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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Are there continuous spacetime events?

What is the formal definition of an event? According to Wikipedia, "an event is a point in spacetime (that is, a specific place and time) and the physical situation or occurrence associated with it." ...
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1answer
87 views

Time independent Kerr metric

The Kerr metric expressed in terms of polar coordinates $r,\theta,\phi$, such that $x = r\sin(\theta)\cos(\phi)$, $y = r\sin(\theta)\sin(\phi)$, $z = r\cos(\theta)$. Then the Kerr metric is given as ...
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52 views

Galileo 5 and 6 satellites testing gravitational time dilation

In today's Guardian there an article titled "Satellite launch accident provides unexpected test of Einstein’s theory" - ...
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570 views

G4v Gravity Theory: Why does this get rid of Dark Energy?

Earlier this year, Carver Mead of CalTech published a paper which seems to be garnering a lot of attention: http://arxiv.org/abs/1503.04866 http://www.npl.washington.edu/AV/altvw180.html ...
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1answer
76 views

Numerical relativity in causally pathological spacetimes

To perform numerical relativity simulations one almost universally adopts the so called "3+1" approach: spacetime is divided up into spacelike slices, each representing a "moment in time". After some ...
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3answers
147 views

From the photons perspective

Probably been answered but couldn't find the answer. From the perspective of a photon: - For the photon to travel from body A to body B would take 0 secs. - The universe would be one point in ...
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1answer
284 views

Does frame dragging apply to linear motion?

Firstly I will admit I do not understand the real cause of rotational frame dragging and some of the math heavy explanations are too complicated for me. To me frame dragging looks like unsubstantiated ...
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2answers
61 views

Light and Gravity

The gravitational force does not affect the speed of light rather affects the frequency of light (hence light changes colors, red to blue and vice-versa). I know this has been verified but I have ...
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0answers
42 views

Sources for black hole geodesic orbits

I am looking for good sources that discuss both Kerr and Schwarzschild particle orbits (geodesics). Most sources write down the geodesic equations, constants of motion and the Hamiltonian, but do not ...
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1answer
136 views

Is max speed of causality (light) proven experimentally?

Is it possible to have an alternative theory which is consistent with experiments supporting GR, but which doesn't mandate a speed limit on causality? In other words, I understand there is ...
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0answers
27 views

Are only measurements registered as events?

When we measure an electron or some other system behaving quantum mechanically, we observe something. Now, this can be called as an event in relativity terms meaning if we live in 1-D spacetime, only ...
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1answer
63 views

Is there a way to write the Lorentz force in terms of one field, $L$, and one charge, $X$?

I have heard that physicists like to write electromagnetism as one force (the Lorentz force) and define it as $\vec{F_L}\left(q, \vec{v}, \vec{E}, \vec{B}\right) = q\left(\vec{E} + \vec{v} \times ...
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1answer
55 views

Show that $R_{\mu\nu}=C g_{\mu\nu}$ from the vacuum Einstein equation with a nonzero $\Lambda$ [closed]

If I begin with the vacuum field equation with a nonzero cosmological constant: $$R_{\mu\nu}-\dfrac{1}{2}g_{\mu\nu}R+g_{\mu\nu}\Lambda=0$$ How can I show that $$R_{\mu\nu}= ...
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1answer
177 views

Finding diffeomorphism given vector fields [closed]

Given a vector field how do you find the associated diffeomorphisms? Say I am given a vector field in Minkowski space $$\xi = x \frac{\partial}{\partial t} + t \frac{\partial}{\partial x}.$$ How do ...
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0answers
38 views

Gibbons-Hawking Variation

I know there already exist some questions about this and some very good answers. However, I am still having trouble understanding one part of the calculation. The GHY term is given by ...
1
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1answer
113 views

What is the sum of the angles of a triangle on Earth orbit?

Gauss went out and measured triangles made up of mountain peaks to show that the angles sum up to 180 degree. However, general relativity leads to non-Euclidian space and I would like to get a better ...
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0answers
31 views

Non-time orientable quotient of de Sitter space

Examples of non-time orientable spacetimes are pretty scarce, but it seems the big one is quotients of de Sitter space of the form $dS^n/\pi_1$, where $\pi_1$ is some subgroup of the isometries of de ...
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4answers
400 views

What is the general relativity explanation for why objects at the center of the Earth are weightless?

The idea that as you move through the earth you get a symmetric cancelling of gravitational acceleration which approaches zero acceleration due to gravity at the center of the earth makes a lot of ...
2
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0answers
78 views

Two dimensional spacetime and the Gauss Bonnet theorem

Generally two dimensional spacetimes are deemed to be static, as the Gauss Bonnet theorem implies that the Einstein Hilbert action would be a constant independent of $g$. But as far as I can tell, ...
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0answers
60 views

Which property do the word Pressure refer to in General Theory of Relativity?

In this course by MIT Alan Guth while delivering the lecture stated " Both Pressure and Energy densities can produce gravitational fields. Negative pressure creates repulsive gravity and positive ...
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5answers
229 views

Is boundary well defined if variation of metric don't vanish on the boundary?

Suppose that you want to calculate the variation $\delta S$ of an action induced by some arbitrary variation $\delta g_{\mu \nu}$ of the spacetime metric : \begin{equation} S = \int_{\Omega} ...
5
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1answer
231 views

An argument that massive particles don't redshift?

I start with the spatially flat FRW metric in conformal co-ordinates: $$ds^2=a^2(\eta)(d\eta^2-dx^2-dy^2-dz^2)$$ This metric has the following non-zero Christoffel symbols: \begin{eqnarray} ...
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2answers
79 views

If curved paths imply that the vehicle is accelerated, how come do we assume that light gets curved whilst its speed is constant?

I don't understand how we can accept these two sentences at the same time: Light speed is constant, therefore experiences no acceleration. On the presence of a gravitation field, light path is ...
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5answers
661 views

What are some ways to justify the Einstein field equations?

Since they are a postulate of general relativity, it is not really possible to "derive" the Einstein field equations $$R_{ab} + \left(\Lambda - \frac{1}{2}R\right)g_{ab} = -8\pi T_{ab}$$ in any very ...
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0answers
99 views

Can a Set of “Maxwell's Equations” for Newtonian Gravitation be Derived from Newton's Force + Special Relativity?

When I learned about electromagnetism in my first year of undergraduate school, Maxwell's equations were derived roughly in the following way (see also here or in [1]): Gauss's law for a static ...
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5answers
161 views

Local inertial frame

In general relativity we introduce local inertial frames to be such frames where the laws of special relativity holds. Let $\xi^{\alpha}$ the coordinates in the local inertial frame, so we get ...
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2answers
83 views

Form of Spin Four-vector

The spin angular momentum of a gyro is represented, in special and general relativity, by a spin four-vector $S^{\mu}$. In the rest frame of the gyro, the spin four-vector takes the form ...
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0answers
70 views

Integral curves in null hypersurfaces [closed]

Let be $(M^{n+1},g)$ a spacetime (Lorentz manifold, connexe and time-oriented), $n\ge 2$, and $S\subset M$ a null hypersurface (codim $S=1$ and the restriction of $g$ to each tangent space $T_p S$ ...
3
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1answer
99 views

Thought experiment on space curvature due to gravity

Let's say you built a huge, straight rigid beam out in space, far from the sun (outside the orbit of Pluto). It is very long, say 200,000 miles long, but can be very narrow. Then you move it to the ...
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1answer
62 views

Time dilation on Satellites due to GR

I am trying to determine the time dilation onboard a satellite (say GPS @ 20,000km) w.r.t an observer on the earth. I have already determined the special relativity component using: $$ t' = ...
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0answers
10 views

DGP model, minus one dimension

Is there a name for a theory like the DGP model, but with one fewer dimension? That is, a theory whose action consists of the 4D Einstein Hilbert action at long distances, and the 3D one at small ...
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0answers
52 views

How does the expanding of null hypersurface orthogonal geodesic congruence imply a particular result?

Sorry that I do not know how to summarize my problem in the title. First, please go to the website here (free access, even though it looks otherwise) to download the paper done by R. Sashs on ...
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1answer
47 views

how is the state parameter determined?

For radiation, dark energy and dust the pressure and energy density are related, respectively, by: $p=\frac{1}{3}\rho$ $p=-\rho$ $p=0$ My question is why? How does one show that this is how ...
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0answers
32 views

Expression for the energy in the limit case of weak gravitational field

I'm trying to solve the following problem of General Relativity. Consider a particle of mass $m$ which moves following a geodesic in a space-time with metric $$ ds^2 = - ...
81
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10answers
13k views

If gravity isn't a force, then why do we learn in school that it is?

I have studied some of Einstein's Theory of General Relativity, and I understand that it states that gravity isn't a force but rather the effects of objects curving space-time. If this is true, then ...
3
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1answer
455 views

Are some gravitational wavelengths forbidden by causality?

Consider a gravitational wave in linearized gravity $d_{\mu \nu}(X_{\eta}) = D_{\mu \nu} e^{i X_{\eta} K^{\eta}}$ with $K^{\eta} = (-\omega t, \textbf{k})$. Let $d=| \textbf{D}|$ the scalar maximum ...
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0answers
82 views

Gravity's force on space

Here is a quote from Brian Greene, The Fabric of the Cosmos: Space, Time, and the Texture of Reality, p. 273: “The early universe provided an arena in which gravity exerted its repulsive side with ...
4
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3answers
297 views

Is there proof gravity bends space or is it just the most convenient explanation?

I have read this sentence in an article: The theory [of general relativity] holds that gravity is geometry: particles are deflected when they pass near a massive object not because they feel a ...
4
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0answers
68 views

Trajectories in AdS

On page 2 of this paper (http://arxiv.org/abs/1106.6073), Maldacena explains (and has a very nice picture) showing the trajectories that a timelike and null particle would take in AdS space. Of ...
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1answer
78 views

Operational Definition of Reference Frame in General Relativity

Most treatments of GR begin with the assumption that spacetime is a pseudo-Riemannian manifold (or, sometimes, that it is a more general manifold). But this entails quite a few tacit assumptions about ...
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0answers
44 views

What are the definitions and the differences between string “background” and string “vacuum”?

In cosmology one studies perturbations around FRW metric classically (pure GR, we say that we perturbe the FWR "background"). In QFT we have perturbation theory quantistically (we expand around a ...
3
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0answers
113 views

What do quantum theory and general relativity have in common? [closed]

What areas of commonality are there between quantum theory and general relativity? Is it even possible to use the the two when calculating the same physical behaviour? Is there a correlation between ...
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3answers
64 views

Suppose I apply a force to a ball that can then only be slowed down by gravity or, perhaps, relativity. What happens to the ball? What would I see? [closed]

Suppose I'm on planet Earth. I have a ball that, once set in motion, can only be slowed down or stopped by gravity. What will happen to this ball? What would I (an observer on Earth) see? Here's what ...
4
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1answer
114 views

Life of a photon in gravity?

I have a simple thought experiment and I am not sure about the answer: What would happen to a photon that is emitted by an excited hydrogen in an otherwise empty universe? Would gravity of the atom ...
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0answers
75 views

Does rest mass increase in the FRW metric?

The flat FRW metric can be written in conformal co-ordinates: $$ds^2=a^2(\eta)(d\eta^2-dx^2-dy^2-dz^2)$$ where $\eta$ is conformal time. Let us assume that $a(\eta_0)=1$ when $\eta_0$ is the present ...
3
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1answer
120 views

Tensor decomposition

I came across what a Physicist called "decomposing a tensor with respect to a congruence", something I simply cannot grasp. I searched a lot and I couldn't find any reference on that. I know that ...
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0answers
31 views

Black Holes should take infinite time to form with the increase in mass to form one [duplicate]

How can black hole form because as the density begins to increase gravity also start to increase and time starts to slow. wouldn't it take infinite time to form a black hole. how can anything fall ...
2
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0answers
47 views

Quasilocal stress tensor

I have been reading through the paper hep-th/9902121 and have a few questions about the first five lines of the introduction: 1) "In a generally covariant theory, it is unnatural to assign a local ...
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1answer
41 views
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1answer
155 views

Can space have angular momentum that can be transfered to/from physical objects?

This is related to another question that discusses whether space can have momentum and energy. Apparently gravitational waves or ripples in spacetime is how space stores and transfers energy/momentum. ...