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 gravitational time dilation and the time dilation in special relativity independent?

There are two kinds of time dilation: One because the other clock moves fast relative to me (special relativity). Another one because the other clock is in a stronger gravitational field (general ...
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2answers
3k views

What is the definition of a timelike and spacelike singularity?

What is the definition of a timelike and spacelike singularity? Trying to find, but haven't yet, what the definitions are.
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3answers
3k views

Value of the Hubble parameter over time

There is something I don't understand about the Hubble parameter $H$, as it seems to clump two concepts together that I can't quite unify in my head. On the one side, we have $$V = D H$$ which means ...
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6answers
3k views

Why can light (photons) bends in a curve through space without mass? [duplicate]

I've heard that light can form a curve if they travel near high-mass stars or even a black hole with strong gravity. Which is according to this Newtonian formula $$\large ...
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3answers
569 views

Clarifying what metric counts as flat space

In (2D) Cartesian coordinates, the Euclidean metric... $$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$ ...is flat space. If the diagonal elements are exchanged for other real numbers ...
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2answers
728 views

Finding the metric tensor from the Einstein field equation?

I have have set my self a challenge to learn all the maths behind the Einstein field equation (EFE), and from reading it seems that the Metric tensor is the thing we are trying to find (from the 10 ...
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4answers
950 views

Lagrangian for relativistic massless point particle

For relativistic massive particle, the action is $$S ~=~ -m_0 \int ds ~=~ -m_0 \int d\lambda ~\sqrt{ g_{\mu\nu} \dot{x}^{\mu}\dot{x}^{\nu}} ~=~ \int d\lambda \ L,$$ where $ds$ is the proper time of ...
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2answers
195 views

The speed of light as it approaches a massive body

No matter how fast you go, you will aways perceive the speed of light as constant. Taking that as a fact, the special relativity theory was formulated. Now, for what I understand about general ...
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1answer
498 views

A clock in freefall

Time dilation calculated using Schwarzschild metric for a non rotating spherical body is: $$t_0=t_f\sqrt{1-\frac{2GM}{rc^2}}$$ For such a non rotating spherical body, what would the time dilation of ...
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2answers
765 views

What is the correct formula for gravitational time dilation for a satellite in a circular orbit?

In the Wikipedia article on Gravitational Time Dilation I see two formulae for the gravitational time dilation. One contains $\sqrt{1 - r_0/r}$ but the other $\sqrt{1 - 1.5 r_0/r}$. What formula ...
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2answers
941 views

Time Dilation in Orbits in the Schwarzschild Metric

I am wondering if there exist closed form-expressions for the time dilation experienced by an observer in different orbits around a Schwarzschild black hole, outside the event horizon, relative to ...
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1answer
796 views

Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory

In Einstein-Cartan gravity, the action is the usual Einstein-Hilbert action but now the Torsion tensor is allowed to vary as well (in usual GR, it is just set to zero). Variation with respect to the ...
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5answers
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Newton's Bucket

Newton's Bucket This thought experiment is originally due to Sir Isaac Newton. We have a sphere of water floating freely in an opaque box in intergalactic space, held together by surface tension and ...
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5answers
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Is the total energy of the universe constant?

If total energy is conserved just transformed and never newly created, is there a sum of all energies that is constant? Why is it probably not that easy?
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3answers
3k views

How strong were the gravitational waves that LIGO detected at the source?

Congrats to the LIGO team on the announcement of their discovery of gravity waves! The articles I've read say that the distortion we see here is much smaller than a proton. What about at the source? ...
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1answer
792 views

In what limit does string theory reproduce general relativity? [duplicate]

In quantum mechanical systems which have classical counterparts, we can typically recover classical mechanics by letting $\hbar \rightarrow 0$. Is recovering Einstein's field equations (conceptually) ...
11
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2answers
775 views

How (or why) equivalence principle led to Einstein field equations?

If equivalence principle was origin of general relativity what was the process that this principle led Einstein to developed his theory of general relativity?
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2answers
824 views

Is spacetime simply connected?

As I've stated in a prior question of mine, I am a mathematician with very little knowledge of Physics, and I ask here things I'm curious about/things that will help me learn. This falls into the ...
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1answer
713 views

What happens to an embedded magnetic field when a black hole is formed from rotating charged dust?

Black holes have no-hair so there are uniquely specified by a mass, charge and angular momentum. Imagine a cloud of charged rotating dust. There will be a magnetic field associated with the current ...
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1answer
968 views

If two ultra-relativistic billiard balls just miss, will they still form a black hole?

This forum seems to agree that a billiard ball accellerated to ultra-relativistic speeds does not turn into a black hole. (See recent question "If a 1kg mass was accelerated close to the speed of ...
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3answers
8k views

Similarity between the Coulomb force and Newton's gravitational force

Coulomb force and gravitational force has the same governing equation. So they should be same in nature. A moving electric charge creates magnetic field, so a moving mass should create some force ...
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1answer
357 views

How is it that distortions in space can be measured as distances? [duplicate]

Imagine yourself and anything you're able to perceive to be drawn onto a rubber band. Any means of determining distances would be affected by the stretching/contracting of the rubber band. The ...
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2answers
610 views

Introduction to relativity books [duplicate]

Possible Duplicate: Getting started general relativity I am an engineer who loves to read science fiction books especially when there's more science than fiction but usually I see that I ...
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1answer
1k views

Voyager local time dilation (caused by gravity)

Voyager I, as an example, taking account gravity and setting aside effects of speed as cause of time dilation. If it is very far away from earth and sun, so then there must be a difference in the ...
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1answer
1k 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 ...
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1answer
652 views

What makes us think we can actually detect gravitational waves?

This refers to the discussion about gravitational waves for the YouTube video LIGO Gravitational Wave Observatory. I have two questions: When the gravitational wave passes through the space where ...
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2answers
763 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, ...
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442 views

Another faster-than-light question

Imagine we have something very heavy (i.e supermassive black hole) and some object that we can throw with 0.999999 speed of light (i.e proton). We are throwing our particle in the direction of hole. ...
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2answers
226 views

How does the friedmon solution to Einstein's equations resolve paradox of bounded infinities?

This article talks about a potential explanation of dark matter based on something called the "friedmon." I have no interest in the dark matter question, but the article has made me curious about ...
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1answer
142 views

Equivalence principle for test fields

My question is very simple. We all know that, for a test particle(classical) in a gravitational field, the motion is only determined by the geodesic lines(let's forget about the initial conditions for ...
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2answers
328 views

Why doesn't the light get out?

You're standing on a gedanken planet holding a laser pointer straight up. The light doesn't curve round, or slow down as it ascends, or fall down. It goes straight up. Now I wave my magic gedanken ...
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1answer
661 views

How much extra distance to an event horizon?

How much extra distance would I have to travel through space to get from Earth to a stellar mass event horizon? (compared to the same point in space without a black hole)
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3answers
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Gravity as a gauge theory

Currently, (classical) gravity (General Relativity) is NOT a gauge theory (at least in the sense of a Yang-Mills theory). Why should "classical" gravity be some (non-trivial or "special" or ...
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4answers
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Is topology of universe observable?

There is an idea that the geometry of physical space is not observable(i.e. it can't be fixed by mere observation). It was introduced by H. Poincare. In brief it says that we can formulate our ...
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Why does dark energy produce positive space-time curvature?

My understanding is that dark energy, or equivalently a positive cosmological constant, is accelerating the expansion of the universe and I have read that this gives empty space-time positive ...
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3answers
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Nature of gravity: gravitons, curvature of space-time or both?

General relativity tells us that what we perceive as gravity is curvature of space-time. On the other hand (as I understand it) gravity can be understood as a force between objects which are ...
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2answers
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How can I read off the fact that gravity is associated with spin-2 particles from the Einstein-Hilbert action?

I have often heard that the gravitational field has spin $2$. How can I read the spin of the field from the Einstein-Hilbert action $$S=\int \! \mathrm{d}^4x \,\sqrt{|g|} \, \mathcal{R} \, \, \, ?$$
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Why do objects follow geodesics in spacetime?

Trying to teach myself general relativity. I sort of understand the derivation of the geodesic equation ...
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1answer
1k views

Second Law of Black Hole Thermodynamics

I've been looking for a satisfying proof of this, and can't quite find it. I read the brief proof of the black hole area theorem in Wald, which is similar, but doesn't quite come down to the actual ...
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8answers
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What is a rocket engine thrusting against in space?

I know Newton's third law of motion might be the answer for this but still I am wondering how the rockets could thrust in the empty space and move in the opposite direction. I guess an astronaut ...
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2answers
11k views

What is the escape velocity of a Black Hole?

The escape velocity of Earth is $v=\sqrt{\frac {2GM}{R}}$, where $M$ is the mass of the Earth and $R$ it's radius (approximating it as a sphere), and is much less than light speed $c$. But I want to ...
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7answers
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Physical meaning of non-trivial solutions of vacuum Einstein's field equations

According to Einstein, the space-time is curved and the origin of the curvature is the presence of matter i.e. the presence of the energy-momentum tensor $T_{ab}$ in Einstein's field equations. If our ...
11
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2answers
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Explicit Variation of Gibbons-Hawking-York Boundary Term

Are there any references that present the explicit variation of the Hilbert-Einstein action plus the Hawking-Gibbons-York boundary term, and demonstrate the cancellation of the normal derivatives of ...
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1answer
1k views

Potential Energy in General Relativity

I often hear about how general relativity is very complicated because of all forms of energy are considered, including gravitation's own gravitational binding energy. I have two questions: In ...
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2answers
1k views

Is special relativity a special case of general relativity, qualitatively?

Since Einstein name his theory Special Relativity and General Relativity, there should be some expected relationship between them, particularly "Special Relativity" being a special case of the more ...
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2answers
656 views

What is the meaning of the “expansion of space”?

When we say that "the space between galaxies is expanding," what do we really mean? For instance, if I think of space as being a Cartesian grid, then when space expands should I think of it as adding ...
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1answer
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How do Einstein's field equations come out of string theory?

The classical theory of spacetime geometry that we call gravity is described at its core by the Einstein field equations, which relate the curvature of spacetime to the distribution of matter and ...
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2answers
2k views

Have red shifted photons lost energy and where did it go? [duplicate]

I think the title says it. Did expansion of the universe steal the energy somehow?
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5answers
671 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?
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263 views

The arrow of time and the cosmology of a black hole interior

When solving the Einstein field equations in Schwarzschild metric for an observer falling into a black hole the radial coordinate r of the black hole and time t switch roles in the equations when ...