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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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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178 views

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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535 views

What makes the stars that are farther from the nucleus of the galaxy go faster than those in the middle?

It has no sense that stars that have a bigger radius and apparently less angular speed($\omega$) goes faster than the ones near the center.
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In general relativity, do light/time behave as in free space if the net force of gravity is zero?

I mean, if photons/particles in question are on lines equidistant from two bodies of mass (while passing them), does time look the same to them as it would without the bodies of mass? Or is time ...
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159 views

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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85 views

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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1answer
94 views

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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2k views

Ricci scalar for a diagonal metric tensor

I was wondering if there is a general formula for calculating Ricci scalar for any diagonal $n\times n$ metric tensor?
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293 views

A question about motion and time dilation

I was thinking that if you are in empty space with another person (with no other objects around), and from a distance you see that the other person is approaching you a constant speed, you wouldn't ...
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300 views

How much does electromagnetic radiation contribute to dark matter?

EM radiation has a relativistic mass (see for instance, Does a photon exert a gravitational pull?), and therefore exerts a gravitational pull. Intuitively it makes sense to include EM radiation ...
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65 views

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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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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Would the inside of a black hole be like a giant mirror?

As any light reflected or emitted from objects inside a black hole (if it is possible to be there) does not leave the event horizon and comes back inside, would it be like seeing yourself? What I ...
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95 views

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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132 views

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): \begin{equation} \frac{\delta g^{\mu\nu}}{\delta g^{\alpha\beta}}= ...
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53 views

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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1answer
216 views

Lever “paradox”?

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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546 views

Falling into a black hole

I've heard it mentioned many times that "nothing special" happens for an infalling observer who crosses the event horizon of a black hole, but I've never been completely satisfied with that statement. ...
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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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73 views

(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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89 views

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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1answer
2k views

Physical significance of Killing vector field along geodesic

Let us denote by $X^i=(1,\vec 0)$ the Killing vector field and by $u^i(s)$ a tangent vector field of a geodesic, where $s$ is some affine parameter. What physical significance do the scalar quantity ...
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3answers
373 views

Link between Special relativity and Newtons gravitational law

If I make the two statements: General relativity is an extension of special relativity that accounts for gravity. Newton's law of gravitation is a special case of general relativity for when the ...
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1answer
90 views

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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39 views

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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110 views

Covariant Derivative Chain rule? [duplicate]

I want to prove that a covariant derivative of a vector $A^{\mu}(x(z))$ at the point $x(z)$ in general would be defined as $$D_z ...
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55 views

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 ...
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37 views

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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80 views

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 ...
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2answers
99 views

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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26 views

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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2answers
128 views

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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1answer
33 views

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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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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1answer
61 views

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 millimeters (Its Schwarzchild radius) to turn its ...
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37 views

Is there an equivalent force to magnetism for gravity? [duplicate]

In electrodynamics, one way to explain the origin of the magnetic field is to analyze how a moving particle perceives a static electrical field under the effects of special relativity. Due to the ...
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0answers
82 views

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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2answers
72 views

Confused about equations for the Big Bang in general relativity ad loop quantum gravity?

I am trying to get a vague understanding of the mathematical equations for the Big Bang in GR and LQG. My understanding so far is that when the universe is assumed to be homogeneous and isotropic, ...
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71 views

Books on special and general relativity? [duplicate]

I have idea about all the theories related to space and time and stuff. But I wanna dig deep into it and understand all the theories like special and general relativity to begin with for now. Can ...
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1answer
854 views

Does the heat equation violate causality?

I've ran across the idea that, besides simply writing partial differential equations in covariant form, they need to be hyperbolic with all characteristic speeds less than the speed of light. A ...
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1answer
72 views

Why is the value of the action integral in general relativity the same on all regions that are homologous?

In their famous paper Action integrals and partition functions in quantum gravity, Gibbons and Hawking argue that in order to avoid the singularity of a Schwarzschild black hole you can complexify ...
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189 views

Penrose diagram for spacetime which flows to $AdS_{2}$ at infinity

Consider I have the following 2 dimensional spacetime $(t,z)$: $$ds^2=\frac{4}{z^{2}}\left(1+\frac{1}{z}\right)^{-1}(-dt^{2}+dz^{2}).\tag{1}$$ When $z\rightarrow \infty$ we have ...
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1answer
93 views

Scalar field in a Schwarzschild metric

I have found this article recently published in Classical and Quantum Gravity giving the exact solution of a scalar field in the Kerr-Newman metric. These authors also derived Hawking radiation for ...
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1answer
50 views

Is the orbit in Schwarzshild metric a path with maximal proper time?

In curved spacetime particles follow timelike geodesics, which should have maximal proper time (at least locally). I thought this path usually corresponds to a global maximum, and there are only ...
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1answer
565 views

How does time relate to mass and velocity

I understand that the larger the mass the greater gravity is and the slower time is, as well the faster an object is traveling the slower time passes. My question is that since the faster an object ...
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2answers
121 views

What would be the consequences of time not being “relative” [closed]

So far nobody proved Einstein wrong about Theory of relativity and time but I'm curious: What would be the consequences or problems if someone would prove him wrong when it comes to relativity of ...
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68 views

Gravity's effects on photons moving away from source

As a photon has no mass and must always have velocity c, if I were to shine a laser straight up (so Earth's gravity would be pulling straight back on it), what would the effect be on the photon? It ...
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111 views

How is strong time dilation consistent with weak tidal forces?

Nolan's latest film, Interstellar, takes pains to explain to lay audience members that the passage of time slows in the presence of strong gravitational fields (as per Einstein's theory of General ...
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The Pioneer anomaly finally explained?

Pioneer 10 & 11 are robotic space probes launched by the NASA in the early 1970's. After leaving our solar system, an unusual deceleration of both spacecrafts has been measured to be approximately ...
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Explanation for “if all accelerated systems are equivalent, then Euclidean geometry cannot hold in all of them”

I'm doing an EPQ (mini college research paper) on gravity, and I found a site that explained things in simple terms. I am having trouble understanding how Einstein came to his revelation space-time ...