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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2answers
61 views

Schwarzschild radius in black hole density

The textbook from which I teach physics at the end of secondary school has a question about the density of a non-rotating black hole. Because the density at the singularity is perhaps infinite or ...
3
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2answers
92 views

Can a hypothetical universe have more than 2 types of dimensions: spatial and temporal?

Our universe is often described as having 3 space-like dimensions and 1 time-like dimension. Can hypothetical universe exist with more than space- and time-like dimensions? If so how would these ...
2
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2answers
88 views

Neutron star: free fall acceleration

The textbook from which I teach physics at the end of secondary school, has a question about a neutron star: $M_{star}=1.4\cdot M_{sun}$, radius 15km. "Calculate the free fall acceleration at the ...
3
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3answers
171 views

Do massless particles follow the curved spacetime or not?

I am assuming that zero (rest) mass particles don't interact gravitationally with each other and other particles. Does that mean they experience a "flat" spacetime instead of a curved one? I find it a ...
1
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0answers
77 views

Phenomena in the intersection of general relativity and quantum mechanics

I am looking for physical phenomena that have aspects involving both general relativity and quantum mechanics. The only example I know is Hawking radiation. While black holes are objects that cannot ...
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4answers
90 views

How is gravity proportional to space-time curvature in the rubber-sheet analogy?

In General Relativity, Einstein established that gravity is due to the curvature produced by objects in space. We all know that gravity is proportional to mass. The picture Einstein painted looks ...
15
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3answers
2k views

Black hole with two singularities?

I hope this question isn't too naive, but would it theoretically be possible to have a black hole with 2 singularities (or 2 black holes at the same location). If this is possible, would there be any ...
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0answers
32 views

Another universe in the other side of a black hole? [duplicate]

A common notion is that there is another universe in the other side of a black hole, past the singularity point....is this true? does it have any scientific support?
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2answers
986 views

Deriving Birkhoff's Theorem

I am trying to derive Birkhoff's theorem in GR as an exercise: a spherically symmetric gravitational field is static in the vacuum area. I managed to prove that $g_{00}$ is independent of t in the ...
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0answers
34 views

Birkhoff Theorem proof reference [closed]

I am looking for a reference with a clear (and easy to understand) proof of Birkhoff's theorem in general relativity.
3
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1answer
197 views

Wave Packet in Curved Spacetime

It is known that the classical equation of motion for a scalar field wave packet on a curved spacetime background gives the geodesic trajectory (the e.o.m. is $(\nabla_\mu \nabla^\mu + m^2) \Phi=0$). ...
4
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1answer
87 views

Light clocks measure conformal time - detailed argument

Let us assume that an observer is stationary at the origin in expanding space. We assume the FRW metric near the origin is given by: $$ds^2=-dt^2+a(t)^2dr^2$$ Let us assume that the observer ...
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1answer
50 views

Sign of matter Lagrangian term in curved space

In field theory the (matter) Lagrangian $\mathcal{L}_m$ is uncertain upto an overall constant multiplying factor (i.e. $\mathcal{L}_m$ and $a\mathcal{L}_m$ yield the same field equation(s) on ...
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1answer
72 views
2
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0answers
70 views

Schwarzschild metric circular orbits and kepler's 3rd law

I have been looking at the Schwarzschild metric presented to me as the following within lectures: ...
3
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2answers
156 views

Why doesn't the light get out?

You're standing on a gedanken planet holding a laser pointer straight up. The light doesn't curve round, or slow down as it ascends, or fall down. It goes straight up. Now I wave my magic gedanken ...
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0answers
25 views

Accretion disks on neutron star binaries

Why does hydrogen gas from accretion disks not constantly get sucked onto/into a neutron star or into a black hole? I understand that some gets sucked into the black hole and some may come down and ...
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0answers
24 views

Who orbits who? Earth or Sun [duplicate]

We always say that the earth orbits the sun, but how can we prove this? Could we not say that the sun orbits the earth or that the earth orbits Mars?
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0answers
23 views

FRW Metric maximally symmetric, derivation, $R=3K$ or $R=6K$ confusion, two different texts

I'm looking at Tod and Hughston Introduction to GR and writing the metric in the two forms; [1]$$ ds^{2}=dt^{2}-R^{2}(t)(\frac{dr^{2}}{1-kr^{2}}+r^{2}(d\theta^{2}+sin^{2}\theta d\phi^{2})) $$ [2] $$ ...
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2answers
51 views

Is there any physical meaning for the inverse metric?

I've been wondering if we can attribute any physical meaning to the inverse metric. I mean when we talk about the metric itself, there are lots of insights we can have towards its role in spacetime, ...
2
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3answers
253 views

Vacuum-ether and spacetime

In the past you could not give an explanation for various phenomena in which there was an action at a distance, like magnetism or gravity, that occurred in a vacuum; For this reason, ether was ...
3
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0answers
144 views

Curvature and spacetime

Suppose that it is given that the Riemann curvature tensor in a special kind of spacetime of dimension $d\geq2$ can be written as $$R_{abcd}=k(x^a)(g_{ac}g_{bd}-g_{ad}g_{bc})$$ where $x^a$ is a ...
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2answers
137 views

General Relativity visualization software

As I am approaching the study GR, I was wondering if there are softwares that allow a quick visualization of custom metrics, curvature, and particle motion even in the limited context of 2D space. ...
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0answers
40 views

Local translations included in covariant general coordinate transformation

It is known that if we use the constraint $R_{\mu\nu}(P^{a})=0$ , i.e. the curvature of local translations vanishes, then we can modify general coordinate transformations (gct) to a covariant ...
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3answers
109 views

Why would the curvature in space-time attract photons which have zero mass? [closed]

I know that we are surrounded by dark matter, does the dark matter affects space time ???and I know the reason for gravity according to explanations in general relativity. But all the explanation ...
2
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1answer
92 views

How physical are vacuum solutions to Einstein's equations?

It is shown in any standard textbook on general relativity how you might get black holes and gravitational radiation, both of which are vacuum solutions to field equations, i.e., such that ...
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0answers
31 views

What is the speed of gravity? [duplicate]

Hypothetically, let`s say that one day our Sun is suddenly removed from the galaxy. For us, on earth, would take up to 8.3 minutes to notice that the sun was removed, since the distance from the earth ...
0
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1answer
68 views

How can electromagnetic waves be affected by gravity if photons have no mass? [duplicate]

I have found answers that say that gravity interferes with the oscillating electric and magnetic fields of the waves and others that say that since gravity is a bend in space-time, in which case the ...
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1answer
53 views

Lorentz contraction in continuously accelerating rod

I was having a little thought experiment about Lorentz contraction, and I couldn't really figure out what would actually happen. Note that I'm not looking for a answer 'this effect is barely ...
2
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1answer
49 views

Local translations in curved spacetime

A global Poincare transformation on a scalar field induces $$\delta(a, \lambda)\phi(x) = [a^{\mu}+\lambda^{\mu\nu}x_{\nu}]\partial_{\mu}\phi(x). \tag{11.46}$$ In curved spacetime we replace $a^{\mu} ...
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1answer
53 views

Is our locally measured time actually conformal time?

The FRW metric at the origin $r=0$, with $c=1$, is given by: $$ds^2=-dt^2+a(t)^2dr^2$$ Now one can change variables so that near the origin the FRW metric is approximated by the Minkowski metric ...
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3answers
334 views

Recommended books for a “relativity for poets” class?

I teach physics at a community college and have developed a new course titled "Relativity for Poets," which I will be teaching for the first time in spring 2015. As implied by the title, it's a ...
4
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2answers
195 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 ...
0
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1answer
49 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 ...
3
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3answers
163 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 ...
3
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1answer
147 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
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3answers
71 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
53 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
54 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
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2answers
93 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
42 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 ...
2
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7answers
470 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 ...
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1answer
45 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
votes
1answer
53 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
84 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
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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
57 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
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1answer
73 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
501 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
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1answer
52 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 $\bf{F}$ ...