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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Question 17 in section 2.9 in Schutz's A First Course in General Relativity [closed]

The question is as follows: Prove that any timelike vector for which $U^0>0$ and $\vec{U}\cdot \vec{U} = -1$ is the 4-velocity of some world line. I need to show that there exists a 4-vector $\...
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3answers
41 views

What is the gravitational pull if one has as much mass above them as below them? [duplicate]

I understand the previous responses to other answering if you were at the center of a planet, would you be weightless? Yes you would due to the forces of gravity pulling at you from all sides. ...
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48 views

Proper time and asymptotic flatness

I'm trying to understand the concept of asymptotic flatness in general relativity, and came up with the following question: If the proper time $\tau$ is infinite for a timelike geodesic, does it mean ...
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37 views

Breakdown of correspondence principle: null dust case

In both quantum and general relativity theories we are used to provide results in the "limited" conditions to demonstrate a correspondence between new and old formalism. For instance deflection of ...
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Comparing durations for two simply described motions in Schwarzschild geometry

I have some basic qualitative questions about the setup with: one satellite $A$ orbiting freely, on a stable circular path, a spherical non-rotating object of mass $M$; and another participant $B$ ...
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Why are Killing fields relevant in physics?

I'm taking a course on General Relativity and the notes that I'm following define a Killing vector field $X$ as those verifying: $$\mathcal{L}_Xg~=~ 0.$$ They seem to be very important in physics ...
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54 views

How can I prove that the covariant acceleration is normal to the velocity?

I'm trying to show that the covariant acceleration is normal to the velocity for a massive particle. I think that I understand why this has to happen because I understand the covariant acceleration as ...
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132 views

Diffeomorphism group vs. $GL(4,\mathbb{R})$ in General Relativity

I am quite confused with the groups Diff$(M)$ and $GL(4,\mathbb{R})$ in the context of general relativity. I understand that the symmetries of GR are the transformations that leave the equations ...
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75 views

How does bending in space-time caused by mass energy translate into acceleration of object? [duplicate]

Let say we have 2 similar apples separated by a distance apart, just their mass energy alone is sufficient to cause bending in the space-time. I think it is this bending in the space-time that cause ...
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4answers
189 views

What allows us to assume spacetime is flat when no normal matter is present?

Dark matter causes a bend in spacetime. We see this through gravitational lensing. But what allows us to assume spacetime is flat when no normal matter is present? Why can't we say that dark matter ...
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Variation of Bazanski Lagrangian

The Bazanski Lagrangian is defined as $$ L=g_{\alpha \beta }U^{\alpha }\frac{D\psi ^{\beta }}{Ds} $$ and $$ U^{\alpha }=\frac{\mathrm{d} x^{\alpha }}{\mathrm{d} s} $$ $x^{\alpha }$ is the ...
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Why does the curvature of space decrease during inflation but increase after it?

According to the Friedmann equation, curvature of space will increase with time/expansion of space, but I've also read that during Inflation, the expansion caused the Universe to flatten out. What is ...
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157 views

Is there a Maupertuis principle for General Relativity?

The motion of a point particle in classical mechanics is given by Newton's equation, $\mathbf{F}=m\mathbf{a}$. Suppose all forces considered are conservative and we have a constant total energy $h$. ...
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82 views

Can gravitational effects create a plane of the ecliptic?

Lots of questions about the why of the plane of the ecliptic, and good answers, but I was wondering about gravitational effects. If we picture for example, Saturn as being a few degrees above the ...
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546 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 $k:=\...
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How did inflation lead to the expansion of space?

Big bang Theory gives a scientific explanation of the evolution of the Universe, where the scientific picture of it starts with Universe(space) uniformly filled with matter and energy, already ...
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109 views

For a giving metric in GR, how do we learn which observer the metric refer to?

For example, I have been told the Schwarzschild observer is far away from blackhole and events,(namely, I think, the observer is static at infinity of the coordinate.) And the second example,the ...
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Simple quadrupole field not yet in Lorenz gauge?

I'm having trouble reproducing some of the results regarding gravitational waves in the Wald's General Relativity. In section 4.4 of gravitational radiation, eq.4.4.49 shows the far-field generated ...
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131 views

A question about gravity [duplicate]

Some time ago I encouraged by 11 year old son to watch Cosmos: A Spacetime Odyssey with Neil DeGrasse Tyson, and subsequently Cosmos: A personal Voyage with Carl Sagan, as well as other astronomy ...
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1answer
55 views

How does time look relatively in a gravity well? [duplicate]

Relativistically, when two frames, say A & B are moving apart inertially, then the clock of B will look slow compared to that of A; and the same holds for the clock of A from B. What does the ...
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How does Lorentz Contraction apply to the edge of a spinning disk and is Pi still constant?

This may seem like a dumb question, as I'm not really a physicist, but here it goes. So, π (3.14...) is the number of diameter distances required to equal the circumference of a 2D disk. Relativity ...
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Relativity: A modification on Sea Tower experiment

I first read about it on A Brief History of Time(Stephen Hawking). In 1962, a relativity experiment was executed: identical (classical) watches put on a water tower, one is on very high, other one is ...
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Guesses from a Rindler observer

Suppose an observer travels through Minkowski space $M=\mathbb{R}^4=\left\{x_0,x_1,x_2,x_3\right\}$ on a uniformly accelerated path: \begin{equation} \begin{cases} x_0= R \sinh(\frac{\tau}{R}) \\ x_1= ...
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Is this picture of relativity correct? [closed]

Can forces be said to exist in a real sense in general relativity?
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Coordinate Singularity in Metric

Suppose I have some metric $$ds^2=g(t)dt^2+\frac{1}{r}dr^2$$ which has a singularity at $r=0$. However, if I make the coordinate transformation $u=\frac{1}{r}$, then I get: $$ds^2=g(t)dt^2+r^3 du^...
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Launching of artificial satellites [closed]

Whose theory is used today during launching of artificial satellites, Newton's or Einstein's or any other? Which theory is better in launching of artificial satellites and other orbiting bodies, ...
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190 views

Unbounded perturbed geometry due to analyticity

I have an interesting mystery for you, loosely inspired on work related with this question. I have a certain Ansatz for a gravitational wave perturbation of the metric $h_{\mu \nu}$ that is nonzero ...
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Possible inconsistency of mixed index tensor notation

I am posting this here, because in my experience, this sort of thing exists in physics-related works only. Given a local frame $\{e_{(i)}\}$ on some $n$-dimensional manifold $M$, and given a local ...
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Is the equivalence principle Machian?

There is a lot of discussion on the subject of Mach's principle, and whether it has any place in the theory of relativity. But it seems to me that one could argue that Mach's principle is at the heart ...
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Understanding Vaidya metric and pure radiation stress-energy tensor

I am following Vaidya metric and how it is related to pure radiation from Wikipedia. But when it reaches the line where stress-energy tensor is equated to product of two four-vectors, I cannot follow ...
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2answers
132 views

Classical physics in curved space

I'm trying to learn General Relativity. As a stepping-stone between classic (Newtonian) physics and complete relativity, imagine a universe where space is curved, but time is perfectly flat. Also, the ...
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2answers
51 views

Travel by Earth rotation [closed]

why we can't go outside the atmosphere and travel with earth rotation .. and can we travel in the opposite direction of atmosphere by the same speed of atmosphere it’s moving at about 1,000 miles an ...
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spin representations and polynomials

I'm reading Group Theory and General Relativity by Moshe Carmeli and his discussion of spin representations of SU(2) and the isomorphism to the space of homogenous polynomials is confusing me. I'll ...
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What does “the fabric of space and time” actually mean? [closed]

I've heard the term "the fabric of space and time" in both physics and science fiction, and although I know it has something to do with general relativity, I don't understand what, specifically, they'...
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Spherically Symmetric Metric in Nordstrom gravity

Nordstrom's theory of gravity postulates that the metric is of the form $g_{\mu \nu} = \phi ^2 (x) \eta_{\mu \nu}.$ The field equations, in vacuum are of the form $R=0$, where $R$ is the Ricci ...
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Perfect fluid and EM tensor in rest frame

I see that we use perfect fluid which is characterized by a energy density and isotropic pressure for general forms of matter. When guessing the values of energy momentum tensor indices we can use ...
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90 views

Is it possible to tell which way a Universe is spinning?

Imagine a Universe spinning on the x-axis. So there is a centripetal directed away from the x-axis. According to General Relativity this is entirely equivalent to a non-spinning Universe with a ...
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How to obtain the four-velocity of a fluid from the metric?

Let's say I'm working with a metric tensor for some spacetime with components $g_{\alpha \beta}$ relative to some coordinates $(\tau, x, y, z)$. Is there a general way of obtaining the four-velocity ...
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2answers
112 views

Mountains and their local effects on Earth's gravity

I was once a truck driver and can feel the inertia and kinetic energy on heavy loads while traveling. While climbing mountains in the Rockies I noticed gravity was different on the side of the ...
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Looking for a reference for $\gamma_a e^{a}_{\mu} D^\mu \gamma_b e^{b}_{\nu} D^\nu =D^\mu D_\mu - \tfrac{1}{4}R$

I am having trouble finding references for the following identities: Dirac Operator: $$ \gamma_a e^{a}_{\mu} D^\mu \gamma_b e^{b}_{\nu} D^\nu =D^\mu D_\mu - \tfrac{1}{4}R \tag{1} $$ QED Operator: $$ ...
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139 views

What happens 'inside' the event horizon of a black hole, in particular to photon speed

This is a follow-up question to two answers given here and here, where the speed in different coordinate systems is discussed when approaching the Schwarzschild radius. To cite, derived directly from ...
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32 views

Definition of vacuum and occupation number in expanding Universe

Suppose for simplicity we have theory of free quantum scalar field in expanding Universe (metric plays the role of background field) $g_{\mu \nu} = \text{diag}(1, -a^2,-a^2,-a^2)$, where $a(t) \sim \...
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49 views

Leading order approximation of Proper Radial Distance in General Relativity

Context: I'm currently going through this article (http://arxiv.org/pdf/0704.2667v1.pdf). In the 3rd page last paragraph the variable corresponding to the proper distance $y = \int{1/\sqrt{g(l)}}dl$,...
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60 views

Would quantum fluctuations cause problems for scalar-field inflation?

Wheeler once said that spacetime would be highly curved at very small scales because of the uncertainty principle for energy-momentum. In which case the spacetime becomes very bumpy and not smooth ...
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62 views

Time dilation at the Innermost Stable Circular Orbit

According to general relativity the time dilation is given by following formular: $d \tau = \sqrt{g_{\mu \nu} \dot{x^{\mu}} \dot{x^{\nu}}}$ If I'm interestet in the time dilation at the ISCO I set $...
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158 views

Gravity: Why Do things fall to Earth? [duplicate]

If gravity is in reality spacetime geometry why when I drop an object on the surface of the Earth does it fall to the ground? Does spacetime push it?
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87 views

Exact meaning of radial coordinate of the Schwarzschild metric

In this answer as well as on Wikipedia the radial coordinate of the Schwarzschild metric is described as follows: ...the r co-ordinate is the value you get by dividing the circumference of the ...
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Is there something similar to Gauss's Law For Gravity in General Relativity?

In Newtonian Physics there is an equation that for the Gravitational Flux of an object known as Gauss's Law For Gravity. Gauss's Law for Gravity describes the number of Gravitational Field Lines ...
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Age of universe?

Well relativity teaches us that time interval between two events is a frame dependent quantity, then how can we say that our universe is 13.8 billion years old? Should it not depend on who is asking ...
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I don't see that general relativity is really needed for GPS to work correctly [duplicate]

From what I understand, GPS localization is based on the difference in the reception time from the time of emission of a signal from different GPS satellites whose positions are known. For this we ...