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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How does one calculate the full perihelion shift of Mercury, including perturbations from other planets?

I'm talking about the full calculation, including perturbations from other planets. I've seen the general relativistic correction done a half dozen times before, but I can't say that I've seen the ...
10
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3answers
725 views

Why do the Einstein field equations (EFE) involve the Ricci curvature tensor instead of Riemann curvature tensor?

I am just starting to learn general relativity. I don't understand why we use the Ricci curvature tensor. I thought the Riemann curvature tensor contains "more information" about the curvature. Why is ...
3
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0answers
89 views

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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130 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?
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2answers
802 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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1answer
143 views

Can we embed 2+1 space-time of GR in a 4 Dimensional Euclidean space? [closed]

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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1answer
83 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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0answers
119 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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136 views

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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2answers
3k views

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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1answer
84 views

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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3answers
353 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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1answer
171 views

How to find a metric of a general observer?

Yes, that's it. How to find a particular metric of an observer in general relativity? Let's say we have a static metric: $$ds^2=-g_{00}(\vec{r})dt^2+d\vec{r}^2=-g_{00}(\vec{r})dt^2+g_{ij}(\vec{r})dx^...
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1answer
51 views

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 ...
3
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1answer
100 views

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 ...
2
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1answer
55 views

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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1answer
41 views

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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3answers
1k 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 ...
2
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1answer
705 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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2answers
132 views

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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1answer
138 views

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} ...
3
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2answers
506 views

Locally flat coordinate and Locally inertial frame

I am having some doubts on myself regarding the above concepts in General Relativity. First, I want to point out how I understand them so far. A male observer follows a timelike worldline ($\gamma$) ...
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1answer
366 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 ...
2
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1answer
440 views

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 ...
2
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1answer
119 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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45 views

Do GR and SR have to be considered together to determine time dilation? [duplicate]

In another related question: How to connect Einstein's Special Relativity(SR) with General Relativity(GR)? , John Rennie stated that SR is a subset (or rather can be derived from) GR, but not vice ...
2
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2answers
408 views

Curvature gravity and a falling apple? [duplicate]

I know very little of physics after Einstein. I am aware of that Einstein's gravity theory says that the existence of matters creates curvature of a space-time, so that our Earth orbits our Sun. I ...
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2answers
163 views

Is an achronal set contained in its own causal future?

I use Wald's notation: $I^+$ is the chronological future and $J^+$ is the causal future. My confusion arises from the following passage in Wald (1984): Now, let $S$ be a closed, achronal set (...
3
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3answers
129 views

How eliminates the general relativity the Newtonian action at a distance? By the mediation of which “carriers”?

I found in Wikipedia the following statement From a Newtonian perspective, action at a distance can be regarded as: "a phenomenon in which a change in intrinsic properties of one system induces a ...
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2answers
109 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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2answers
4k views

If the Einstein Field Equations are so hard to solve, how did Einstein know they were correct in the first place?

Consider a formula like $y = mx + b$. For instance, $y = 2x + 3$. It is simple to check that $(1,5)$ is a solution, as is $(2,7)$, as is $(3,9)$, etc. So it's easy to see that $y =2x + 3$ is a useful ...
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3answers
170 views

How can an event happening 5.5 billion light years away be witnessed in “real-time”?

This article https://www.ras.org.uk/news-and-press/2578-cosmic-radio-burst-caught-red-handed states that "These bursts were generally discovered weeks or months or even more than a decade after ...
4
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2answers
195 views

What is the mathematical nature of the stress-momentum-energy tensor?

I am confused about the Einstein Field Equations. Specifically, consider \begin{equation} \text{R}_{ab} - \frac{1}{2} \text{R} g_{ab} =\frac{8\pi G}{c^4}\text{ T}_{ab} \end{equation} I understand $...
2
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2answers
103 views

Some confusions about principle of equivalence

By principle of equivalence, an accelerated system and in general a non-inertial system of reference is equivalent to a certain gravitational field. If there is gravitational field, spacetime is then ...
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6answers
450 views

Extended object passing near an event horizon

Suppose a physically realistic object of nontrivial size (such as a star) free-falls past a black hole. The center-of-mass trajectory for the object is hyperbolic and (therefore) completely outside ...
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0answers
66 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 ...
8
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1answer
501 views

What kind of object is the Landau--Lifshitz pseudotensor?

I understand that it's called a pseudotensor because it's not a tensor. Wikipedia says most pseudotensors are sections of jet bundles, which are perfectly valid objects in GR. (http://en....
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1answer
289 views

Lapse function definition

Let $t$ be a time function and $t^a$ the time flow vector such that $t^a\nabla_a t=0$. Let $\Sigma_t$ be a hypersurface of constant $t$ with unit normal $n^a$, $n^a n_a=-1$. Wald (1984), p. 255 ...
2
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0answers
69 views

Why do black holes have a finite size? [duplicate]

There is one piece of information that makes me wonder why finitely sized black holes are even possible: to an observer from afar, anything that approaches a black hole's event horizon is never ...
4
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0answers
84 views

Are there relativistic theories with spacetime modelled on $\mathbb C^4$ rather than real Minkowski space $\mathbb R^4$?

Does anybody know of references to theories where relativity & spacetime is modelled on a (complex/Kähler) manifold which is locally diffeomorphic to $\mathbb C^4$ rather than $\mathbb R^4$, hence ...
2
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1answer
45 views

Is it possible for the phase of electric charge to change over large general relativistic distances?

Jackson provides examples of how magnetic charge and electric charge form together to create complex charge, \begin{align} \rho = \rho_e+i\rho_m \end{align} which gives rise to the complex faraday ...
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votes
1answer
69 views

Two different expressions for the Schwarzschild Radius? [closed]

This might sound as quite an obvious question at first, but in most places the expression I've seen for this radius is: $$\frac{2GM}{c^2}$$ but in other places, I've seen the expression as:$$\approx \...
5
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2answers
696 views

Open source computer algebra systems for general relativity

I would like to use an open source computer algebra system (CAS) for research in general relativity. Kindly suggest a good choice between Ipython and Sage. I am more interested in the theoretical ...
0
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1answer
183 views

Metric Tensor Identity Manipulation

If I take the metric identity in 4d minkowski spacetime $$ g_{uv}\frac{dx^u}{d\tau}\frac{dx^v}{d\tau}=1, $$ where $\tau$ is proper time parameterisation. Can I conclude that $$4=g^{uv}\frac{d\tau}{...
13
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2answers
464 views

Definition of stress at the microscale

Take, for simplicity, a Lennard-Jones fluid below the critical temperature, which is to say that there is a phase separation into fluid and gas and thus an interface is formed. The macroscale picture ...
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6answers
855 views

Mass without Matter?

My cursory studies of general relativity had introduced me to the concept of how gravity is associated with the warping of spacetime and that the presence of matter in space warps space and this ...
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0answers
59 views

On GR with perturbation

Could anyone explain to me what I have misunderstood/missed when trying to understand this paper on GR perturbation? The paper is http://arxiv.org/pdf/0704.0299v1.pdf In equation 25 for $R_{00}$, $...
9
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1answer
292 views

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 ...
3
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2answers
136 views

Why does General Relativity predict more light deflection than Netwonian Physics?

If one looks at the limit as light's mass approaches zero, Newtonian Physics predicts a deflection of light (this can be seen by the fact that all objects are accelerate the same due to gravity.) ...
0
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1answer
111 views

Geodesic equation proof confusing me

I was looking through this proof and have no idea where the $u$ comes from. Any help is appreciated. This is from here; I want to know how they got from eqn 5 to eqn 6.