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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Using metric tensor to contract

Can the metric tensor also contract the indices in the $$\epsilon^{\tau\lambda\mu\nu}~?$$ For example, if we have ...
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Influence of spacetime curvature on electromagnetic wave propagation

Classical physics assumes that spacetime is evenly distributed in the sense that Coulomb's Law predicts that a charged particle will create a spherically symmetric electric field around its location. ...
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41 views

Do clocks measure conformal time (new argument)?

Assuming the spatially flat FRW metric for simplicity: $$ds^2=c^2dt^2-a(t)^2(dx^2+dy^2+dz^2)$$ where $t$ is cosmological time, $a(t)$ is the scaling factor and $x,y,z$ are co-moving spatial Cartesian ...
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Is an event horizon absolute to all observers?

Recently I had discussion whether the event horizon of a black hole is absolute or relative to different (outside) observers. Does someone just 1m above the horizon perceive it at the same depth as ...
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1answer
26 views

The significance of the pressure term within the momentum-energy tensor [duplicate]

EDIT: this question is based around my notion regarding the possible role of potential energy in the momentum energy tensor T$_{\mu\nu}$, The answer below resolves the question and I have deleted ...
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55 views

Suggestions for GR solved problems books

Study Topic: General Relativity I'm looking for a recommendation for either a dedicated problems and solved solutions book or, failing that, a textbook with a separate comprehensive solutions ...
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43 views

Contraction of Kronecker delta = 4 [duplicate]

This suggests, as a shortcut notation, the concept of lowering indices; from any vector we can construct a (0, 1) tensor defined by contraction with the metric: $$A_\nu ≡ g_{\mu\nu}A^\mu$$ so that ...
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1answer
37 views

Confusion about two forms of connection coefficients

I am new to GR. In one book I found that the connection coefficient expression is given by $$ \Gamma^\mu_{\nu\lambda} = -\frac{1}{2} g^{\mu\rho} (\partial_\nu g_{\lambda\rho} + \partial_\lambda ...
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“Shortest” path in general relativity

My professor in mechanics course sneakily teach us some basic idea of general relativity. Which one of the basic assumption is particle walks in shortest world line. I understand shortest path in ...
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1answer
43 views

How much is time slowed down inside a planet or star?

An answer to What would be the rate of acceleration from gravity in a hollow sphere? states "that according to General Relativity time passes more slowly inside a hollow massive sphere than it does ...
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1. How is Newtonian calculations compatible with curved spacetime? and 2. multiple competing reference frames for gravity [duplicate]

Since spacetime is curved, and since the measurement of distance on a curve is along a geodesic, how is it that Newtonian (non-curved) physics can be successfully deployed to calculate distances, ...
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21 views

Vector fields corresponding to null geodesic congruences in general relativity

I'm working in Minkowski space, and I'm considering some 2D surface, $S$. On each point of the surface, I've computed a null vector, $k^a$, which is orthogonal to it. There will be a unique null ...
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1answer
80 views

Can Bosons couple to gravity? Why do we need vielbein?

It is said that In theories such as Supergravity where there are fermions coupled to gravity, one must use an auxiliary quantity, the frame field (vielbein). In supergravity, can a boson be coupled ...
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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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1answer
45 views

Spinning micro blackholes power conversion

In the context of energy extraction of spinning black holes, there are two known mechanisms: the Penrose process and the Blandford-Znajek process. The former relies on fragmentation of accreting flow, ...
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2answers
113 views

How does warped space actually look (visually)?

Recently, I was reading about space warping due to extreme gravity and at speeds approaching c, but in books, they always show space in 2D and depth to show space distortion. I was wondering how ...
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50 views

Can't derive FRW Christoffel symbol [on hold]

I'm trying to confirm that the $\Gamma^1_{01}$ Christoffel symbol of the FRW metric is $\dot{a}/a$. I have the FRW metric: $$ds^2=-dt^2+a(t)^2\left[\frac{dr^2}{1-kr^2}+r^2(d\theta^2+\sin^2\theta\ ...
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Does fixing a metric component have anything to do with diffeomorphism invariance?

It is well known that in general relativity, the metrics $g_{\mu \nu}$ and $g_{\mu \nu} + \epsilon L_\xi g_{\mu \nu}$ are physically equivalent, where $L_\xi g_{\mu \nu}$ is the Lie derivative of the ...
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1answer
52 views

Uncertainty principle within a neutron star or black hole

Take the time-energy uncertainty relation, $\Delta$$E$$\Delta$$T$$\ge$$\hbar/2$. My question is based on my confusion about the effect this relation may have within the interior of a highly ...
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1answer
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Does Birkhoff's theorem apply to rotating collapsing stars?

Birkhoff's theorem states that every spherically symmetric vacuum solution to $R_{\alpha\beta} = 0$ is static, which greatly assists in the solution to the Schwarzschild solution by eliminating time ...
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A Relativity question about radial acceleration? [duplicate]

How do you calculate the radial acceleration of a stationary observer in the Schwarzschild coordinates? I have calculated the 4-velocity and 4-acceleration but not sure how to proceed?
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2answers
161 views

Relativity question about 4-velocity

Given a 4-velocity $u^0$, how do you find $u_0$? Do you use $u_{\alpha}u^{\alpha} = -1$?
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1answer
27 views

When does light reach a shell observer in Schwarzschild metric?

I am trying to simulate the trajectory of light in the Schwarzschild metric (as seen by a far away observer) with fixed $\theta = \pi/2$. According to my source (Chapter 18, section 18.5) the ...
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Tangent Vector Field from Metric

Question: Starting from an arbitrary spacetime metric, how does one obtain a tangent vector field? (We might need to assume certain geodesic congruences but my understanding is very limited.) Build ...
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Question about wormholes with ends moving relative to one another [duplicate]

Let's say the two ends A and B of a wormhole are moving relative to one another. If I stick a starship halfway into end A of the wormhole, does the part of the starship that sticks out of end B move ...
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1answer
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Do we weigh more when standing near massive buildings?

I'm very new to the concepts of SR/GR and curvature of spacetime. My understanding is that the bending of spacetime is the causation of gravity, and that matter is the causation of the bending of ...
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A general relativity question about the Einstein equations?

Assuming a Robertson-Walker metric to describe homogeneous and isotropic cosmological models, Einstein equations with cosmological constant reduce to these 3 non-linear ordinary differential equations ...
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Does General Relativity imply loops in space?

Everyone who has been interested in modern science has heard explanations (certainly simplifications) of general relativity, mostly that space is curved. The analogy with a rubber sheet is popular. In ...
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A General Relativity question? [closed]

The line element for the outside of a spherical star\black hole is given by the Schwarzchild line element : $$-c^{2}d\tau^{2} = ds^{2} = -\left(1-\frac{2m}{r}\right)c^{2}dt^{2} + ...
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2answers
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Is the time “direction” in General Relativity equivalent to a spatial volume [on hold]

Most G.R.textbooks introduce time as an extra dimension, i.e. -ict. (see EDIT below for clarification). So although I can not mentally imagine this, I think of it as an extra line, "orthogonal" to the ...
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0answers
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Killing vectors of AdS space with the metric given in Poincaré coordinate [closed]

I am trying to solve this problem: Find the Killing vector correspond to the symmetry of the scale invariant for the AdS(n+1) $$ (t,{\bf x}) \rightarrow (at, a{\bf x}) $$ when the metric of the AdS ...
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20 views

DGP brane world model

Can we think of interaction between dark energy and dark matter within the brane in DGP model like in case of GR?
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1answer
64 views

What are Einstein constraint equations?

Yesterday, I met Einstein constraint equations in a thesis? I failed to understand them. Do they have physical meaning? And what do they "constrain"?
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Momentum conservation in FRW spacetime

The spatially flat FRW metric in Cartesian co-ordinates is given by: $$ds^2 = -dt^2 + a^2(t)(dx^2 + dy^2 + dz^2)$$ As I understand it, since the metric does not depend on the spatial co-moving ...
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Seeing in shell reference frame in general relativity

I'm trying to understand how an observer in a shell reference frame sees an object (star) near a black hole. I'm specifically trying to understand the equation: $$\tan \theta_{shell} = ...
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2answers
59 views

Schwarzschild metric: motivations and applications in physics

I have a mathematical background and I have just derived the expression of the Schwarzschild metric. Now I was wondering what were the motivations and applications in physics of this metric. Any info ...
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100 views

$AdS_2$ Black Hole [on hold]

I know that $AdS_2$ black hole has the following metric: $$ ds^2=(r^2-a^2)dt^2+\frac{dr^2}{r^2-a^2}.\tag{1} $$ Here $a$ is constant. On the other hand I am regularly facing with the following ...
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Is macroscopic causality an issue in the context of certain quantum experiments?

In order to formulate my question properly I need to explain a few things. Cramer_Herbert Zych_Brukner Reference 1. - John Cramer, Nick Herbert, "An Inquiry into the Possibility of Nonlocal Quantum ...
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1answer
48 views

Laplace-Beltrami vs d'Alembert operators in flat vs curved space-time

I am confused with the difference between Laplace-Beltrami (LB) and d'Alembert operators in flat/curved space-time. d'Alembert operator in flat space-time (Minkowski) is defined as $$\Box= ...
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2answers
49 views

Relativistic rigid motion

In Bryce DeWitt's Lectures on Gravitation, in eq. 2.7 on page 25 when he describes the rigid motion of a continuum he states $$x^\mu(\xi,\tau)=x^\mu(0,\sigma)+\xi^in^\mu_i(\sigma)\,\,\,(i=1,2,3) \, ...
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1answer
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Is there a way to describe a point in time that accounts for time dilation? [closed]

After watching the movie "Interstellar", I had this thought that a traditional way to describe a point in time might not account for time dilation. What I mean is that if time flows at a different ...
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1answer
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Observers in different planets viewing each other

I'm a newbie to relativity, so If the question is idiotic, please excuse me. My question is, as in Interstellar movie suppose one person is sitting in a planet A whose 1 hour equals to 6 years of ...
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1answer
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Fibre bundles and space-time

I'm having some trouble understanding the concept for this more than likely due to my lacking mathematical background. I am currently reading Roger Penrose's The Road to Reality page 394 ...
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2answers
104 views

Intuitive understanding of the elements in the stress-energy tensor

There is an image in the Wikipedia about the stress-energy tensor: I have a rough understanding of the stress tensor: you imagine cutting out a tiny cube from the fluid and form a matrix out of the ...
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1answer
51 views

The divergence of the Stress Energy Tensor

I have been studying general relativity and I have often seen in textbooks that the divergence of the stress energy tensor is zero. $$T^{\mu\nu}_{;\nu} = 0$$ but is it possible to contract and ...
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1answer
87 views

Carroll's derivation of the geodesic equations [duplicate]

In Carroll's derivation of the geodesic equations (page 69, http://preposterousuniverse.com/grnotes/grnotes-three.pdf), he starts with ...
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Computer simulation/visualization of a ray of light passing near a massive object

I'd like to write a computer program that simulates and visualizes the trajectory of a ray of light as it passes near a massive object (e.g., neutron star). In other words, I'd like to model light ...
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Understanding gravitational time dilation / Schwarzschild metric

I've had a look at the answers to these sorts of questions already, but feel like I'm still missing something. Starting with this question, and this one and even this one here. I'm looking at this ...
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2answers
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Can gravity be interpreted as the acceleration of spacetime towards an object? [closed]

Greetings StackExchange! We were having a conversation with a peer about stupid ways of interpreting theories. We would go to and fro with an interpretations, but we would always find a way to ...
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2answers
101 views

“Derivation” of Minkowski metric?

Is there a deeper meaning behind the the Minkowski metric? Does it just come from the SR formulae? Or is there some deeper geometrical meaning, maybe in the context of GR?