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Is rotation invariant under gravitational time dilation?

is vertical rotation an invariant in general relativity or not? The answer is no. First let us consider a small flywheel. If you were to place this flywheel in an elevator and descend with it, into a ...
KDP's user avatar
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Definition and mathematical description of comoving reference frame and locally inertial frame

A will choose a "moving coordiante",which is a series of coordinate system,and not "a" coordinate system in which the metric tensor can be written as η. This is not correct. Time ...
Dale's user avatar
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Photonic black holes

The existing answers don't mention a crucial fact, which is that the $M$ in the Schwarzschild metric is an invariant parameter, whereas a photon's energy is frame dependent. So a single, free photon ...
Eric Smith's user avatar
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-1 votes

What is the gravitational field of a hole in an infinite perfect crystal?

This can be used for reactionless propulsion. Am I missing something or have I discovered (effective) antigravity? You are forgetting the role of the mind in all of this, which, a unified field ...
Victor Bergman's user avatar
1 vote

A question about Quantum entanglement, 45° Light Polarization, and faster than light communications

When the photons leave the crystal, their polarization is in superposition. They have no definite polarization. When they hit a polarizer, 50% of them pass through, regardless of any entanglement. ...
Jakob Heitz's user avatar
1 vote

Distance and luminosity distance

Using the inverse square law we can deduce that the flux F(watts/m^2) received from a source with an intrinsic luminosity L(watts) diminishes as a function of distance squared so $F \propto L/D_e^2$ ...
KDP's user avatar
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3 votes

Necessity of Singularity in General Relativity

Well the famous singularity theorems show (very very roughly speaking) that in the theory of classical GR, collapse beyond horizon implies a singularity. Classical GR is not the true theory of physics,...
Joe Schindler's user avatar
6 votes

Can perfectly stable orbits exist in GR?

In the 1979 paper "Time without end", Freeman Dyson calculates a time in the order of 1020 years until the earth would fall into the sun due to gravitational decay alone, based on the ...
HugoRune's user avatar
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9 votes

Can perfectly stable orbits exist in GR?

As you say, GR implies that all orbits lose energy (very slowly) over time, due to gravitational waves. Also the vacuum of space is not true vacuum and there is some drag from the intergalactic medium ...
KDP's user avatar
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1 vote

Necessity of Singularity in General Relativity

What is it that preludes the predicted field, even at $r<r_{Schwarzschild}$, from simply terminating at the surface of a collapsar of dense matter, and taking some other form inside it? This is ...
safesphere's user avatar
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We know there is no aether, so what is being dragged in frame dragging?

Michaelson Morley did not disprove the Aether theory; it just showed a null result. If MM had Ligo as a detector or something more sensitive, how would the result have been interpreted? MM never took ...
Clifton Odenwalt's user avatar
10 votes

Can perfectly stable orbits exist in GR?

In the literature, the orbits you are looking for a called “floating orbits”. Floating orbits are not possible in plain GR (See e.g. 1302.1016).
TimRias's user avatar
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Boundary conditions on transition maps on general relativity

There's nothing fancy going on with transition maps. What a mathematician means by a "transition map", in the setting of general relativity, is nothing more or less than a coordinate change ...
Lee Mosher's user avatar
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How exactly does curved space-time describe the force of gravity?

If we ... use a fictional device to cancel all the inertia of the particle, it is obvious that the curve of space-time is towards the star but what is not obvious is what would make the particle begin ...
KDP's user avatar
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1 vote

Hawking Temperature of the BTZ Black Hole

Another option for finding the Hawking temperature of the BTZ black hole is by the formalism of the surface gravity $\kappa$ which connected to the Hawking temperature via: $$T_H=\frac{\kappa}{2\pi}$$ ...
Daniel Vainshtein's user avatar
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Clarification of Weinberg's cosmology book eqns 5.1.44-5.1.47 for scalar perturbation

$B^S_{ij}$ does have terms on the diagonal. It is just that the trace is zero. Here's an example of a $3x3$ matrix with terms on the diagonal but zero trace $$ \begin{bmatrix} 1 & 0 & 0 \\ ...
Andrew's user avatar
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2 votes
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Two contradictory derivations of Killing equation

As an overall comment, I stress that conservation of $Q$ is valid for the Killing vector $\xi$ if the considered curve is a geodesic. Let us come to the issue. First of all, generally speaking, the ...
Valter Moretti's user avatar
2 votes

Two contradictory derivations of Killing equation

Both approaches are fine. In the first approach, the analysis is done at the coordinate/component level of the equations. Simply asking the question how does $Q$ very with $\tau$ if we write ...
TimRias's user avatar
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1 vote
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Cause of Coordinate Acceleration in Free Fall

The acceleration on a particle following a geodesic is defined by the Christoffel symbols which are in turn defined in terms of the metric. More properly, all inertially-moving objects not affected by ...
controlgroup's user avatar
1 vote

Trying to understand a visualization of contravariant and covariant bases

Given the metric tensor for the basis vectors $$A = \begin{bmatrix}\mathbf e_1 \cdot \mathbf e_1 & \mathbf e_1 \cdot \mathbf e_2 \\ \mathbf e_2 \cdot \mathbf e_1 & \mathbf e_2 \cdot \mathbf ...
Antoni Parellada's user avatar
5 votes

Is the size of a black hole singularity smaller than a fundamental particle?

We know that black hole is infinitely densed. More exactly: The theory of general relativity predicts that the center of a black hole is infinitely dense. This theory predicts very well everything ...
Thomas Fritsch's user avatar
6 votes

Is the size of a black hole singularity smaller than a fundamental particle?

While @paulina's answer: we don't know is correct, because quantum gravity is not understood, I'll answer for a classical Schwarzschild blackhole as described by Kip Thorne. The size is zero, however ...
JEB's user avatar
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7 votes
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Is the size of a black hole singularity smaller than a fundamental particle?

The very short answer to this is: We have no idea. General relativity predicts that the singularity of a Schwarzschild black hole (which I assume is what you mean by "actual black hole") is ...
paulina's user avatar
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1 vote

Two contradictory derivations of Killing equation

I think the problem lies in the notation. I guess Tong is treating the components $\xi_\mu$ as scalars for which we have $\frac{\mathrm{d}}{\mathrm{d}\tau}=u^\alpha\partial_\alpha$. And the ...
Silas's user avatar
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0 votes

Spatial Curvature of Universe at recombination vs now

We do not use CMB data to directly measure the curvature of the universe. Instead, we use CMB data to estimate the average density (as well as the size of density fluctuations) in the early universe. ...
gandalf61's user avatar
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-3 votes

Does black hole formation contradict the Pauli exclusion principle?

In actuality, there is no such thing as this so called singularity... It's a convenient mathematical invention to represent something of which we understand very little. Although quantum physics can ...
dfreshMC's user avatar
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Do you always experience the gravitational influence of other mass as you see them in your frame?

These are excellent questions! They involve the interrelation of various physics concepts. And we would expect physics to be internally consistent, generally speaking. But since your insights are not ...
Colin MacLaurin's user avatar
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As per Friedmann Equations, is big-bang singularity necessary?

In a closed (unlikely, but still possible within the measurement accuracy) dark energy dominated universe where $\Omega_{\rm K}=1-\Omega_{\Lambda}$ (which it was during inflation if there was any, ...
Yukterez's user avatar
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1 vote

What is the gravitational field of a hole in an infinite perfect crystal?

... overdensity attracts underdensity and underdensity repels overdensity ... Yes, in an empty universe a pair of matched positive and negative masses initially at rest would be self-accelerating ...
A.V.S.'s user avatar
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0 votes

Time dilation in a centrifuge: effect of velocity and acceleration?

Stop debating and do the experiment. Put a radioactive substance in an ultracentrifuge and see to what degree the decay rate changes.
jamesraymond's user avatar
2 votes

What is the gravitational field of a hole in an infinite perfect crystal?

The equations that govern gravitational fields and matter simply don't make sense when you apply them to an "infinite" volume of matter. Mathematically, we have $\nabla^2 \phi = 4 \pi G \...
Michael Seifert's user avatar
3 votes

What is the gravitational field of a hole in an infinite perfect crystal?

If you put overdensity next to underdensity, overdensity attracts underdensity and underdensity repels overdensity. They chase each other forever with runaway acceleration. Not true. A volume with ...
gandalf61's user avatar
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3 votes
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Analog between Electromagnetism and Gravity

In electromagnetism, if you have a $$ \mathcal{L} = -\frac{1}{4} F^2 + A_\mu J^\mu $$ where $F^2=F_{\mu\nu}F^{\mu\nu}$ is the Maxwell term ($F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$), the ...
Andrew's user avatar
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3 votes
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Memory effects from black hole migration in the early universe

I can look at the black hole after some time when it has moved away a little bit. Now the region of space that was previously inaccessible to me is accessible. I think your misconception is thinking ...
gandalf61's user avatar
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How does brain perceive time dilation due to gravity?

I believe since the person is on another planet with less gravitational force or medium or slightly less and the time to rotate the sun one complete rotation time varies from planet to planet. So ...
Subramanian G's user avatar
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David Tong, notes on General Relativity, pg. 25

I was puzzled enough to look at what the notes actually say. You have the quote right though. I think he starts from $$ \sqrt{a+x}= {\sqrt a}\sqrt{1+ \frac x a}\\ \approx \sqrt{a}\left(1+ \frac 12 \...
mike stone's user avatar
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2 votes

Cone vs. small circle parallel transport

This is in a way a Riemann-geometric analogue of the Aharonov--Bohm effect in quantum mechanics. Consider a manifold $M$ equipped with a linear connection $\nabla$. It is well-known that the parallel ...
Bence Racskó's user avatar
1 vote

Question on spatiotemporal dimensionality about the contradictions of time being a dimension

There's a lot of misconceptions here. I will try to clear them all up one by one, but first we should review what a dimension is in the mathematical context of analytic geometry. A dimension in this ...
paulina's user avatar
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3 votes

GR and Riemann Surfaces -- does the complex plane have anything to do with it?

This question seems mainly spurred by a conflation of a Riemann surface (which is a 1-dimensional complex manifold), and a (pseudo)Riemannian manifold (which is the underlying geometry of GR).
Qmechanic's user avatar
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What actually is Boyer-Lindquist coordinates?

For me, the main difference between spherical and BL coordinates is related to the Cartesian coordinates which are as follows: spherical coordinates $$ x = r\sin\theta\cos\varphi $$ $$ y = r\sin\...
Cornelius Fyla's user avatar
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Confused about Weinberg's result of gravitational time dilation

I think the confusion comes from my misunderstandings of coordinate time $dt$ and proper time $\Delta t$. Actually the reading on the stationary clock is the proper time. Therefore, to compare two ...
rioiong's user avatar
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2 votes

Is tetrad postualte independent of gauge field?

As @Prahar's comment pointed out: The tetrad $e^{a}_{\nu}$ is invariant under the Yang-Mills gauge transformations, such as the $U(1)$ gauge transformation related to $A_{\mu}$. Therefore the ...
MadMax's user avatar
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1 vote

Viable values for the $K$ parameter in the FLRW metric

$$c^2 d\tau^2 = c^2 dt^2 - \frac{a(t)^2}{(1-KX^2)} dX^2. $$ For this metric expression, if you set $K=1$, then the spatial surfaces are hyperspheres of radius $a$. Every position on these ...
Sten's user avatar
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2 votes

Viable values for the $K$ parameter in the FLRW metric

First, define a new time coordinate $\eta$ through integrating $$ d\eta = \frac{c dt}{a(t)}.$$ This time coordinate is often called conformal time. With this coordinate, the condition for a radial, ...
11zaq's user avatar
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1 vote

Can a light signal from Earth reach a galaxy outside the Hubble Horizon?

Here are some more reasons a light signal from Earth must be able to reach and pass the Hubble Horizon: The total velocity of a photon is given by its peculiar velocity and its recession velocity as ...
KDP's user avatar
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1 vote
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Energy-momentum tensor and equation of motion in Einstein-Dilaton theory

Given an action $$S[\psi]=\int d^4x \mathcal{L}(\psi,\nabla_\mu \psi),$$ how do we find the equations of motion? The principle of stationary action says that the equations of motion can be found by ...
Omar mandour's user avatar
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Cone vs. small circle parallel transport

The path the vector you are describing takes on the cone is a closed circle while the cone is rolled, but it is no longer a closed circle once the cone is sliced and flattened!
mike1994's user avatar
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18 votes
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Does the cosmological constant entail a mass for the graviton?

No, you don't get a mass term in the propagator, and there is no graviton mass for GR with a cosmological constant. If you linearize about Minkowski space, $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}$, then ...
Andrew's user avatar
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1 vote

Confused about Weinberg's result of gravitational time dilation

That the clock rate for a stationary clock deeper in the potential well is slower can easily be established from the Schwarzschild metric with $dr= d\theta = d\phi= 0$ for two clocks at different ...
ProfRob's user avatar
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