A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

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4
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2answers
182 views

How do we age if we tunneled to Earth's core?

Scenario Suppose there exists an advanced technology that can hypothetically transport living humans to study the center of the Earth, as they goes deeper underground most of the Earth's mass would ...
1
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1answer
88 views

Covariant derivative of Levi-Civita tensor [closed]

I'm currently studying Carroll's GR book Spacetime & Geometry, and ran into some trouble understanding the text at page 99 which says: By using metric compatibility $$(\nabla_{\alpha}g)_{\mu ...
0
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1answer
45 views

Does one *feel* the electrostatic force while not resisting it?

Suppose that I put lots of big magnets around me, or say, that I charge myself up to a macroscopic charge. Now, suppose that there's a huge magnet in front of me (or a huge object with opposite ...
2
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1answer
101 views

Question about universe expansion

In general relativity, we cannot determine the global structure of the universe (since it is not flat), therefore all measurements and observations are only meaningful locally. In particular, we can ...
3
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3answers
159 views

How can space be euclidean when light bends?

I have read people arguing that tridimensional space sections of space time continuum (whatever its number of dimensions) appears to be euclidean from empirical evidence. I cannot reconcile it with my ...
4
votes
1answer
132 views

Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?

The definition of the SI unit "second" is stated as The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground ...
0
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2answers
106 views

why do x Schwarzschild radii equal time dilation effects of speed of light going y times faster than an object^2?

let me walk you through the math. First you start with the gravitational time dilation formula where: $$ T_1=T\sqrt{1-\frac{2GM}{rc^2}} $$ and rather than entering $r$ for the radius we replace $r$ ...
3
votes
1answer
136 views

Regarding the possibility of Closed Timelike Curves

I've been looking a lot at Closed Timelike Curves, and how if a theory allows for these curves it doesn't respect causality. I understand that about the curves themselves (Grandfather Paradox), but ...
0
votes
3answers
66 views

What will be the gravitational pull of the Sun if the Sun contracts to a black hole?

What will be the gravitational pull of the Sun if the Sun contracts to a black hole, and would the Sun be a Schwarzschild black hole or not?
2
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1answer
45 views

Gravity of photons in different reference frames

I know that photons have gravity because they contribute to the stress energy tensor, but this means that observers in different reference frames experience a different gravitational force from the ...
1
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0answers
49 views

Is the Weyl Postulate correct?

The Weyl postulate in cosmology states that worldlines do not intersect but it can be shown in GR that using Raychaudhuri equation that geodesics can intersect if there is curvature so I'm really ...
3
votes
2answers
78 views

Why is $p_\phi$ conserved in a Schwarzschild orbit?

This arises from the question What is the relationship between $a$ and $m$, which I'm afraid I answered just by looking it up in Schutz's book. However Schutz (as he frequently does) glosses over ...
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0answers
41 views

Problem on finding the spatial components of canonical momenta in Fierz-Pauli Lagrangian

My problem is about finding the spatial components of canonical momenta $\pi_{i j}=\frac{\partial \mathcal{L}}{\partial \dot{h}_{i j}}$ corresponding to the Fierz-Pauli Lagrangian. I am using the ...
6
votes
1answer
130 views

Non-trivial scalar quantity

Is there any scalar quantity made of only the Christoffel symbols, determinant of a metric and tensors, not derivatives? In other words, can we construct a scalar quantity which cannot be written in ...
-2
votes
0answers
46 views

Can the Milky Way's halo be considered to be curved spacetime? [duplicate]

Scientists are beginning to understand dark matter fills 'empty' space. Dark matter which fills 'empty' space would be displaced by the matter. The Milky Way's halo would be the state of displacement ...
2
votes
7answers
428 views

Curvature of Spacetime

I have been exploring for some time both the Special and General Relativity, hoping to glean at least a conceptual grasp of their basic tenets. In reading the book "Gravitation" by Misner, Thorne and ...
8
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3answers
1k views

Is gravitational time dilation different from other forms of time dilation?

Is gravitational time dilation caused by gravity, or is it an effect of the inertial force caused by gravity? Is gravitational time dilation fundamentally different from time dilation due to ...
1
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1answer
41 views

Symmetry in gravitational time dilation

In special relativity, when two observers move in respect to each other, each observes the other's clock tick slower. An observer floating in space far from gravitational fields, observes earth clock ...
-1
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1answer
51 views

What is the relationship between $a$ and $m$

$a$ is defined in HERE What is the relationship between the length-scale $a$ and the mass $m$?
3
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0answers
65 views

Maxwell's equation in curved spacetime - how come? And experimental evidence?

I'm trying to understand the generalization of Maxwell's equations to curved spacetime. In FLAT (Minkowski) SPACETIME: If we define the "four-potential" as $$\ ...
0
votes
0answers
21 views

circular orbits in general relativity [duplicate]

I am studying the derivation of the circular orbits of particles in general relativity (Derivation) Question 1: What is the meaning of the constants $a$ and $b$, it says they are " length-scales", ...
1
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1answer
45 views

Problem in one step of deriving Einstein's Field Equation from Caroll's book

I have the proposed solution stated as: $R_{\mu \nu} -\frac{1}{2} g_{\mu\nu}R=\kappa T_{\mu\nu}$ (4.43) Caroll says:"note that contracting both sides of (4.43) yields (in four dimensions)" $R = - ...
0
votes
1answer
58 views

Metric inside a sphere of uniform density?

Is an exact solution to Einstein's Field Equations known for the interior of a sphere of uniform density (to approximate a star or planet, for example?)
15
votes
1answer
493 views

A Theorem Due to Hodge: Hawking/Ellis

This is probably quite an obscure question but hopefully somebody has a simple answer. I'm studying the proof of the topology theorem on black holes due to Hawking and Ellis (Proposition 9.3.2, p. 335 ...
0
votes
1answer
49 views

How do I construct the Maxwell tensor $\bf{^*F}$ from Fadaray one $\bf{F}$ in a non-flat spacetime?

In the book Gravitation (Misner, Throne and Wheeler), it's said that to consider the line element of the flat space on the derivation of Maxwell tensor $\bf{^*F}$ from the Fadaray tensor $\bf{F}$ ...
2
votes
1answer
46 views

Do all “normal” black holes rotate?

Can we assume that most (if not all) black holes are rotating, due to conservation of momentum? I am excluding the micro world from this question, just thinking of the range of stars on the main ...
1
vote
0answers
22 views

Are atomic energies increasing as the Universe expands? [duplicate]

Starting from the FRW metric (for simplicity flat space, radial direction only): $$ds^2=-c^2dt^2+a(t)^2dr^2$$ If we take $dt=0$ then the proper distance $ds(t)$ between two spatially separated ...
0
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0answers
56 views

The Einstein-Cartan equation as the “living heart of gravity”?

I recently read in A Journey into Gravity by Wheeler that "The Einstein-Cartan equation gives us the most vivid image that mankind has ever won of the living heart of gravity" (P.118) ...
0
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0answers
27 views

Seeking a coordinate-free expression of the orbital period for uniform circular motion around a non-rotating point-like mass

Consider a point-like (non-rotating, uncharged) mass $M$ and five separate participants (uncharged and of masses negligible in comparison to $M$) where participants $\mathsf A$, $\mathsf B$, ...
6
votes
4answers
3k views

What experimental proof has been found of Einstein's theory?

As a casual science reader, I've always found the implications of relativity (inconsistent clocks after near-light-speed travel and various space-time paradoxes) to be confusing and magical-sounding. ...
1
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5answers
528 views

Why dark matter and general relativity?

My knowledge on this subject is minimal, so sorry if my question is obvious. But why is the current consensus that there is something called dark matter rather than that our current theory of gravity ...
0
votes
1answer
26 views

Does the readoption of the cosmological constant apply across all models of GR?

I'm currently reading about cosmology, and the reintroduction of the cosmological constant, Lambda, into the field equations, to give a more accurate model for cosmology. My question is this: If it ...
1
vote
1answer
87 views

How can the Schwarzschild radius of the universe be 13.7 billion light years?

So i was reading about Schwarzschild radius on Wiki and I found a interesting thing written there link. It says that the S. radius of the universe is as big as the size of the universe? How is this ...
0
votes
1answer
69 views

Would Special Relativity Predict Time Dilation of a Geostationary Satellite Compared to an Observer on Earth?

Consider a geostationary satellite at some arbitrary distance above the Earth's equator and consider a person directly below it, standing on the Earth's equator. Both satellite and person exist on the ...
0
votes
1answer
56 views

EM Field tensor of a point charge [closed]

If I say the Reissner-Nordstrom metric $$ ds^2=-\left(1-\frac{2m}{r}+\frac{e^2}{r^2}\right)\text d t^2 + \left( 1-\frac{2m}{r}+\frac{e^2}{r^2}\right)^{-1}\text d r^2 + r^2 \text d \Omega^2 $$ is the ...
1
vote
2answers
123 views

Special Relativity - Distance Not Increased?

I just watched the movie Interstellar and the question was asked of why/how high-speed travel would slow time within an area. Curious as I am, I watched several YouTube videos to quickly 'educate' ...
0
votes
1answer
46 views

Reference frame of high speed rocket [duplicate]

Imagine a high speed rocket, traveling past a star. In the rocket's reference frame, the star's length is contracted. This is a lot a mass in a thin line, so it the rocket's reference frame, could it ...
1
vote
1answer
88 views

Eternal black holes and Hawking radiation

I have a fairly simple question which is confusing me a lot. As Hawking showed, a black hole originated by collapse will emit Hawking radiation. This process will reduce the mass of the black hole ...
0
votes
1answer
51 views

How does a wormhole form? [duplicate]

I heard about wormholes. I know that they are paths that can be got by contracting spacetime. But, how does a wormhole form?
0
votes
1answer
23 views

How to calculate angular momentum (J) in the Kerr parameter equation?

The Kerr-parameter is given by the following equation: $a = \frac{J}{Mc}$ How to calculate J? Can we just calculate the cartesian product which simplifies to $J = r * M * v$ ? with $r$ = ...
0
votes
1answer
61 views

Connection between two Petrov classification schemes

For the Weyl scalars of all spacetimes, at any point, possess one special structure, the so called principal null directions. Consider a general null tetrad $\{ l_a,n_a,m_a,\overline{m}_a \}$, we ...
0
votes
0answers
28 views

Gravitational Wave Interference [duplicate]

Can gravitational waves interfere like water waves and light waves? If not, can someone explain what about these waves make them uninterferable?
1
vote
2answers
217 views

Visualizing GR spacetime distortion in 1+1D spacetime instead of 2D space

Usually spacetime distortion due to mass in GR is visualized as a rubber sheet distorted under some massive object, like this: source or as shown in this link. But what has always bothered me is ...
1
vote
0answers
34 views

Why should we want to quantize Gravity? [duplicate]

I understand that it will be "nice" to have a quantum description of Gravity as well, just like the other 3 forces. I would like to find out what problems arise in existing theory (not counting String ...
3
votes
1answer
86 views

Frequency of gravitational waves

Is there a way by means of dimensional analysis we can obtain the order of frequency of gravitational waves emitted by massive bodies?
-1
votes
2answers
89 views

Is Gravitational Lensing Wrong?

Could gravitational lensing be the refraction of hydrogen, helium, gases and cosmic dust? Refraction is the change in direction of propagation of a wave due to a change in its transmission medium. ...
-2
votes
1answer
52 views

Does this identity that applies to the metric tensor also apply to the stress-energy tensor?

Okay so if the $g_{00}$ component of the metric is $-c^2$ and $g_{11}=g_{22}=g_{33}$ and all the other other components are zero, the question is simple, would similar identities apply to the ...
0
votes
0answers
36 views

From String Frame to Einstein Frame for 10D supergravity

This question is related to but not answered in the post String frame and Einstein frame for a Dp-brane, so it should be treated as a separate question. Beginning with the gravity action $$S = ...
1
vote
1answer
275 views

Questions about MTW's “thousand” tests of the Einstein principle

In Misner, Thorne, Wheeler (henceforth written as "MTW"), "Gravitation", Box 16.4, there's an experimental setup construction (or method) presented by which "Each geodesic clock is constructed and ...
1
vote
1answer
76 views

Covariant formulation of physical equations?

Is it possible to rewrite equations like the Klein-Gordon, the Dirac or the Proca equation in a generally covariant way? And if yes, how and how can the general covariance be shown? (I searched ...