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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How to prove that zero Weyl tensor predicts no deflection of light?

There is Nordstrom theory, which can be given as $$ C_{\mu \nu \alpha \beta} = 0. $$ The solution of Einstein equations for this case is conformally flat metric: $$ g^{\mu \nu} = e^{\epsilon \varphi ...
4
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2answers
169 views

I need help understanding a step in the derivation of the Schwarzschild solution

I am looking at Wikipedia's article on deriving the Schwarzschild solution. In the section "Simplifying the components", it says, On the hypersurfaces of constant $t$ and constant $r$, it is ...
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4answers
269 views

The universe is expanding but why the galaxies have no motion?

It is said that the universe is expanding and the galaxies are moving apart. I understand that the space between every two galaxies is increasing. Doesn't this seem to imply that the galaxies will ...
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2answers
193 views

Metric Expansion Of Space

I just do not understand this concept of metric expansion of space. Shouldn't the galaxies move away from each other. How can the space between them expand if the galaxies are not moving away from ...
2
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0answers
53 views

Will accelerating a massive particle generates a blackhole? [duplicate]

I have a naive question about blackhole. If I accelerate a massive particle very close to the speed of light, the particle will have large energy-momentum tensor. Will it become a blackhole?
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71 views

4 of Einstein equations without 2nd order time derivative

This question is related to my previous one and it was a homework problem and was due two weeks ago. Problem:prove that four of Einsteins' equations $$ G_{0\nu} = 8\pi T_{0\nu} $$ have to 2nd order ...
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3answers
147 views

Gravity on the International Space Station - General Relativity perspective

My question is an extension to this one: Gravity on the International Space Station. If all the outside views of the ISS was sealed, then the crew inside would not be able to tell whether they were ...
4
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0answers
130 views

Calculating Forces via Feynman diagrams?

How would one go about calculating forces that test objects feel using Feynman diagram methods? For example, say we have a massive object in GR so that the metric takes on the standard ...
3
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2answers
416 views

How do gravitons and curved space time work together? [duplicate]

I've heard two different descriptions of gravity, and I'm wondering how they work together. The first is Gravitons: "The three other known forces of nature are mediated by elementary particles: ...
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0answers
44 views

Allowed transformations in General Relativity [duplicate]

So in Special Relativity we have: $$ \Lambda \eta \Lambda^T=\eta $$ Is there an analagous formula for the metric in General Relativity?
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1answer
172 views

Riemann curvature tensor symmetries confusion

In the context of spacetime, reading Schutz, I'm confused about the symmetries of the Riemann curvature tensor, which I understand are: ...
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1answer
96 views

Best way to check for anisotropy given a metric tensor

Carroll gives the definition of isotropy at a point as given vector $V$ and $W$ in $T_{p}M$, there is some isometry that can push $V$ forward such that it ends up parallel to $W$. I understand what ...
2
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1answer
71 views

causal sketches [closed]

I don't have much of an idea of how to draw causal sketches. I know that you need to work out the gradient of the light cones, which can be done using a given metric and using null vectors. But how do ...
3
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1answer
175 views

Better explanation of the common general relativity illustration (stretched sheet of fabric)

I've seen many science popularisation documentaries and read few books (obviously not being scientist myself). I am able to process and understand basic ideas behind most of these. However for general ...
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0answers
42 views

Hubble's law for the Kasner solution

I'm puzzled with the following question: find an analog of the Hubble's law for the Kasner solution. Kasner metric is a solution to the vacuum Einstein equations ...
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2answers
153 views

Do electromagnetic fields gravitate?

It's well known that electromagnetic fields contains energy but do they gravitate ? When we talk about the composition of the universe it's now accepted that the 74 % is dark energy , the 22 % is ...
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0answers
73 views

Relativistic Black Hole? [duplicate]

So recently, looking at high energy particles through the lens of General and Special Relativity has peaked my interest. One thing I was considering, using the electron as the first example, is as ...
0
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1answer
75 views

Is there a minimum mass is required for light to be noticeably bent?

The sun bends the trajectory of light slightly. And a black hole will bend the trajectory entirely. This is all dependent on the proximity to the source of gravity. For a given angle, is there some ...
1
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1answer
137 views

Specify the Stress Energy Tensor and Calculate the Curvature

I have a simple question about general relativity and the Einstein field equations, I wonder if you can specify the stress energy tensor, i.e. specify some mass distribution in space and then ...
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1answer
72 views

Why we can set variations for the metric and its derivatives to zero at infinity?

This question is the continuation of the following one. I still don't understand why $(1)$ may be set to zero. This refers to the zero value variations of metric and its derivatives on the infinitely ...
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1answer
146 views

Are there any good references on the “gravitational” curvature of spacetime of a moving mass being distorted due to special relativity?

In this Wikipedia paragraph suggesting an explanation for the phenomenon of inertia, it claims: Another physicist, Vern Smalley, has derived the Lorentz transformation for mass by assuming that ...
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1answer
217 views

Einstein action and the second derivatives

I have naive question about Einstein action for field-free case: $$ S = -\frac{1}{16 \pi G}\int \sqrt{-g} d^{4}x g^{\mu \nu}R_{\mu \nu}. $$ It contains the second derivatives of metric. When we want ...
2
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0answers
119 views

How do we derive force/acceleration vectors from Einstein's field equations?

I'm new here and I don't have any formal experience in physics beyond A-level. I've been exploring an idea for a space sim game someone else is developing in which propulsion of a spacecraft is ...
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1answer
178 views

Relation between symmetries and Killing vectors by Weinberg

In his book, "Gravity and Cosmology", Weinberg talks about relations between homogeneous metric spaces and Klling vectors. First he says about infinitesimal isometrics $$ x^{\alpha}{'} = x^{\alpha} + ...
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3answers
136 views

Is light slower when traveling inside a gravity field?

This question is not about phase velocity changed which causes refraction, but about the real time itself being slower by the gravity of any object (from general relativity). If so, would this mean ...
4
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2answers
136 views

Proof that higher genus surface admits a metric of negative Ricci scalar everywhere

In the Green, Schwarz and Witten Superstring Theory textbook, the paragraph below equation 3.3.15 says, For genus greater than one, it can be shown that the surface admits a metric of everywhere ...
5
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1answer
323 views

6 independent Einstein field equations?

I can't understand the comment on page 409, Gravitation, by Misner, Thorne, Wheeler It follows that the ten components $G_{\alpha\beta} =8\pi T_{\alpha\beta}$ of the field equation must not ...
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0answers
76 views

Weak gravitational lensing multispectral, multibackground correlations

My understanding of weak gravitational lensing is that it assumes random alignment distribution of galaxies in order to estimate statistical shear and convergences, which are used to estimate matter ...
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1answer
105 views

Gravitational interactions by energy or by mass?

The mass-energy equivalence, first established by Einstein is an important and highly discussed phenomenon in physics. Without claiming much knowledge about high-end discussions on this topic, I would ...
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2answers
166 views

A complicated question about $E=mc^2$

I know this is a little outside the normal question and there may not be a direct answer, but it is an interesting thought experiment. Starting with a supermassive black hole, if you were able to ...
3
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2answers
457 views

How to obtain the field equations in Brans-Dicke theory from the action?

The action for the Brans-Dicke-Jordan theory of gravity is $$ \\S =\int d^4x\sqrt{-g} \; \left(\frac{\phi R - \omega\frac{\partial_a\phi\partial^a\phi}{\phi}}{16\pi} + \mathcal{L}_\mathrm{M}\right). ...
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2answers
46 views

Are high redshift masses corrected for relativistic mass dilation? They would appear more massive right?

A distant quasar would be less massive in its frame of reference than our observations would suggest. Are such highly red-shifted objects corrected for relativistic mass dilation?
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0answers
21 views

Method of determining peculiar speed of the galaxy which moves on celestial sphere and emits the light

This question is the continuation of this one. I came up with solution, but I'm not sure that it is correct. Can someone check it? Let's introduce transverse (to the observer) proper speed ...
3
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1answer
126 views

Gravitational waves as information carriers

Is it possible to utilize gravitational waves as a delivery system for information between two observers straddling the event horizon of a black hole? And why ?
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44 views

How to find proper speed (relate to homogeneous cosmic background) of the galaxy by given redshift z and observing angular velocity?

The galaxy moves of the celestial sphere. It is given that proper speed is transverse to the observer and it must to find this speed in the moment of light emission. The motion is in the FLRW ...
0
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1answer
63 views

A simple derivation

During the study of a paper I see that its author defines $$\frac{dh^{ab}}{d\tau}:=h^{am}h^{bn}\frac{dh_{mn}}{d\tau}$$ and from this concludes that ...
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0answers
43 views

Differential equation for speed relate to the homogeneous cosmological background in FLRW metric

How to derive DE for the speed (which relate to the homogeneous cosmological background) of the observer which moves with constant proper acceleration in spatially flat FLRW universe?
4
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0answers
74 views

What are the current experimental restrictions of the possible speeds of gravitation?

Somewhere I read that the Hulse-taylor binary pulsar can not differentiate between competing theories assuming different speeds of gravity. Is it mathematically true in general, that the orbital decay ...
2
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1answer
265 views

Non-linear Dirac equation in Einstein Cartan theory

Can someone explain this Wikipedia article, specifically the section on Einstein-Cartan theory? I have no idea how the equation ...
6
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1answer
238 views

Dirac Lagrangian density in curved spacetime

I'm trying to derive this form of the Dirac Lagrangian density in curved space-time: $$ \mathcal{L}~=~\det\left(e\right)\bar{\Psi}\Bigg ...
3
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0answers
82 views

On the Geroch's argument

During the study of Geroch's argument to prove positive mass theorem, I faced a problem explained below: Suppose $(M,g_{\mu \nu})$ is a four dimensional Lorentzian Manifold and $\Sigma$ is a ...
2
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2answers
349 views

First integral of relativistic Euler-Lagrange equations

Connsider a pseudo-Riemannian ($4$-dimensional) manifold $M$ with a pseudometric $g_{ab}$. The Lagrangian of a free particle in $M$ (in analogy to the flat case) is $$\mathcal ...
4
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1answer
431 views

Lie derivative of Riemann tensor along killing vector ( = 0 )

I'm currently learning the mathematical framework for General Relativity, and I'm trying to prove that the Lie derivative of the Riemann curvature tensor is zero along a killing vector. With the ...
5
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1answer
134 views

Lower limit of the size of the Universe? (WMAP)

The measurement of the WMAP satellite resulted a planar geometry of the universe with a 0.4% uncertainity (http://en.wikipedia.org/wiki/Shape_of_the_universe). If there is a little deviation from the ...
2
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1answer
88 views

What does it mean for a metric to be regular?

A problem in Carroll (a general relativity textbook) asks if a certain metric is regular. What does it mean for a metric to be regular?
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2answers
147 views

How is Space-Time curved?

How does space-time curved by mass/energy if there's nothing to be curved? I haven't seen any satisfying answer.
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2answers
289 views

Einstein equation and scalar field stress-energy tensor

Let's have interaction between gravitational and scalar real fields. For an action of gravitational field in vacuum I add term $S_{m} = \int d^{4}x\sqrt{-g}L_{m}$, where $$ L_{m} = \frac{1}{2}g^{\mu ...
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1answer
117 views

Combined speed of Earth in Space is 1.5 million mph - how much slower is time for Earthlings as a result?

Theres a problem for intergalactic astronauts which is finding their way back to Earth. Combining all the rotational speeds, we are spinning and orbiting the sun, in our solar system which is spinning ...
12
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1answer
371 views

How does one measure space-like geodesics? Or: What is the physical interpretation of space-like geodesics?

In general relativity, time-like geodesics are the trajectories of free-falling test particles, parametrized by proper time. Thus, they are easy to interpret in physical terms and are easy to measure ...
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2answers
339 views

How to show that every Killing vector field is a matter collineation?

Various texts make this claim, but no proof is given. Explicitly, let $L$ denote the Lie derivative. Suppose $L_X g_{ab} = 0$ for some vector field $X$, called a Killing vector field. Suppose that ...