A theory that describes how matter produces and responds to 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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Are the gravitational redshift and blueshift factors inverses of each other? [closed]

at a point in gravitational field assuming swcharzschild metric and the exact analysis. The other point in context is infinity. It would be helpful if you can provide citation/source of the ...
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57 views

Local Acceleration of an observer near a black hole

In the first page of this link https://www.math.ku.edu/~lerner/GR/Schwarzschild.pdf they calculate the magnitude of acceleration felt by an observer at $r$ from the black hole: ...
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41 views

Can someone clarify how many metrics exist that satisfy the EFEs?

As I currently understand it, there are two ways to work with the Einstein Field Equations: (1) exact solutions and (2) approximations that work under certain conditions. I also understand that ...
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64 views

Calculation of co-moving coordinate separation for a moving object in a time-varying spacetime metric

My calculus has 30+ years of rust on it and I am stuck on the integration of the interval in General Relativity... I wish to calculate the spatial coordinate at time t of an object moving with ...
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322 views

What's the relationship between quantum entanglement and the relativity of time?

Apologies in advance for what may be a stupid question from a layman. In reading recently about quantum entanglement, I understood there to be a direct link between entangled particles, even at ...
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206 views

Changing vector basis in AdS$_3$

I have AdS${}_3$ given as a surface embedded in a 4 dimensional pseudo-Riemannian space $$x^2+y^2-u^2-y^2=-l^2$$ With metric: $$ds^2=dx^2+dy^2-du^2-dv^2$$ I have Killing vectors of that space ...
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56 views

Stress-energy tensor for a fermionic Lagrangian in curved spacetime - which one appears in the EFE?

So, suppose I have an action of the type: $$ S =\int \text{d}^4 x\sqrt{-g}( \frac{i}{2} (\bar{\psi} \gamma_\mu \nabla^\mu\psi - \nabla^\mu\bar{\psi} \gamma_\mu \psi) +\alpha \bar{\psi} \gamma_\mu ...
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Can curvature waves in f(R) theories explain gravitational lensing in cluster collisions?

The Einstein-Hilbert action leading to Einstein's equations is $$S\sim\int R \sqrt{-g}\, {\rm d}^4 x$$ There is a class of modifications of Einstein's relativity called $f(R)$ theories of gravity ...
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144 views

Geodesic Deviation between Test Particles from Gravitational Wave

I'm having trouble understanding how Carroll (Spacetime and Geometry, p.296) explains the effect of a passing gravitational wave on test particles. If we have two geodesics with tangents $\vec{U}$, ...
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Geodesic deviation

In S. Carroll Lecture Notes on General Relativity, chapter 6, pages 152-153 we have equation (6.62) $$\tag{6.62} \frac{\partial^2}{\partial t^2} S^\mu=\frac{1}{2} S^\sigma \frac{\partial^2}{\partial ...
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How does Space-Time Cloak work?

Well, scientists have achieved Spacetime cloaking to make events fully disappear. Currently, it works only for a trillionth of a second, but here's real-world scenario from linked page: In theory, ...
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Why isn't the center of the galaxy “younger” than the outer parts?

I understand that time is relative for all but as I understand it, time flows at a slower rate for objects that are either moving faster or objects that are near larger masses than for those that are ...
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32 views

Relativity and Galaxy Rotation Speed

If time travels slower nearer gravity wells, why can't the galaxy rotation speeds being faster on the outer edges than the inner areas be explained by relativity? What necessitates dark matter?
2
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173 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 $(\nabla_\mu \nabla^\mu + m^2) \Phi=0$). ...
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825 views

Can a non-Euclidean space be descripted through an Euclidean space of higher dimension? So why use non-Euclidean?

If you draw a big triangle in Earth 2D surface you will have an approximated spherical triangle, this will be a non euclidean geometry. but from a 3D perspective, for example the same triangle from ...
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42 views

Can we embed 2+1 space-time of GR in a 3 Dimensional Euclidean space?

Wikipedia says that inflation is the exponential expansion of space in the early universe.I'm trying to have a physical picture of this.Given that I can't visualize 3+1 pseudoriemannian manifolds,I'm ...
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5answers
177 views

Does coordinate time have physical meaning?

I have always been a little confused by the meaning of the "$t$" which appears in spacetime intervals or metrics in general relativity. I concluded that $t$ was just a mathematical thing which allow ...
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145 views

Coordinates for FLRW metric

In GR, coordinate are just a tool for us to describe the physics, they should be equivalent. However, in standard form of FLRW metric, it can be inferred that the universe is expanding, but we can do ...
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38 views

Post-Newtonian approximation for binary gravitating system

I have been studying gravitation waves radiated by a binary source. I have linearised Einstein's field equation and approximated the source to a Quadrupole moment to get the power radiated by the ...
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430 views

Suggested reading for quantum field theory in curved spacetime

I want to learn some QFT in curved spacetime. What papers/books/reviews can you suggest to learn this area? Are there any good books or other reference material which can help in learning about QFT ...
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61 views

What's the best GR book for recreational study? [closed]

I currently have four books. Hartle Schutz Cheng Carroll (lecture notes) Which one is best for me to read easily? (especially, for foreigners) Or Do you guys can give good recommendations that ...
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Norm of Killing vector field

Let us suppose we have a Killing vector field with $X^a = 1/2$ and $X^b = 1/3$ and $g_{ab}=1$ where the other $c$ and $d$ components are zero. Now we want to find its norm: The formula for finding ...
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Does the escape velocity of a black hole exceed $c$ *before* a singularity is created?

As an offshoot of the question Can we have a black hole without a singularity? I'm curious if the point of no return at which the massive object is condemned to become a singularity happens before its ...
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geometry inside the event horizon

I'm trying to understand intuitively the geometry as it would look to an observer entering the event horizon of a schwarszchild black hole. I would appreciate any insights or corrections to the above. ...
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Is this cosmological scenario possible?

Is it possible that the universe is infinitely large and contains an infinite amount of mass that is distributed in such a way that gravitational force is never infinite? If so, is it possible that ...
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51 views

How would an observer feel the Einstein Thirring Lense Effect?

The Einstein Thirring Lense Effect, also known as Frame Dragging, is what happens when cellestial bodies have rotation. It states that when a body of mass is rotating around an axis it drags space and ...
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Naturalness of tensor fields in general relativity?

In the third chapter of the book The Large Scale Structure of Space-Time, the authors say regarding the matter fields in general relativity: These fields will obey equations which can be expressed ...
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Does the payload of an Alcubierre drive have to be on board during the preparation phase?

I was thinking about the practical aspect of using an Alcubierre drive, assuming one existed. I'm no expert, but my understanding is that, since the destination has to be in the forward light-cone of ...
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71 views

How strong must gravity be to stretch time?

I'm not sure if this is true or not but I heard that gravity has the ability to stretch time, and I was wandering if this is true. If so, how intense/powerful does the gravitational force have to be ...
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isotropy of 3-space and spacetime metric

The most general spacetime metric is given by $$ds^2=g_{\mu\nu}dx^\mu dx^\nu=c^2dt^2+g_{0i}dtdx^i-g_{ij}dx^i dx^j$$ Why does the second term said to violate isotropy of 3-space? It is true that, ...
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96 views

At what rate does light 'bend' around the surface of the earth?

Since the g force of earth is 9.8 m/s*2 does that mean light 'drops' at that rate as it travels past earth? Or is general relativity a lot more complex than that?
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544 views

Effect of space time relativity on the age of the universe?

So we all heard about the twins paradox to explain einstein's time space relativity. Wikipedia Quote :" In physics, the twin paradox is a thought experiment in special relativity involving identical ...
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Our Universe Can't be Looped? [duplicate]

With reference to the Twin-Paradox (I am new with this), now information of who has actually aged comes from the fact that one of the twins felt some acceleration. So if universe was like a loop, and ...
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558 views

How will the Twin Paradox become, for Time Dilation, if no acceleration was ever involved?

I think one catch in Twin Paradox was about the big acceleration that can turn back the traveling twin from light speed outward bound, to become light speed inward bound. What if there is strictly no ...
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121 views

Twin paradox where the twins start at different locations

Suppose we have this scenario with twins A and B: 1) Instead of the twins starting at the same location, let's say the twins start out some distance apart, in the same reference frame. 2) The ...
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Twin paradox - observers counter orbiting Earth

Imagine three observers - one (A) stationary on the surface of Earth (latitude 0 deg) and two others orbiting the planet in the same circular equatorial orbit just in the opposite direction. When the ...
4
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2answers
139 views

Twin paradox with two intertial frames in general relativity

I assume the twin paradox from special relativity is well known. I wish to focus on the apparent symmetry of the problem: both observer seems to move away from each other, and then come back. Yet, the ...
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Symmetrical twin paradox

Take the following gedankenexperiment in which two astronauts meet each other again and again in a perfectly symmetrical setting - a hyperspherical (3-manifold) universe in which the 3 dimensions are ...
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Twin paradox on a cosmic scale

I am referring to yet another version as the classical twin paradox. In my version the moving apart of the twins is entirely induced by space expansion between them and they move apart each other at ...
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How is the classical twin paradox resolved?

I read a lot about the classical twin paradox recently. What confuses me is that some authors claim that it can be resolved within SRT, others say that you need GRT. Now, what is true (and why)?
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Why does $\frac{d\tau}{d\sigma} = L$?

I am given a (3+1)-dimensional spacetime that has the line element \begin{equation} ds^2 = -\left(1-\frac{2M}{r}\right)dt^2 + \left(1-\frac{2M}{r}\right)^{-1} dr^2 + r^2 d\phi^2 \end{equation} ...
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Book on optics in curved space-time

As evidenced from my earlier questions on vision and curved space, I am struggling a little bit with visual perception in curved space-time. I would like a book recommendation on optics and vision in ...
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1answer
49 views

Gravitational time dilation in changing curved space time

Imagine a portion of spacetime which is changing its spacetime curvature because of an object with great mass travelling nearby. For instance, before it was flatter, and after the object passes it ...
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3answers
700 views

Where do I start with Non-Euclidean Geometry?

I've been trying to grok General Relativity for a while now, and I've been having some trouble. Many physics textbooks gloss over the subject with an "it's too advanced for this medium", and many ...
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1answer
40 views

Acceleration of stationary observers in their own reference frame?

In the beginning of this link: https://www.math.ku.edu/~lerner/GR/Schwarzschild.pdf they calculate the acceleration of a stationary observer. As I understand, this accleration is seen by an ...
11
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999 views

Can we have a black hole without a singularity?

Assuming we have a sufficiently small and massive object such that it's escape velocity is greater than the speed of light, isn't this a black hole? It has an event horizon that light cannot escape, ...
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Is quantum gravity, ignoring geometry, the theory of a fictitious force?

This question is motivated by this question and this one, but I will try to write it in such a way that it is not duplicate. In short, I don't understand the motivation for a "quantum theory of ...
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What is the largest disparity of gravitational time dilation from earth's that life can survive?

In certain theoretical scenario's a human can be in a gravitational field where he would age half as fast as on earth's surface. However, for light to travel half as fast in one direction, we are ...
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48 views

What is an “equation of motion” as used in context of geodesic equation?

I am studying general relativity and using the book Gravity by James Hartle. On page 170, he provides the following table: I don't understand what he means by "equation of motion" nor do I ...
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Value of the Hubble parameter over time

There is something I don't understand about the Hubble parameter $H$, as it seems to clump two concepts together that I can't quite unify in my head. On the one side, we have $$V = D H$$ which means ...