Tagged Questions

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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Spacetime diagram of a collapse of a rotating star

There is a well-known "standard" spacetime diagram (Kruskal and Penrose) for the collapse of a spherically symmetric star to a Schwarzschild black hole (for example here, or here in EF), which stands ...
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Derivation of Kerr metric, is there any reference?

In studying general relativity, many text deals with the derivation of Schwarzschild metric starting from generic metric form. After that impose static, spherical symmetry and obtain the desired ...
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Why is $p\cdot u_{\mathrm{obs}} = -E$ valid in curved spacetime for a stationary observer?

An observer stationed at a fixed Schwarzschild radial coordinate R near a spherical star of mass M observes a photon moving radially away from the star and measures its energy to be E. What are the ...
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A particular coordinate transformation of a metric tensor

So, this was a problem set question for my GR class due yesterday, and I can't for the life of me solve it, it seems I am missing something very trivial. Either the given answer is wrong, or I am. ...
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Is there a peak gravitational force between bodies?

Suppose Object A is exerting gravitational force on Object B. Object A increases in mass, and so increases in volume, increasing the gravitational force on Object B. But, since mass occupies space the ...
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Different between $\mu$ and $T_{00}$ in perfect fluid solutions?

In the perfect fluid solution for general relativity, you get $$T_{ab} = u_a u_b (\mu + p) - g_{ab} \, p$$ I've seen varying descriptions of what $\mu$ is, and some places describe it as the local ...
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entropy-infomartion correlation at preliminary universe?

according to the theory of cosmic inflation after Alan Guth, the information should have travelled 100 times the speed of light at the very beginning after the big bang. -when we talk about ...
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Time slowed by gravity

If time moves more slowly on Earth (due to our proximity to a gravitational body) than for someone orbiting Earth in a spaceship, yet the opposite occurs in the frequently cited "twin paradox" of the ...
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Can some components of metric be Finslerian while the others be Riemannian?

A Finsler metric reduces to a Riemann metric in case it loses its dependence on velocities. Now, my question is this: Can we have a Finsler metric in which some components of the metric have velocity ...
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Interpreting the Kretschmann scalar

How do you interpret the Kretschmann scalar (in general relativity)? What can you tell from it? The Kretschmann scalar is defined as $$K = R_{abcd} R^{abcd}$$ where $R_{abcd}$ is the Riemann ...
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A test for virtual particles by measuring gravity fluctuations possible?

Ok to begin I will begin by talking briefly about my discussions with my Quantum Mechanics (specializes in Particle physics) professor and my Cosmology Professor (who studies particle physics with ...
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Is four-current a vector or a vector density?

According to MTW, $$F^{\alpha\beta}{}_{;\beta} = 4\pi J^\alpha$$ and we can infer that the four-current must be an ordinary vector field because the left side is tensorial. But Wikipedia says that ...
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In general relativity, do light/time behave as in free space if the net force of gravity is zero?

If photons/particles are on lines equidistant from two bodies of mass, does time look the same to them as it would without the bodies of mass? Or is time slowed regardless? (Given massive bodies $a$ ...
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Can I practically demonstrate Gravitational Time Dilation by spinning a wheel very fast? [duplicate]

In an attempt to demonstrate gravitational time dilation, I was curious if it were practical to mount a clock to a fast spinning wheel, with the centripetal acceleration of the wheel being equivalent ...
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The relationship between the structure of spacetime and the existence of spinor field?

We all know that the existence of spinor fields implies that spacetime must be time-orientable. Thus that spacetime is time-orientable is a necessary condition for existence of spinor fields. Geroch, ...
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If you are not given a metric, which one is more fundamental: a vector or a covector? [closed]

If we do not have the metric $g_{\mu\nu}$ for a given spacetime, are vectors $x^\mu$ more fundamental than covectors $x_\mu$ or vice versa? Why? (if the metric were given we could just raise/lower ...
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Gravitational force of several massive bodies, from the viewpoint of general relativity

According to Wald's GR, "absolute gravitation force has no meaning". The text goes on to describe two cases: one where a gravitational force can be defined, and one in which it cannot. I'd like to ...
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Computing the Ricci Tensor for a Spherically Symmetric Spacetime

For a homework question, we are given the metric $$ds^2=dt^2-\frac{2m}{F}dr^2-F^2d\Omega^2\ ,$$ where F is some nasty function of $r$ and $t$. We're asked to then show that this satisfies the Field ...
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Variation of the metric with respect to the metric

For a variation of the metric $g^{\mu\nu}$ with respect to $g^{\alpha\beta}$ you might expect the result (at least I did): \frac{\delta g^{\mu\nu}}{\delta g^{\alpha\beta}}= \delta^\...
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Why does rotation simulate gravity if motion is relative?

In Einstein's theory of relativity, if motion is truly relative, then why would somebody in a rotating space station experience (artificial) gravity? I mean, I get why they experience gravity IF the ...
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Can a gravitational wave produce oscillating time dilation?

I was reading about gravitational waves and about laser based detectors. I also read this. As mentioned in the answer, when ever there is a deformation in spacetime, doesn't it also create a minute ...
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A true singularity at $t=0$, coordinate independent Big Bang

Consider a flat Robertson-Walker metric. When we say that there is a singularity at $t=0$, clearly it is a coordinate dependent statement. So it is a "candidate" singularity. In principle there is ...
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Is there a binary black hole system in the middle of the galaxy? [closed]

We have observed gravity effects from black holes in the center of galaxies, but galactic centers are dusty so we can’t tell if it’s one black hole or two black holes in a binary system in there. A ...
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Let's say we have a lever with two weights A and B with the same mass overlapping at the midpoint. Suppose they start to separate with each other at the speed of light simultaneously. From our point ...
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All geodesics are inextendable?

I think the title is true, because geodesics has a tangent vector with a constant length parametrized by an affine parameter. Probably, it is easier to think about timelike or spacelike geodesics. ...
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What does this depiction of a black hole in the movie Interstellar mean?

I was expecting a whirlpool in 3D and the matter glowing from friction as it nears the center, as I expected a event horizon to be negligible visually. How does this depiction work? How big is the ...
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Is time dilation a mechanical slowdown only? [duplicate]

I've recently read about the time dilation occurs at very high speeds. But I'm really wondering if it is just a mechanical slowdown of the clock only? What if we use clocks that does not use moving ...
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Can a ultracentrifuge be used to test general relativity?

With today's ultracentrifuge technology, they can spin so fast that the sample can be subjected to accelerations of up to 2 millions Gs. That is equivalent to two solar masses. Has someone tried to ...
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How does Gravity behave at high energy?

At super high energy, Strong Force becomes weak to act like Electroweak Force (Grand Unification Theory; hand-waving version 2.2). Well, I am NOT trying to find Theory of Everything with this hand-...
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Can a body ever experience acceleration this strong?

Using the Schwarzschild radius formula, I approximated the Sun's Schwarzschild radius to be $3\text{ km}$. Now assuming I have a body (not a human body) which is at a distance of $10\text{ km}$ from ...
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Do black holes have transient color charge?

In the membrane model, when a baryon hits the event horizon its spatially separated quarks will impact the membrane at different times. Doesn't this necessarily mean that black holes acquire, however ...
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Can a quark irreversibly pass though an event horizon?

This is an attempt to transform a question I asked about a year ago into a binary yes-or-no question: Since a quark has electrical charge, can it irreversibly pass though an event horizon? The ...
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What is the correlation between dark matter and Einstein Rings?

I have once heard a TED Talk about Dark Matter, Einstein Rings and gravitation lenses. http://ed.ted.com/lessons/patricia-burchat-sheds-light-on-dark-matter I don't think I understood the talk well. ...
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With what fraction photon quanta emission rate is decreased in the expanding universe? [closed]

Light from edge of the observable universe has travelled 13.8 billion light years so far. And, that edge itself has travelled 32.2-33.2 billion light years (that's why actual radius of observable ...
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Proper time in general relativity

For general relativity, Wald's GR states that timelike curves, with the norm $g_{ab}T^{a}T^{b} < 0$, can be parameterized by the "proper time" $$\tau = \int (-g_{ab}T^{a}T^{b})^{1/2} dt.$$ This ...
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Meaning of general covariance

Quoting from Wald's GR: In the context of special relativity, the principle of general covariance states that the spacetime metric $\eta_{ab}$, is the only quantity pertaining to spacetime ...
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Time should run slower near massive body

We have considered that time should run slower near massive body like Earth, BH. There is no gravity in space, means time is faster in space compare to earth. Then How is it possible that man who ...
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(Scalar) Ricci flatness of a metric

What is the physical meaning to vanishing Ricci scalar $R=0$ of a metric in general relativity? Note that this is not the same questions as the geometric meaning of $R_{\mu\nu}=0$ which has been asked ...
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Increase in momentum of a particle falling into a black hole

From the point of view of an external observer at a fixed distance above a black hole, the linear momentum a free falling particle increases exponentially with Schwarzchild time. (This happens when ...
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Relation between $f(R)$ gravity and Tensor–vector–scalar (TeVeS) gravity

We know that there is a relation between f(R) gravity and scalar-tensor gravity. By applying the Legendre-Weyl transform, we can receive brans-dicke gravity from $f(R)$ gravity. If we start with the ...
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Is the event horizon also the boundary region of the mass contained by a black hole?

I was recently playing around with classic Newtonian mechanics and calculated that the Earth would have to be compressed to a spherical region of $8.8 \ mm$ (Its Schwarzchild radius) to turn its ...
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Einsteins gravity Space time

I'm having a difficulty in understanding Einstein's version of gravity as "space time curvature" (I could be a total physics idiot, please point out !). How does an object on the surface of earth ...
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Would a wormhole in space look like anything at all?

In movie "Interstallar", the wormhole is elaborately depicted as a sphere, complete with explanation about why it is spherical, and as it is approached, it looks like a sphere containing fabulous ...
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Can all fundamental forces be fictitious forces?

After reading many questions, like this and this, I wonder: is it possible to consider also the other fundamental forces, the electroweak interaction and the strong interaction or ultimately the ...
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Length of Day and year on massive Earth

Say, a planet has the same orbital periods as Earth (365 days in a year, 24 hours in a day, etc. with respect to Earth-bound clocks), but the planet has double the mass. So, time must pass more slowly ...