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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Transpose of (1,1) tensor

When we transpose a (1,1) tensor, shall we simply switch the two indices while keeping their upper/lower positions or switch them and also switch their upper/lower positions? In general, would the ...
2
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3answers
781 views

Notation for anti-symmetric part of a tensor

I know that $A_{[a} B_{b]} = \frac{1}{2!}(A_{a}B_{b} - A_{b}B_{a})$ But how can write $E_{[a} F_{bc]}$ like the above? Can you provide a reference where this notational matter is discussed?
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2answers
467 views

Watching something fall into a black hole from far away

I am observing (theoretically) an object falling into a black hole from a safe distance away. My understanding is that from far away it appears as if the body will asymptotically approach the event ...
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3answers
213 views

Speed of light originating from a star with gravitational pull close to black-hole strength?

Imagine you have a star which is on the brink of turning into a black hole. Lets say it is infinitely close to become a black hole, but not there yet. Since there is no event horizon, but a great ...
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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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Bending of light - photon's inertia instead of mass

Using classical mechanics, the formula for gravitational attraction is $$F = G\frac{m_1m_2}{r^2}.$$ This formula does not work for photons, and we need to use Einstein's theory of gravity to ...
3
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1answer
196 views

Local translations in curved spacetime

A global Poincare transformation on a scalar field induces $$\delta(a, \lambda)\phi(x) = [a^{\mu}+\lambda^{\mu\nu}x_{\nu}]\partial_{\mu}\phi(x). \tag{11.46}$$ In curved spacetime we replace $a^{\mu} ...
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1answer
151 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
859 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 ...
0
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1answer
595 views

Space expansion looking like time dilation

Space looks like time depending on the motion of the observer so I was going to ask if space expansion was the same as the unfolding of time, but this was asked on physics.stackexchange before and the ...
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4answers
474 views

At which point of the universe $R_{\mu \nu}=0$ if there is a source of gravitation (point mass)

Schwarschild found his solution to Einstein's field equations for vacuum ($T_{\mu \nu}=0$) by placing a point-mass in the center of origin. Since the Ricci tensor $R_{\mu \nu}$ and the Einstein ...
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2answers
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Layman's explanation and understanding of Einstein's field equations

Most of us have heard of Einstein's amazing equations which describe the universe around us, yet only some of us understand what the equations are actually saying. What are these equations ...
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4answers
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What is the physical meaning of the connection and the curvature tensor?

Regarding general relativity: What is the physical meaning of the Christoffel symbol ($\Gamma^i_{\ jk}$)? What are the (preferably physical) differences between the Riemann curvature tensor ($R^i_{\ ...
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5answers
4k views

How does “warp drive” not violate Special Relativity causality constraints?

I'm talking about this nonsense: http://www.washingtonpost.com/news/post-nation/wp/2014/06/11/this-is-the-amazing-design-for-nasas-star-trek-style-space-ship-the-ixs-enterprise/ Now, I'm aware that ...
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8answers
2k views

How precisely does a star collapse into a black hole?

I think we all heard general statements like "once big enough star burns out there is nothing to prevent the gravitational collapse ending in a black hole". But I can't remember even seeing the ...
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2answers
2k views

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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2answers
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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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4answers
4k views

What is the exact gravitational force between two masses including relativistic effects?

I was wondering if there is a closed-form formula for the force between two masses $m_1$ and $m_2$ if relativistic effects are included. My understanding is that the classic formula $G \frac{m_1 m_2}{...
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3answers
2k 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 ...
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4answers
7k views

Why you need a graviton when you have the higgs boson?

Since I studied General Relativity I had this question running on my mind. As I see it (just taking lectures of Quantum Field Theory right now) "Why you need a gauge boson for gravity when the higgs ...
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5answers
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Could gravity accelerate light? [duplicate]

Gravity causes anything with energy to accelerate toward the source. Black holes, for example, have such strong gravity that they pull in light and don't let any escape. But can acceleration still ...
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4answers
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Can spacetime be non-orientable?

This question asks what constraints there are on the global topology of spacetime from the Einstein equations. It seems to me the quotient of any global solution can in turn be a global solution. In ...
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2answers
847 views

How can we recover the Newtonian gravitational potential from the metric of general relativity?

The Newtonian description of gravity can be formulated in terms of a potential function $\phi$ whose partial derivatives give the acceleration: $$\frac{d^2\vec{x}}{dt^2}=\vec{g}=-\vec{\nabla}\phi(x)=\...
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3answers
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Does a Weak Energy Condition Violation Typically Lead to Causality Violation?

In the answer to this question: ergosphere treadmills Lubos Motl suggested a straightforward argument, based on the special theory of relativity, to argue that light passing through a strong ...
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2answers
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is there a way to split a black hole?

Classically, black holes can merge, becoming a single black hole with an horizon area greater than the sum of both merged components. Is it thermodynamically / statistically possible to split a black ...
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3answers
733 views

Extremal black hole with no angular momentum and no electric charge

A black hole will have a temperature that is a function of the mass, the angular momentum and the electric charge. For a fixed mass, Angular momentum and electric charge are bounded by the extremality ...
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3answers
683 views

Visualizing GR spacetime distortion in 1+1D spacetime instead of 2D space

Usually spacetime distortion due to mass in GR is visualized as a rubber sheet distorted under some massive object, like this: source or as shown in this link. But what has always bothered me is ...
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5answers
946 views

Does GR provide a maximum electric field limit?

Does GR provide a limit to the maximum electric field? I've gotten conflicting information regarding this, and am quite confused. I will try to quote exactly when possible so as not to confuse ...
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5answers
3k views

Naive visualization of space-time curvature

With only a limited knowledge of general relativity, I usually explain space-time curvature (to myself and others) thus: "If you throw a ball, it will move along a parabola. Initially its vertical ...
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1answer
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Angular deficit

If one starts with a flat piece of paper, removes a wedge, and tapes the paper together, you get a cone. The angle of the removed wedge is called the "angular deficit". Now if this is done in 3 ...
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1answer
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Infinitesimal transformations for a relativistic particle

The action of a free relativistic particles can be given by $$S=\frac{1}{2}\int d\tau \left(e^{-1}(\tau)g_{\mu\nu}(X)X^\mu(\tau)X^\nu(\tau)-e(\tau)m^2\right).$$ If we then make an infinitesimal ...
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2answers
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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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6answers
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In GR, why should the spacetime manifold be differentiable?

In general relativity (GR), spacetime is viewed as a differentiable manifold of dimension $D$ with a metric of Lorentzian signature $(-,+,+,...,+)$. My question is why differentiable?
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2answers
268 views

5D Ricci Curvature

As part of a hw problem for a class, we're supposed to be deriving the equivalence given in equation 2.3 of this paper http://arxiv.org/abs/1107.5563. I was wondering if there is some special ...
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9answers
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How does this thought experiment not rule out black holes?

How does the following brief thought experiment fail to show that general relativity (GR) has a major problem in regards to black holes? The full thought experiment is in my blog post. The post ...
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5answers
858 views

How are the comoving coordinates NOT a prefered reference frame?

Physics me this: The equivalence principle has rigorous physical definitions that say, for one, that the laws of physics are the same in all inertial reference frames. This is to say that the ...
2
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2answers
949 views

How long does it take for a black hole to form?

The well-known fable of an astronaut sending signals out to an external observer while falling toward an event horizon states that the time lapse between such signals becomes greater even if in the ...
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6answers
118k views

How exactly does time slow down near a black hole?

How exactly does time slow down near a black hole? I have heard this as a possible way of time traveling, and I do understand that it is due in some way to the massive gravity around a black hole, but ...
11
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2answers
3k views

Why is light described by a null geodesic?

I'm trying to wrap my head around how geodesics describe trajectories at the moment. I get that for events to be causally connected, they must be connected by a timelike curve, so free objects must ...
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2answers
3k 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 ...
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2answers
151 views

What kind of fundamental interaction is gravitation?

Einstein showed that gravitation is not a force but a effect caused by curvature of space time. Then why does theories of quantum gravity treats gravitation as one of fundamental force?
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4answers
2k views

Inertial frames of reference

I'm struggling with the notion of an inertial frame of reference. I suspect my difficulty lies with the difference between Newtonian and relativistic inertial frames, but I can't see it. I've read ...
2
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2answers
705 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 ...
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3answers
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Mechanism for the gravitational field generated by photons

This question follows from a schooling I received in this thread. I figured that photons do not interact with gravity, except when they've spontaneously converted into a particle-antiparticle pair. ...
12
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3answers
568 views

Which clock is the fastest inside an accelerating body?

The picture shows an accelerating spaceship with two clocks inside it. It is so far away from all other bodys that gravity is of no importance. Will the bottommost clock be slower than the topmost ...
10
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1answer
676 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
1k views

Is there an energy density limit in GR?

I am speaking about GR with classical fields and energy. One question, spread over three increasingly strict situations: Is there an energy density limit in GR? (literally, can the energy density ...
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2answers
2k views

What is the likelihood of ever discovering the graviton?

How would one look for and confirm existence of a graviton? Someone was speaking to me about perhaps one day discovering the graviton, but to me it seems unlikely, although I'm young and essentially ...
6
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1answer
778 views

When a neutral star with a magnetic field collapses to form a black hole, what happens to the magnetic field?

By the no-hair theorem, black holes are only characterized by mass, charge and angular momentum. If the star is neutral, the black hole will have only mass and angular momentum - and therefore it ...
6
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3answers
528 views

Charging a black hole?

What would happen if we have a black hole and we start shooting at it a single electron at a time, and go on doing it forever? Would the electrons start to bounce off eventually?