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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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 ...
2
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2answers
366 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 ...
7
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2answers
2k views

What does it mean for objects to follow the curvature of space?

In science documentaries that touch on general relativity, it is often said that gravitational pull isn't an actual a pull (as described by classical physics), but rather one body travelling in a ...
3
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3answers
465 views

How to connect Einstein's Special Relativity (SR) with General Relativity (GR)?

How Einstein's SR becomes GR? $$ds^2=dr^2-c^2dt^2,$$ $$ds^2=g_{\mu\nu}dx^{\mu}dx^{\nu}.$$ When the $s$ is constant $ds^2=0$, isn't it true? How to connect Einstein's SR with GR? What is the ...
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0answers
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 ...
3
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3answers
124 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 ...
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 ...
4
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2answers
189 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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3answers
164 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 ...
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3answers
301 views

What besides the metric do you need to set up the EFEs and the geodesic equation?

One of my professors wrote on the board (1) Mass tells spacetime how to curve $\to$ Metric/Einstein Field Equations (2) Spacetime tells mass how to move $\to$ Geodesic equation Suppose I am given ...
5
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2answers
656 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 ...
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1answer
247 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 ...
4
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0answers
82 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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0answers
68 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 ...
2
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1answer
43 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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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 ...
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2answers
148 views

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 ...
0
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1answer
173 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 ...
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6answers
775 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 ...
1
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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 $R_{00}$, ...
5
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2answers
2k views

What are the units of the quantities in the Einstein field equation?

The Einstein field equations (EFE) may be written in the form: $$R_{\mu\nu}-\frac {1}{2}g_{\mu\nu}R+g_{\mu\nu}\Lambda=\frac {8\pi G}{c^4}T_{\mu\nu}$$ where the units of the gravitational constant $G$ ...
3
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2answers
128 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.) ...
2
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1answer
178 views

Should gravitational waves be discovered already? [closed]

Gravitational waves are not discovered directly (yet). But does this have any consequences? Should we suspect out theories are wrong or not yet? I found some data about gravitational waves suspected ...
0
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1answer
110 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.
6
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3answers
232 views

Is it in general true that $\nabla_\mu T^{\mu\nu}=0$ implies the matter equations of motion?

I know of several cases where the covariant conservation of the energy momentum tensor $\nabla_\mu T^{\mu\nu}=0$ can be used to derive the equations of motion of the matter fields. Is this in general ...
0
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2answers
505 views

Why does moving near light speed keep you young? [duplicate]

As was shown in the movie Interstellar, when you go close to a black hole or move near the speed of light in space, then your clock runs slower than a clock on Earth. In the movie, Matthew ...
1
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1answer
250 views

What is an “Einstein transformation” in general relativity?

When introducing the vielbein formalism in general relativity, I came across the use of an infinitesimal general transformation, or Einstein transformation. The latter term seems not to be covered on ...
14
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4answers
2k views

Can spacetime be non-orientable?

This question asks what constraints there are on the global topology of spacetime from the Einstein equations. It seems to me the quotient of any global solution can in turn be a global solution. In ...
4
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5answers
672 views

Space Expansion vs. Relative Motion

Given 2 objects moving at some velocity $v$ relative to one another, is it possible to determine whether they are moving or whether the space between them is expanding?
4
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3answers
147 views

Is a metric tensor field the same thing as $ds² = -dt² + dx²+ dy² + dz²$?

I am having trouble understanding the nature of the metric tensor field on spacetime manifolds. In particular, a Riemannian manifold $(M,g)$ is defined as a real smooth manifold $M$ equipped with an ...
4
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3answers
137 views

How do we expect distance measurements to compare inside and outside the event horizon of a black hole?

I've read that as one approaches the event horizon of a black hole, time is dilated relative to time measured farther away from the event horizon (clocks tick slower near the event horizon). I've ...
0
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1answer
75 views

Where is the mass energy of potential energy (such as for the universe?)

As you know, energy has mass via $E=mc^2$. If I understand right, mass must be inside of a particle, and can not just be "free floating." Gravitational potential energy (or what ever its equivalent ...
1
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1answer
198 views

Geodesic equation from the proper time integral

This is something that has been bothering me for a little while. The usual procedure that I've seen is to write the proper time as the line integral $$\tau=\int_\gamma d\tau$$ along some curve ...
2
votes
2answers
125 views

Are time and gravity affected when at rest compared to free fall?

A falling object moves along a geodesic path ('straight path') in spacetime. When it comes to rest it now follows a 'curved path' through spacetime. Is the passage of time and force of gravity ...
5
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1answer
141 views

Curved paths through spacetime when standing still?

I have heard that falling objects fall at the same rate irrespective of their mass. They are 'following straight line paths through curved spacetime'. Does this mean that objects that accelerate in ...
1
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1answer
174 views

GR exercise: falling particles on earth's surface

I'm having some trouble with Exercise 5.1 in Shapiro's BH,WD&NS book, which goes as follows: Consider two particles of mass $m$ at distance $r$ and $r+h$, such that $h\ll r$, on the same ...
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3answers
202 views

Expanding universe as predicted by the Einstein Field Equation

Without the cosmological constant, the Einstein field equation predicts the universe is expanding. Why is that? It is counter-intuitive because generally gravity should pull things closer and shrink ...
4
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1answer
289 views

Gravitational wave solutions to the Einstein field equations

It is well known that general relativity predicts gravitational waves, but I would like to know how. What solution(s) to the Einstein field equations yield something which can be interpreted as a ...
1
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1answer
148 views

General relativity: is curvature of spacetime really required or just a convenient representation?

I'm not really far into the general theory of relativity but already have an important question: are there formulations that can do without spacetime curvature and describe the general theory of ...
2
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2answers
283 views

Difference between the metric tensor in general relativity and the metric tensor in mathematics?

Is the metric tensor in general relativity the same as the metric tensor in maths, or is there a difference?
0
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0answers
25 views

Einstein's equation: good, intuitive introduction anywhere? [duplicate]

Baez - like most others - gives (IMHO) a quite unsatisfactory introduction to Einstein's equation. They all start with the equivalence principle or similarly unintuitive reasoning, relating it to ...
9
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3answers
747 views

How does a rotating object cause frame dragging?

Frame dragging is a consequence of general relativity. But I don't really understand it. Of course I can find metaphors like the "honey metaphor" where stirring a honey can move the specks even if ...
1
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1answer
71 views

How to demonstrate frame dragging through the Kerr metric?

I derived the Kerr metric, but in a form which doesn't seem to relate to frame dragging. I have been trying this for some time, so how do we relate the Kerr metric to frame dragging?
0
votes
2answers
138 views

Why is the cosmological constant a scalar?

Maybe my understanding is just off, but the cosmological constant is just a scalar, right? What are it's units? Why a scalar? - was a tensor 'cosmological constant' ever considered or is it just not ...
4
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3answers
189 views

What is the evidence of interpreting $g_{\mu\nu}$ as the metric of space-time?

I think if we don't mention the meaning of $g_{\mu\nu}$ as the metric of space-time, we can still construct the equation of motion and Einstein field equation in a way such that $g_{\mu\nu}$ is just a ...
1
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1answer
413 views

Galactic Rotation Speeds - Ehrenfest Paradox, Gravitational time dilation, Dark Matter - all of the above?

The observed paths and speeds of objects, part of some distant galaxy, do not match up with speed vs distance curves it seems - the observed speeds are not falling off in fact they're trending as ...
6
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1answer
224 views

Null Coordinates

I have a very basic question: what are the advantages of writing a metric in the null coordinates? Which extra insight do they provide? I've looked in Caroll's "Spacetime and Geometry" and Wald's ...
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0answers
63 views

Does relativistic glider violate principle of equivalence?

The relativistic glider proposed can slow down the fall of an object in gravitational field. Will this violate the principle of equivalence which says that one cannot distinguish between free falling ...
1
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1answer
225 views

Junction conditions in GR including electromagnetism

I have recently learned about the Israel junction conditions in GR (as explained in for example Gravitation by MTW). I then tried to generalize it when including Electromagnetism, i.e. matching two ...
2
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2answers
789 views

Curvature of spacetime as a real thing?

I get the curvature tensor in General Relativity, it is “just” math. Does space-time REALLY curves as a tangible thing, or is Einstein proposing a mathematical abstraction? More naively, please ...