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.
2
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1answer
344 views
Stokes' theorem in GR
I read this formula in Sean Carroll's book of GR:
$$\int_{\Sigma}\nabla_{\mu}V^{\mu}\sqrt{g}d^nx~=~\int_{\partial\Sigma}n_{\mu}V^{\mu}\sqrt{\gamma}d^{n-1}x$$
where n is the 4-vector orthogonal to ...
2
votes
1answer
297 views
Discrete point particles stress energy tensor
I am trying to solve an exercise in Sean Carroll's GR book "Spacetime and Geometry". Basically we need to derive the stress-energy tensor of a perfect fluid (ie $T^{\mu\nu}=(\rho +p)U^{\mu}U^{\nu} + ...
2
votes
2answers
120 views
How to test whether galaxies are moving away from each other in a static background or whether space is being created beween them?
Observations show that galaxies are moving away from one another on the macroscopic scale.
Now, scientists interpret this by saying this happens not because galaxies are really moving away from each ...
2
votes
1answer
157 views
Contraction of indices
We use contraction of indices method to manipulate Tensors. However, I cannot relate that manipulation visually. We can change covariant tensor to contravariant tensor and vice versa by contracting ...
5
votes
2answers
544 views
Visualizing Ricci Tensor
By definition Ricci Tensor is a Tensor formed by contracting two indices of Riemann Tensor. Riemann Tensor can be visualized in terms of a curve, a vector is moving and orientation of the initial and ...
7
votes
1answer
88 views
Fourier Methods in General Relativity
I am looking for some references which discuss Fourier transform methods in GR. Specifically supposing you have a metric $g_{\mu \nu}(x)$ and its Fourier transform $\tilde{g}_{\mu \nu}(k)$, what does ...
3
votes
2answers
1k views
Riemann Tensor Calculation trick(number of element)
When we calculate Riemann Tensor for different curvature we have lots of components. However, there are many components that are zero. How can we argue, based on the symmetry of connection , that ...
2
votes
1answer
212 views
Thought experiment about acceleration
Case 1: two people wake up in spaceships accelerating at 1g. They can measure or observe anything inside the room but not outside. They couldn't determine if they were on a spaceship or on earth. ...
3
votes
2answers
188 views
Foliation of hypersurfaces in General Relativity
As I understand it, it is usual in GR to define a foliation of Spacetime by a family of spacelike hypersurfaces "indexed" by the time variable. Then, in the context of Schwarzschild metric in ...
3
votes
3answers
285 views
storing energy (as mass)
When chemical energy is released mass is reduced, if only by a negligible amount. Presumably that's true for all energy. And presumably that works in reverse as well: storing energy involves an ...
1
vote
1answer
302 views
Blandford-Znajek process: Why/how does the current flow along the magnetic field lines
Related: How would a black hole power plant work?
I have put a bit of commentary enumerating my confusions in parentheses
I read in Black Holes and Time Warps (Kip Thorne), that quasars can generate ...
1
vote
1answer
121 views
Are there any clear and expressive plainword sense of metric tensor components?
Can the following groups of components of metric tensor can assigned a clear sense?
https://docs.google.com/drawings/pub?id=1kVqkN1gT-a2fDy2S851l9iQKaMfaatCDo517OSZBHEo&w=467&h=228
I have ...
0
votes
2answers
167 views
Should $E$ and $B$ change with Gravity?
Lets examine a typical GR metric:
$$ds^2=g_{00}dt^2-g_{11}dx^2-g_{22}dy^2-g_{33}dz^2$$
The "d" going with ds has its correct meaning when the path is
specified with respect to a one dimensional ...
2
votes
3answers
184 views
Why can't we think of free fall as upside down rocket?
/\
/ \
| |
| m |
| |
------ <--- floor (Rocket A)
This rocket is accelerated (g) upwards then mass(m) falls on the floor.
...
2
votes
1answer
281 views
Superposition of Ricci scalars [closed]
Suppose I have two point/line singularities in spacetime (what is important to me is that they are localized). Also suppose I have some fields in spacetime and that the two singularities interact with ...
1
vote
2answers
248 views
What does a closed time-like curve look like?
I want to see a plot of closed time-like curve in $(t,x)$.
$t$ - vertical axis
$x$ horizontal axis
(the usual setting just neglect $y$ and $z$ components of $(t,x,y,z)$).
What does it look like?
5
votes
1answer
189 views
Are objects in a gravitational well shortened?
Bob is in a gravitational potential well, he moves a long vertical stick up and down a distance of 1 meters. Alice observes the upper end of the stick, at upper location.
There is the phenomenon of ...
5
votes
2answers
623 views
Incompatibility Between Relativity and Quantum Mechanics
Why does Gravity distort space and time while the electromagnetic, strong, and weak forces do not?
Does this have to do with why Quantum Mechanics and Relativity are incompatible?
4
votes
1answer
106 views
Can dark matter and energy be formulated as local perturbations of the metric
Note, my formal physics education ended over ten years ago so I may be missing some obvious piece of understanding.
The relationship between space-time and matter/energy distribution is described by ...
1
vote
6answers
1k views
Does light have acceleration?
Light travels with the largest speed in our universe. Does light have acceleration?
6
votes
4answers
462 views
Are there controversies surrounding the principle of general covariance in GR?
I'm a physics graduate now working with computers. I study GR in my spare time to keep the material fresh. In the Wikipedia article about the mathematics of GR, one can read the following:
The ...
5
votes
2answers
519 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 ...
2
votes
2answers
273 views
What is the inertial frame that explains the Foucault Pendulum?
I know that the Foucault pendulum rotation in relation to Earth is a proof that the object is inertial in relation to the distant stars. But what makes them more important than the Earth? Are they an ...
1
vote
4answers
263 views
Is there a universal rest frame of reference?
I am still struggling with C being a constant and what that implies.
So can an experiment be done to find the resting state for the universe?
Take a device with an observer and a light source and two ...
1
vote
1answer
433 views
Is the curvature of space around mass independent of gravity?
Is the curvature of space caused by the local density of the energy in that area?Could gravity be a separate phenomenon only arising from the curvature of space? For instance if the density of energy ...
5
votes
1answer
116 views
Source term of the Einstein field equation
My copy of Feynman's "Six Not-So-Easy Pieces" has an interesting introduction by Roger Penrose. In that introduction (copyright 1997 according to the copyright page), Penrose complains that Feynman's ...
1
vote
1answer
298 views
How does Newton's 2nd law correspond to GR in the weak field limit?
I can only perform the demonstration from the much simpler $E = mc^2$.
Take as given the Einstein field equation:
$G_{\mu\nu} = 8 \pi \, T_{\mu\nu}$
... can it be proved that Newton's formulation ...
1
vote
4answers
239 views
Freefall in/out of an enclosed environment
I've just been learning about Einstein, relativity, and the equivalence principle in Physics. I'm fascinated with the idea of being inside a free-falling enclosed environment (such as, e.g., rocket, ...
2
votes
4answers
567 views
How long would it take to travel through a wormhole?
Assuming wormholes exist and you put some matter into one, how long would it take to reach the other end versus how far apart the two ends are? Basically, by how much does a wormhole stretch ...
1
vote
0answers
148 views
Modification of de Donder gauge
The de Donder gauge is often used to simplify the linearised equations of motion of general relativity. If the metric is linearised as $g_{ab} = \bar g_{ab} + \gamma_{ab}$, then the de Donder gauge ...
2
votes
2answers
158 views
What are the limitations of the FLRW metric?
I was wondering, given how in any other area of life making an explosion spherically symmetric is more or less impossible is there any reason to expect that the universe is? I appreciate that the FLRW ...
4
votes
2answers
356 views
Why is Mendel Sachs's work not taken seriously? Or is it?
Back in college I remember coming across a few books in the physics library by Mendel Sachs. Examples are:
General Relativity and Matter
Quantum Mechanics and Gravity
Quantum Mechanics from General ...
3
votes
4answers
422 views
What is a gauge transformation of the metric in GR?
I'm confused by this question:
Why can't General Relativity be written in terms of physical variables?
I can't quite see how you can make any change to the metric without either: (a) changing ...
1
vote
1answer
116 views
Do we need a quantum theory of gravity in order to describe photons blueshifted past planck energy?
If yes, then how does this accord with relativity: the laws of physics are the same in all reference frames? We can move from a reference frame in which the photon has near zero energy density, to a ...
1
vote
0answers
78 views
How complete is our understanding of general-relativistic solutions for extremal black holes?
Putting aside quantum mechanics (or at least putting aside the question of fermions), is our knowledge of extremal General-Relativity solutions good enough that we would be able to rule out a ...
5
votes
1answer
158 views
Why are geons unstable? Are there other problems with geons?
I read in various places geons are "generally considered unstable." Why? How solid is this reasoning?
Is the reason geons are not studied much anymore because we can't make more progress without ...
1
vote
2answers
175 views
Could gravity hold electron charge together?
Could the gravitational force be what holds the charge of the electron together? It seems to be the only obvious possibility; what other ideas have been proposed besides side-stepping the issue and ...
3
votes
1answer
170 views
Could strings be geons?
Is it possible that string theory strings are geons? This may be an overly speculative or naive question, but is there an obvious reason why not? Both strings and geons seem to have roughly the same ...
1
vote
1answer
127 views
The Light Ray Bends Round!
Let's consider the equation y=x in the x-y rectangular Cartesian frame in flat space time. We use the transformations in the first quadrant:
$$y=y'^2$$
$$x=x'$$
$$t=t'$$
For the first ...
5
votes
2answers
84 views
Torsion and gauge invariant EM kinetic term
Everytime I hear about adding torsion to GR, something struggles me: how do you create a kinetic term for the electromagnetic field that is still gauge-invariant? One of the consequences of torsion is ...
9
votes
3answers
885 views
Why can't General Relativity be written in terms of physical variables?
I am aware that the field in General Relativity (the metric, $g_{\mu\nu}$) is not completely physical, as two metrics which are related by a diffeomorphism (~ a change in coordinates) are physically ...
2
votes
2answers
636 views
Proof that Energy Momentum Tensor of Scalar Field Theory satisfies Weak Energy Condition
It's a question on Sean Carroll's Spacetime and Geometry, where we are supposed to prove that the energy momentum tensor of scalar field theory satisfies Weak Energy Condition (WEC). The energy ...
5
votes
2answers
511 views
Why is spacetime near a quantum black hole approximately AdS?
In this link, one of the answers contains the statement
If you examine the space-time near a finite area quantum black hole,
you will see an approximate AdS space.
Presumably "approximate" ...
2
votes
1answer
237 views
Why dynamic Casimir effect does not appear in static gravity field?
Dynamic Casimir effect tells us that a constantly-accelerated mirror should emit radiation due to interaction with vacuum. Following principle of equivalence, a similar mirror placed in static ...
3
votes
2answers
84 views
How can I vizualize and understand curved spaces in general relativity?
I'm taking a basic physics class and the teacher described space with a special table that has curves and black holes etc. He would throw a metal ball down onto it and the class would watch it circle ...
3
votes
1answer
70 views
General parameters of the stress energy tensor in local inertial frame
A general 4x4 symmetric tensor has 10 independent components. How many components are we free to prescribe in the local inertial frame?
For example, relativistic dust is $\mbox{diag}(\rho c^2, 0, 0, ...
11
votes
1answer
206 views
Lagrangian for Euler Equations in general relativity
The stress energy tensor for relativistic dust
$$
T_{\mu\nu} = \rho v_\mu v_\nu
$$
follows from the action
$$
S_M = -\int \rho c \sqrt{v_\mu v^\mu} \sqrt{ -g } d^4 x
= -\int c \sqrt{p_\mu ...
3
votes
2answers
81 views
What is wrong in this representation of relative reference systems?
Up until now I've explained relative time to myself as looking at the 3D world from different four-dimensional perspectives, analogous to how looking at a 2D-ish object (eg. a sheet of paper) from ...
2
votes
4answers
315 views
Reducing General Relativity to Special Relativity in limiting case
I understand that general relativity is applicable to gravitational fields and special relativity is applicable to case when there is no gravity. But is there a derivation on how to reduce General ...
1
vote
1answer
379 views
If photons are deflected by a strong gravitational field, then how come photons do not have mass? [duplicate]
Possible Duplicate:
Explain how (or if) a box full of photons would weigh more due to massless photons
It has been proved and showed through experiments that light can be bent by the Sun or ...
