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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Is critical mass of fissile material the same in gravitational fields with different force?

Let's take plutonium-239 for example. $10\, Kg$ (sphere $9.9\, cm$) need for a nuclear reaction. Are we talking about these numbers in Earth environment with $\approx 9.8\, m/s^2$ gravitational ...
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0answers
23 views

Lorentz surfaces, conformal metrics and eigenvalues

From what I understand of Lorentz surfaces (spacetimes of dimension 2), it seems that, according to Kulkarni's theorem, two reasonable enough Lorentz surfaces (I am only interested in surfaces with ...
5
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1answer
197 views

Geometric formulation of the equivalence principle

Let $(M,g)$ be a $4$-dimensional Lorentzian manifold. It is well know that given $(U,\psi=(x^1,\ldots,x^4))$ local chart around some $p\in M$, it is posible to find a change of coordinates given by $(...
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1answer
27 views

Interpretation of the operation $v^\alpha \nabla _\alpha v^\mu$

In general relativity, we can write the geodesic equation as a contraction $v^\alpha \nabla _\alpha v^\mu = f(\lambda)v^\mu$ along a path defined by coordinates $x^\mu(\lambda)$, and where $v^\mu = \...
2
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1answer
628 views

The role of the affine connection the geodesic equation

I apologise in advance that my knowledge of differential geometry and GR is very limited. In general relativity the equation of motion for a particle moving only under the influence of gravity is ...
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2answers
108 views

How to calculate the event horizon and the cosmological radius in a metric?

From reading about general relativity, the event horizon and the cosmological radius are the radius when $f(r)=0$, in the metric $$ ds^{2}=-f(r)dt^{2}+\frac{dr^{2}}{f(r)}+r^{2}d\Omega^{2} $$ However, ...
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0answers
23 views

How do I use the value I get from the gravitational time dilation formula to calculate dilated time?

I am trying to calculate gravitational time dilation with the following formula: $\exp\left(\dfrac{1}{c^2}\cdot-\dfrac{GM}{h}\right)$, where $-\dfrac{GM}{h}$ is the integral of the g function, and $\...
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2answers
76 views

How Smooth is an Event Horizon?

For a non-rotating Black Hole, the event horizon can be described by the Schwarzschild metric as a sphere. Assuming external observer, away from the Black Hole and also assuming that there is no ...
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2answers
334 views

Interpreting the Kretschmann scalar

How do you interpret the Kretschmann scalar (in general relativity)? What can you tell from it? The Kretschmann scalar is defined as $$K = R_{abcd} R^{abcd} $$ where $R_{abcd}$ is the Riemann ...
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0answers
47 views

What is the difference between intrinsic and extrinsic curvature? [migrated]

In general relativity, energy bends spacetime. However, this doesn't mean that a fifth dimension for spacetime to "bend into" exists." That is, spacetime isn't embedded in a higher dimensional space, ...
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25 views

Independant verification [on hold]

Historically, new theories were developed to explain observed phenomena and it was expected that the theory would make predicitions that could be used as a test of the theory and provide independant ...
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3answers
675 views

Noether's theorem in general relativity

Noether's theorem yields a conservation law for every symmetry. Is that independent of the Lagrangian i.e. when $\mathcal{L}\neq T-V$? In general relativity the integral that is minimised will be the ...
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0answers
88 views

Intuition behind deriving the FRW metric

I am studying the FRW metric and am looking at a motivation for it here. The motivation seems to use four spatial dimensions. Why do we need the fourth spatial dimension in this? This doesn't seem ...
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2answers
99 views

What is “a general covariant formulation of newtonian mechanics”?

I am a little confused: I read that there are general covariant formulations of Newtonian mechanics (e.g. here). I always thought: 1) A theory is covariant with respect to a group of transformations ...
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1answer
44 views

Maximum Angular Momentum for an orbit in GR

[The reference for this question is the book Gravitation by Misner,Thorne, & Wheeler.] The trajectories of massive particles around a spherically symmetric body is governed by the effective ...
3
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3answers
772 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
19
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6answers
2k views

Does curved spacetime change the volume of the space?

Mass (which can here be considered equivalent to energy) curves spacetime, so a body with mass makes the spacetime around it curved. But we live in 3 spatial dimensions, so this curving could only be ...
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3answers
167 views

Do gravitational waves propagate backwards in time?

Gravitational waves are spacetime waves, which stretch and squeeze both space and time. Since relativity puts space and time (almost) on an equal footing, it seems to me that since gravitational waves ...
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0answers
24 views

How To Arrive At Ground State Metric of Kaluza-Klein Theory

The ground state metric, after an extra dimension of space is compactified (to a circle) in Einsteinian gravity, is the metric which corresponds to the R_4 × S_1 geometry of the separated dimensions. ...
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4answers
7k views

What is the physical meaning of the affine parameter for null geodesic?

For time-like geodesic, the affine parameter is the proper time $\tau$ or its linear transform, and the geodesic equation is $$\frac{\mathrm d^{2}x^{\mu}}{\mathrm d\tau^{2}}+\Gamma_{\rho\sigma}^{\mu}...
4
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2answers
269 views

The ADM Energy of Gravitational Waves?

I have been looking for books about this question for several days. However, almost all books use Landau–Lifshitz pseudotensor to calculate the energy of Gravitational Waves.And they said the result ...
6
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1answer
115 views

Why gravitational waves are not produced by objects moving at constant velocity?

Gravitational wave is produced by change in gravitational field, source. If something is moving away from me at constant speed, its gravitational field will vary. But why only accelerating bodies ...
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1answer
48 views

Confirmation of a concept under General Relativity and Frames of Reference

I would like to preface this by saying that this isn't necessarily meant to be a full question, though it may become that, but it rather a confirmation of my understanding of a concept. Newton would ...
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0answers
29 views

What is the minimum math level required to comprehend general relativity? [duplicate]

I am currently working on a B.S. In chemistry and only need to go up to Calculus II, though I like to dabble in physics. What other math classes could I take to gain greater understanding of higher ...
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0answers
90 views

If the four velocity of a photon is undefined, what can we say about the velocity of a photon? Is Brian Greene right about motion through spacetime? [on hold]

Edit: THIS QUESTION IS ASKING ABOUT THE FOUR VELOCITY OF A PHOTON. THE PREVIOUS QUESTION DOES NOT. PLEASE ANSWER THIS QUESTION, WHICH HAS NOT BEEN ASKED. If the four velocity of a photon is ...
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0answers
26 views

Kerr Metric and Asymptotically Static Frame

Suppose we are given a Kerr spacetime (e.g. containing a single uncharged rotating black hole). How does one know that the coordinates chosen is rotating or non-rotating as seen from infinity? And how ...
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1answer
52 views

How do gravitational waves transfer momentum?

In Electromagnetism I understand it in terms of the Lorentz force: the E-component of the field causes the charge to respond infinitesimally with a $\vec{v}$ in the E-direction such that the $\vec{v}\...
4
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1answer
246 views

Closed timelike curves in the spin-2 gravity formalism

Let's say we take some topologically trivial CTC spacetime, like the Gödel metric: $$ds^2 = -dt^2 - 2e^{\sqrt{2}\Omega y} dt dx - \frac{1}{2}e^{\sqrt{2}\Omega y} dx^2 + dy^2 + dz^2$$ And then I ...
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0answers
36 views

how to work out the probability of walking through a wall [closed]

I was in science on Friday and I asked my teacher how to calculate the probability of walking through a wall.I just was curious because I like learning quantum mechanics
2
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1answer
61 views

Is the age of the Universe relative to where you are within it? [duplicate]

The accepted age of the Universe is 13 billion years give or take. If you were a super space being and hypothetically had spent a large portion of this time sitting next to a black hole then your ...
2
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2answers
76 views

Projection of a tensor

Consider the following tensor (abstract index notation, e.g. Wald's) $B_{ab}$ and timelike vector field $X^{a}$ such that $X^aX_a=-1$ and \begin{equation} B_{ab}=\nabla_bX_a \end{equation} Then one ...
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2answers
81 views

General relativity applications other than gravity

Do the Einstein field equations successfully predict/describe physical processes other than gravitational ones?
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2answers
922 views

Is Earth's orbit around the Sun affected by the ~8 minutes light delay?

Gravitational change occurs at the speed of light. As a consequence, we experience on Earth the gravitational attraction of the Sun based on its position relative to us ~8 minutes ago. How does this ...
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3answers
585 views

General relativity vs graviton discovery

Will the discovery of the graviton lead to the redundancy of general relativity even though it has been so well established. If not, will it mean that gravity will have two separate theories that ...
26
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3answers
958 views

Do intergalactic magnetic fields imply an Open Universe?

According to a paper on the arXiv (now published in Phys Rev D), they do. How credible is this result? The abstract says: The detection of magnetic fields at high redshifts, and in empty ...
2
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0answers
85 views

(1+1)-General Relativity

Goodevening everyone, my question is: What is the interest of studying the (1+1)dimension General Relativity? Can you explain please? Thank's in advance!
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0answers
29 views

Can orbiting a black hole 99.99% speed of light make other object with relatively fast clock travel faster than light, relative to me?

If i orbit a black hole, 99.9% speed of light, time for me is moving slowly, relative to me, planet earth is aging fast, and i have traveled 10 years into the future(relatively) in 1 second, suppose ...
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0answers
24 views

How small can a sample size be of space to detect space-time curvature?

What is the minimal sample size of space necessary to detect space-time curvature?
3
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1answer
84 views

Metric with Harmonic Coefficient and Stress-Energy Tensor in General Relativity

I have two question: Is there any possible implies or interest to use in general relativity a metric whose coefficients are harmonic functions? What is the meaning (physical) if the stress-energy ...
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1answer
52 views

Black hole gravity at bottom (deepest end) [closed]

If black holes are hole in space and time then at bottom or below bottom there is no more gravity of black hole. As any hole has an end (Deepest end). Is this true ? ******** EDIT *********** http:/...
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0answers
51 views

Does gravitational radiation have a formalism similar to Wheeler-Feynman electrodynamics?

Binary systems radiate energy away in gravitational waves as the orbits of the two masses spiral in towards each other. My understanding of gravity is that we think of it as a mediator of particle-...
3
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5answers
561 views

Where does the idea gravity=curvature of spacetime really come from?

I have been searching for quite a while but mostly found the answer: Einstein's genius. Quite unsatisfactory. I know and understand that the idea gravity=curvature of spacetime works. Furthermore I ...
4
votes
2answers
123 views

What does string theory predict for the singularity inside a black hole?

The usual explanation for what's going on inside a black hole goes something like "General Relativity predicts a singularity with infinite curvature, but when matters gets so tightly compressed we ...
8
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1answer
231 views

Homotopy proof of the lack of foliation of the Gödel metric

A common proof of the lack of foliation of the Gödel universe, apparently mostly copy pasted from Hawking and Ellis, goes thusly : A closed timelike curve must cross a spacelike hypersurface ...
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0answers
41 views

Lagrangian density

I really wonder : Why do we take Lagrangian density as zero for the Stokes theorem in Minkowski-space at infinity? Is there a proof of this situation?
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0answers
99 views

Deriving the field equations for a dark energy / modified gravity effective field theory

Question I'm trying to derive the modified gravity EFT field equations and, from their 00 component, this Friedmann equation: \begin{equation} H^{2}+H\frac{\dot{\Omega}}{\Omega}=\frac{\kappa \rho_{m}+...
2
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1answer
131 views

What is the metric of a constant electromagnetic (pure electric or pure magnetic) field?

For example, imagine a magnetic field $B_x$ directing in $\hat{x}$ direction filling all the space. What is its associated metric field? I can construct the electromagnetic stress-energy tensor for ...
3
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1answer
83 views

Exotic differentiable structures in physics

When reading a bit on exotic spheres and exotic $\mathbb{R}^4$'s, I came across some papers of Carl H. Brans and Torsten Asselmeyer-Maluga: "Exotic differentiable structures and general relativity" (...
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0answers
49 views

Einstein's quote relating to absoulute frame [closed]

There were two main objections to the concept of Absolute Space,as written in Relativity SPECIAL, GENERAL, AND COSMOLOGICAL by Wolfgang Rindler. They are (i) Absolute space cannot be ...
10
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3answers
2k views

Will a giant ball of protons form a black hole?

Suppose you have enough energy and resources to put together (in a momentarily static configuration in which they are all at rest at the same time) as many protons as you want to form a "proton star". ...