide, then each of them behaves as a tennis ball, studied it Physics 101: it falls to the ground and bounces back, ...
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Required cushion/foam width to meet reduced force level in event of impact

Certainly experiments can be done; here are the objectives. The objective of a helmet is twofold: 1) to prevent skull fracture and penetration in the event of a point impact, and 2) to dissipate the ...
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1 vote

A new video about the "Real Cause of Gravity" that claims all other videos are wrong

It is a good video in my opinion because it tries to separate relativity from gravity. As it notes somewhere, the Newton-Cartan approach uses the machinery of differential geometry (spacetime ...
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4 votes

A new video about the "Real Cause of Gravity" that claims all other videos are wrong

I wouldn't say that "time dilation is the cause of gravity", but it's certainly related to gravity and I can see why a pop-sci description of gravity might come out like that. But really ...
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1 vote

A new video about the "Real Cause of Gravity" that claims all other videos are wrong

Disclaimer: I'm not a GR expert, but I know enough about the topic to answer. Well certainly, it wasn't derived like so. In other words, Einstein didn't think (at least in the beginning) like this, ...
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2 votes

When does a collapsing star become a black hole?

The temperature of Hawking radiation goes like $T\sim 1/M$: more massive black holes have lower temperatures. For a given spherically-symmetric mass distribution, the pressure at the origin diverges ...
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1 vote

Can gravity exist without time?

In general most notions of gravity depend on energy, and energy is the conserved current generated by invariance of translations in time. Moreover, I don't think there's any physically realistic ...
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3 votes

Can gravity exist without time?

It depends what you mean by 'exist without time', and also whether we're talking about our Universe or a different hypothetical one. I've given two possible answers below, but you can clarify which ...
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-1 votes

Measuring the speed of light with a black hole

Speculation: It is an idea for measuring the one way speed of light, that is deemed impossible, if you search the site. Let me try to see whether it can be done by observation of black holes as the ...
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Initial velocity of a body when the distance travelled by it in the last second before reaching its maximum height is $5\ \textrm{m}$

We know $$S=ut+\frac{1}{2}at^2$$ Substitute $S=h$, $t=t_{f}$ $$h=ut_{f}+\frac{1}{2}at_{f}^2$$ Use the quadratic formula, to solve for t setting the discriminant to be zero, since because this is the ...
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1 vote
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Initial velocity of a body when the distance travelled by it in the last second before reaching its maximum height is $5\ \textrm{m}$

The question has either an infinite number of answers, or no answer. It's convenient to follow the motion for the one second AFTER the ball reaches the peak of its trajectory. (Or run time backwards ...
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Initial velocity of a body when the distance travelled by it in the last second before reaching its maximum height is $5\ \textrm{m}$

Assume that the velocity of the body right before the last second starts is V. It decreases to zero in 1s with an acceleration of g, about $10m/s^2$. So, V must be 10 m/s. Alo, the time to drop from ...
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Initial velocity of a body when the distance travelled by it in the last second before reaching its maximum height is $5\ \textrm{m}$

Supposing the ball is thrown up vertically (otherwise the answer is undefined because the problem has not been given enought parameters): Acceleration along $z$ is $a=-g=\ddot z$ where $g\approx 9.806$...
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Time dilation in quantum gravity

Ignoring considerations for a viable theory of quantum gravity for now, QFT in curved spacetime has a very dubious definition of what a particle is. As per the Unruh effect, an observer under the ...
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13 votes
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Schwarzschild metric in terms of a falling observer's coordinates

Habouz asked: "What's the Schwarzschild metric in terms of a falling observer's coordinates?" The transformation rule can be found here and here: $${\rm dt = d\tau+dr \ v} / \hat g_{\rm tt} ...
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2 votes

What exactly does Einstein's gravitational constant $8\pi G/c^4$ mean?

If you write Einstein field equation as $$T_{\mu\nu}=R_{\mu\nu}\cdot \kappa^{-1}, $$ you can interpret $\kappa^{-1}$ in terms of maximal possible force in the nature, see https://physics.stackexchange....
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What exactly does Einstein's gravitational constant $8\pi G/c^4$ mean?

Dale's answer ("just a conversion factor between stress-energy and curvature in SI units") is correct for the numerics, but I beg to disagree on a dimensional level. When constants like $c$, ...
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3 votes

What exactly does Einstein's gravitational constant $8\pi G/c^4$ mean?

It is just a conversion factor between stress-energy and curvature in SI units. Usually when doing General Relativity we prefer to use natural units where it is equal to 1. SI units are just not very ...
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How can gravity change the wavelength of a photon without the two peaks or troughs to accelerate one from the other?

Gravity field is an area where optical density of space is higher than that of empty space. Gravity field is an area where refractive index of space is higher than one. So here is a video about light ...
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-1 votes

How can gravity change the wavelength of a photon without the two peaks or troughs to accelerate one from the other?

How can gravity change the wavelength of a photon without the two peaks or troughs to accelerate one from the other? There is a basic misunderstanding here. It is classical electromagnetic radiation ...
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How can gravity change the wavelength of a photon without the two peaks or troughs to accelerate one from the other?

How can gravity change the wavelength of a photon without the two peaks or troughs to accelerate one from the other? So is it possible that gravity accelerates light? Yes. In general relativity the ...
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2 votes
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Do black holes exert infinite forces?

There are important points necessary to answer the question: black holes do not have infinite mass; black holes are not well described by Newtonian gravity (unless at a really large distance). The ...
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1 vote

Apparent speed of an object in a circular orbit in Schwarzschild geometry

Yes, an orbiting object is the prototypical clock. Like any clock it is subject to gravitational time dilation.
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3 votes

Would a person split in half if entering a portal to a "mirrored world"?

The force of gravity on one's own body weight pulling in opposite directions is not nearly enough to split someone in half. Note that this is basically what happens when you grab a pull-up bar and ...
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1 vote

How does string theory relate superposition and general relativity?

Unlike what you may hear in many places, we have a perfectly good theory of quantum gravity: you just treat general relativity as a quantum field theory! Now, it's true that the result is non-...
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AdS-CFT correspondance from 1D to 4D

A $d$-dimensional conformal field theory with the right properties is `holographic', meaning that it's dual to a $(d+1)$-dimensional gravitational theory in AdS. But that $(d+1)$-dimensional theory ...
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1 vote

How exactly did Einstein check if his equation on general relativity was correct?

Various experiments can be done to prove einsteins theory correct. Einstein theory predicts the bending of light due to gravity. He took photos of a constellation of stars at night , when the sun is ...
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4 votes

Do Two IDENTICAL Bodies Cancel-out Each-other's Gravity?

"Do two identical bodies cancel out each other's gravity?" In general, no. According to Newton's law of universal gravitation the two bodies will attract each other with a force that is ...
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