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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Big Bang Quarks Travelling at Light Speed [closed]

When I think of an explosion it lasts a fraction of second. When the entire mass of the universe explodes how much time passes before the perfect sphere slows from traveling at/near the speed of light ...
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4answers
270 views

Up or Down? A Question about Relativity

The standard text discussion of the equivalence principle and the bending of light rays goes like this. We, as observers watch a glass elevator ascending. A light beam is fired from left to right. The ...
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2answers
244 views

Non-trivial scalar quantity

Is there any scalar quantity made of only the Christoffel symbols, determinant of a metric and tensors, not derivatives? In other words, can we construct a scalar quantity which cannot be written in ...
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448 views

Do light waves precisely follow null geodesic paths in General Relativity?

In special relativity one may show that a plane wave solution of Maxwell's equations (in a vacuum), of the form $A^a=C^a\mathrm{e}^{\mathrm{i}\psi}$ has the following properties: The normal ...
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44 views

Where other frame observer will put new stick [on hold]

my question is with relativity, if we draw two circle of same radii and fill the perimeter with stick (very small so it cover whole perimeter) now if we rotate a stick with veey high speed ...
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3answers
722 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 ...
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287 views

why do x Schwarzschild radii equal time dilation effects of speed of light going y times faster than an object^2?

let me walk you through the math. First you start with the gravitational time dilation formula where: $$ T_1=T\sqrt{1-\frac{2GM}{rc^2}} $$ and rather than entering $r$ for the radius we replace $r$ ...
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305 views

How long can a particle survive inside of the horizon of a black hole?

By examining the causal structure of a Schwarzschild black hole, one can see that a particle in region II is unable to escape to $r=\infty$. Such diagrams do not show, however, how long a particle ...
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739 views

Interpretation of a singular metric

I'm interested to find out if we can say anything useful about spacetime at the singularity in the FLRW metric that occurs at $t = 0$. If I understand correctly, the FLRW spacetime is a combination ...
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2answers
195 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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71 views

Quantum teleportation + time dilation = time travel? [on hold]

Thought of this a while back and thought it was pretty funny, not sure if there's been similar ideas discussed elsewhere. I can think of at least 2 reasons this won't work: 1) As far as I know, ...
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84 views

Non-Euclidean mechanics; is it useful?

Special relativity has the following single-particle Lagrangian: $$S = \int_{t_0}^{t_f}\sqrt {\langle \mathrm d\vec{s},\mathrm d\vec{s}\rangle}.$$ Clearly it is based on Euclidean norms; it is in ...
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49 views

Shapes in a black hole

A question around an answer of Timaeus What happens to a particle in the exact center of a Kerr black hole?-answer Outside both is a normal type region of spacetime. In between the two the $r$ ...
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221 views
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142 views

Why acceleration cannot vanish everywhere?

In attempt to introduce gr concepts When there are gravitational accelerations present, as for example in the gravitational field of the earth, the space cannot be the flat Minkowski space. Indeed, ...
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1answer
53 views

What happens if locally manifold is seen as an Euclidean space? [closed]

I have been trying to understand the definition of a manifold and I have found out that the most common definition can be paraphrased as: A manifold is a space that has a complex "topology" globally ...
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628 views

Why do people put exponentials there

In his book, Sean Carroll, says p. 194 chapter 5: To impose spherical symmetry, we begin b writing the metric of Minkowski space in polar coordinates $x^{\mu}=(t,r, \theta, \phi)$: $$ ...
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39 views

Two black holes prepared from different initial states

I have asked a similar question, I would like to reformulate it in more details. Here is a thought experiment: Assuming we can create black holes by squeezing photons, we can then prepare two ...
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22 views

A problem with ADM mass in the derivation of 1st law of black hole thermodynamics

The definition of ADM mass is $M=\frac{1}{16\pi}\lim_{r\rightarrow\infty}\int(\frac{\partial h_{\mu\nu}}{\partial x^\mu}-\frac{\partial h_{\mu\mu}}{\partial x^\nu})N^\nu dA$ according to Wald. ...
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1answer
75 views

Components of dual vectors

(This is a close retelling of Wald, problem 2.4b. Not for homework; just curiosity and an increasingly alarming suspicion that I've never actually understood anything.) Let $Y_1 ... Y_n$ be a ...
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66 views

Gravitational waves: novel or confirmatory?

If the rumors are true and gravitational waves have been detected, would we learn any new fundamental physics from them? Or is this simply an important confirmation of a prediction of general ...
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591 views

Movie Interstellar - Followup Question to Escape Velocity

Continuing the discussion on this thread: Movie Interstellar - Question about Escape Velocity The movie Interstellar shows people on a water planet where time is dilated so much that 1 hour is equal ...
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99 views

If gravity is due to curvature, how does gravity work in situations with no curvature?

The strength of the gravitational field falls off as the inverse square of the distance from a spherical source. It only falls off as the inverse of the distance from an extended cylindrical or line ...
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2answers
92 views

How much additional light does Earth receive from the Sun due to Earth's gravitational field?

I was reading about how gravity affects light, and that got me wondering how much additional light is collected by the Sun due to the Earth's gravitational field. Is it a significant amount of light ...
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2answers
116 views

Redshift due to a static gravitational field and the conservation of energy [duplicate]

I am standing on the surface of some planet. Gravity is described via General Relativity with some static metric (e.g. the Schwarzschild metric, so static means no time dependence, but the metric may ...
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Obtaining a copy of Hawking's Ph.D thesis - Properties of Expanding Universes

Due to its popularity, I am interested to know the 4 chapter titles and topics covered in S.W. Hawking Ph.D, Properties of Expanding Universes. I also ask this because that thesis is hardly available. ...
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54 views

A possible proof that time traveling to the past with the aid of a wormhole is impossible?

Suppose a wormhole connects two part of the place where I live. I find myself in a spaceship attached to one side of the hole, and my wife on the other side, so we can see and talk to each other. Now ...
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36 views

Gravity, Acceleration, Time Dilation and the Equivalence Principle

Three clocks are started at exactly the same time on Earth. The first and second clocks are taken into the vacuum of space. The first clock accelerates until it reaches 100,000m/s, then stays at this ...
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2answers
454 views

Time dilation in a gravitational field and the equivalence principle

A clock near the surface of the earth will run slower than one on the top of the mountain. If the equivalence principal tells us that being at rest in a gravitational field is equivalent to being in ...
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4answers
438 views

What truly is mass, and is there a direct way to measure it?

We know a mass of an object of one kilogram as an object that weighs W = mg = 9.8 N and we reference it to that, (when it should as a fundamental parameter describe weight not the opposite). But if we ...
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1answer
46 views

Divergence of inverse of metric tensor

I know that the Levi-civita connection preserves the metric tensor. Is the divergence of the inverse of metric tensor zero, too?! I'm not so familiar with the divergence of the second ranked tensor. ...
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2answers
37 views

Is there a doppler effect on the images of stars around rotating black holes?

I'm an illustrator working on a project involving rotating black holes like those discussed in "Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar" by James, ...
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1answer
49 views

Evaporating black hole Penrose diagram

The context for this is the diagram from From where (in space-time) does Hawking radiation originate? - the more I think of it, the less it makes any sense ) This particular question is about ...
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2answers
94 views

Does time have a minimum 'speed'?

Sorry if this is an ignorant question, but I've been having some trouble grasping some concepts related to time dilation. So far, my understanding of the concept says that if I am in a certain frame ...
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59 views

When is a spacetime a black hole?

While reading $\textrm{Present status of the Penrose Inequality}$ by Marc Mars, 2009, I was confused with the following statement: ... in order to determine whether a space-time is a black hole, ...
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1answer
117 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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How much does the curvature of space change the volume of Earth by?

If we assume space is flat the volume of Earth is: $$ V = \frac{4 \pi R^3}{3} = \frac{4 \pi (6378.1 km)^3}{3} = 1.086 \times 10^{21} m^3 $$ The Einstein field equations, however, predict that the ...
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0answers
40 views

Worldlines in Schwarzschild geometry

I have an observer and a photon on a hypersurface $ \theta=\pi/2$ . My observer has $e, l$ constants of motion (energy and angular momentum divided by mass) and photon has $e',l'$. What conditions ...
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1answer
45 views

Graviton detector thought experiment

I was recently thinking of a thought experiment: Assumptions Graviton detectors can exist The equivalence principle will hold in the final theory of quantum gravity We can accelerate the graviton ...
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100 views

Literature request for books / review papers on gravitation, gauge theories and related mathematics [duplicate]

Similar to this reference, are there more such references / works [including textbooks] available in the literature? (A list would be greatly welcomed and appreciated.)
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2answers
320 views

Locally flat coordinate and Locally inertial frame

I am having some doubts on myself regarding the above concepts in General Relativity. First, I want to point out how I understand them so far. A male observer follows a timelike worldline ($\gamma$) ...
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2answers
561 views

Introduction to relativity books for an engineer [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
41 views

Conditions at black hole's event horizon

This question had, at least partially, been discussed here before, but I feel that the record has not been set straight. There seem to be lack of agreement regarding conditions (like gravitational ...
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5answers
7k views

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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4answers
307 views

A ball in the gravity potential field of a black hole — seems a paradox

As illustrated in the following diagram (A, B, C, D are 4 specified space points, and C is close to a black hole), a small ball at distance of a black hole is stationary (suppose now it's mass is m0) ...
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5answers
125 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 ...
3
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2answers
116 views

How is the Ricci scalar $R=0$ here?

Given the metric in the form: $$ds^2 =-A(r)dt^2 +B(r) dr^2 dr^2 +r^2(d\theta ^2 +\sin^2\theta d\phi^2)$$ Papapetrou in his book said that $R=0$ But when I performed it I didn't get zero. For ...
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1answer
78 views

Duality and 1 forms

How is a dual map defined if we are talking about partial derivatives and 1 forms?
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123 views

Falling with same acceleration and meaning of gravity

My question is what does falling with same acceleration has to do with what Einstein concluded concerning the gravity in terms of the curvature?
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242 views

How to eliminate this cross term?

Given $$ds^2=-A(r)dt^2+B(r)dr^2+2C(r)drdt+D(r)r^2(d\theta^2+\sin^2d\phi^2),\tag{23.1}$$ How can we eliminate the cross term?