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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117 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. ...
0
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1answer
37 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
57 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
71 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
26 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
44 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 ...
4
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2answers
142 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
47 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 ...
9
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0answers
235 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 ...
0
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6answers
160 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
51 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
199 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 ...
2
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2answers
68 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
57 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.
3
votes
1answer
97 views

Should gravitational waves be discovered already?

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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2answers
125 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
175 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 ...
6
votes
3answers
148 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 ...
1
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3answers
133 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 ...
4
votes
3answers
65 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 ...
4
votes
3answers
113 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
votes
2answers
88 views

Tensors as multilinear maps

Sean Carrol's in his book on GR introduces tensors as a multilinear map of a set of dual vectors and vectors onto R. I usually think of tensors as a multidimensional array of numbers with fixed ...
0
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1answer
54 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
60 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 ...
4
votes
3answers
121 views

How to visualize the gradient as a one-form?

I am reading Sean Carrol's book on General Relativity, and I just finished reading the proof that the gradient is a covariant vector or a one-form, but I am having a difficult time visualizing this. I ...
2
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2answers
90 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 ...
4
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1answer
118 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 ...
0
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0answers
24 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 ...
1
vote
1answer
96 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 ...
3
votes
1answer
89 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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3answers
93 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 ...
2
votes
2answers
161 views

Books on cosmology

I am a 14 year old who is independently studying physics. I finished the book: Spacetime and Geometry: An Introduction to General Relativity by Sean Carroll. I am specifically interested in cosmology, ...
0
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1answer
29 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
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1answer
83 views

Schwarzchild solution

I'm able to derive the Schwarzschild solution under the assumptions that the metric is (1) static (2) spherically symmetric and that the space is the vacuum. However, I have read that the ...
5
votes
1answer
53 views

How much additional light does Earth receive from the Sun due to Earth's gravitational field?

I was reading about how gravity affects light, and that got me wondering how much additional light is collected by the Sun due to the Earth's gravitational field. Is it a significant amount of light ...
1
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2answers
129 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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2answers
92 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 ...
1
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1answer
100 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 ...
3
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0answers
46 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 ...
2
votes
1answer
120 views

How did Einstein arrive at the right hand side of his general relativity tensor equation?

It seems Einstein postulated the right hand side of his field equations… I see in books that tell the story of how he arrived at what to put on the right hand side of his tensor equations, the physics ...
2
votes
2answers
171 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 ...
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1answer
112 views

Can we manipulate gravitation? [closed]

When I studied general relativity, my teacher said that what we knew today about gravitation was no better than what we had already known since Newton's time, because so far we could only propose ...
4
votes
3answers
158 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 ...
0
votes
1answer
33 views

Flatness and Kinetic Energy

Why the curvature parameter can be interpreted as the difference between the average potential energy and the average kinetic energy of a region of space? Curvature ...
4
votes
3answers
121 views

Does gravitational time dilation affect apparent mass?

Suppose I'm on a highly elliptical orbit around some massive body. As I get closer, I start to experience time dilation due to the object's gravitational field - time starts passing slower for me than ...
0
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2answers
56 views

Time Dilation Properties

I've read up on time dilation and how gravitational/kinematic time dilation work but I have not received a clear answer on how the two work together. If you are observing something traveling at a ...
2
votes
2answers
381 views

Spacetime geometry around two black holes

For space-time geometry we all know images like he one below. But if I were to take a neutron star and put it right next to but not touching a black hole what effect would that have on the geometry of ...
10
votes
2answers
274 views

Feynman's statement of the Einstein Field Equations

In Feynman's Lectures on Physics (Volume 2, chapter 42) he states that Einstein's field equation is equivalent to the statement that in any local inertial coordinate system the scalar curvature of ...
0
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1answer
68 views

Post-Newtonian acceleration formula

First of all, I have to say that I know very little about tensors and partial differential equations, as I've never done them at school. I'm developing an application which simulates the motion of ...
0
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4answers
82 views

Effect of expansion on time?

We know that for moving body times moves at a slower rate, but can this happen for Universe itself whose rate of expansion is accelerating?