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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Unknown functions in Schwartzchild Metric

I was reading through MTW and they made a big deal about how we were able to make an astute choice of coordinates to eliminate unknown functions from the most general form of the metric for a ...
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1answer
94 views

What happens to objects sucked into a black hole after the black hole evaporates away?

Suppose an object falls into a black hole that's so massive that it wouldn't get torn apart at the event horizon. What happens to it after the black hole evaporates away? According to the theory ...
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79 views

At a center of Gödel's universe

A few quick questions clarifying a picture about Gödel's universe, they bug me badly! Taken from here. So Gödel's universe is made out of dust particles. All of them have angular velocity. Do this ...
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57 views

Energy of a particle as measured by an observer at infinity

I'm wondering if it is possible to make a definition for the energy of a particle as measured by an observer at infinity. I've looked through Wald for this but wasn't able to find anything - I may be ...
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1answer
33 views

About relativity [duplicate]

We know that the curvature of spacetime is gravity itself and it is not a force.so,why do we feel our weight in a curve spacetime but not in a straight(I mean not curve) space time like zero gravity ...
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1answer
56 views

Testing General Relativity using radioactivity on the Moon

I was reading a question involving an ultracentrifuge to test General Relativity. Instead of using an atomic clock the asker posited using radioactive decay as the metric to evaluate time dilation ...
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43 views

Negative Mass's Effect on Gravitational Time Dilation [duplicate]

When I was playing around with the equations for Gravitational Time Dilation, I discovered that when a negative value was plugged in for $M$, the equation gave the exact same answer, and it would ...
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3answers
165 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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1answer
5k views

Is there such thing as imaginary time dilation?

When I was doing research on General Relativity, I found Einstein's equation for Gravitational Time Dilation. I discovered that when you plugged in a large enough value for $M$ (around $10^{19}$ ...
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64 views

how are the infinitesimal generators of translation related to the lagrangian?

In studying analytical mechanics (or it's quantum analog), one will come across statements such as: $$f(x^{i}+\delta x^{i})=f(x^{i})+\delta f(x^{i})=f(x^{i})+\frac{\partial f(x^{i})}{\delta x^{i}}\...
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82 views

Straight line null geodesics in Minkowski, De Sitter and Schwarzschild

I'm trying to understand which part of the following metric determines whether photons travel on a "straight" line (thinking of $(t,r,\theta,\phi)$ as a flat background), the metric I'm considering is:...
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25 views

Gravitational lensing and cosmic strings

Say we have a straight cosmic string lying along the $z$-axis, with energy-momentum tensor $$T_{\mu\nu}=\mu\delta(x)\delta(y)\operatorname{diag}(1,0,0,-1)\tag{1}\label{1}$$ for some small positive ...
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19 views

Can redshift occur from relative velocity or just from expanding space

With sound the Doppler effect is caused by the wavelength of the sound being affected by the relative velocity between the observer and emitter, eg. If they are moving toward each other the observed ...
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1answer
63 views

Why does two masses with energy attract each other?

I have heard that every mass attract another mass with a force directly proportional to the multiplication of their masses and inversely proportional to the square of distance between them, but newton ...
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2answers
72 views

Gravity and circular logic [closed]

My research into gravity indicates that warped spacetime, with time as the major influence, is gravity. It also indicates gravity causes time dilation. Why is this not a circular argument. It is ...
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0answers
38 views

How does one derive Christodoulou Memory Effect?

There is a non-linear effect associated to the permanent displacement of test masses when a gravitational wave interact with them. This is called the Christodoulou memory effect. How does one obtain ...
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1answer
43 views

Traveling slower by traveling in opposite direction as the Earth rotates

I know that if I were to travel fast, the time would pass by fast for me. But if I were to travel fast in the opposite direction of the earths rotation while I'm still on earth, would the time pass by ...
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2answers
125 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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1answer
46 views

Wormhole Construction & ~ “Jump Conditions”

Throughout the literature Wormholes are typically constructed by "Minkowski" or "Schwarzschild Surgery" (see e.g. Visser, Lorentzian Wormholes...), i.e. under quite simple and/or highly symmetric ...
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0answers
29 views

Applying AdS-CFT to traversable wormholes? [closed]

ER=EPR recently brought up the connection between non-traversable wormholes and entanglements. What about traversable wormholes? Can we apply AdS/CFT to traversable wormholes?
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1answer
59 views

Conservation of Komar Mass

The definition of Komar Mass in GR is associated with one asymptotically flat end. However, a hypersurface may contain more than one end, such as the spacelike Einstein-Rosen bridge in Kruskal ...
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2answers
102 views

Can bending spacetime produce electromagnetic fields?

Let's say that we can somehow bent spacetime, can this produce electromagnetic fields? or EMF can only be emitted from charged particles of matter?
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17 views

Is the distortion of spacetime caused by frame dragging continuously changing, or fixed?

Consider a very heavy star and let´s take a look at the distorted spacetime accompanying the star. Does the spacetime gets increasingly wind up, or is it stationary? If it´s not stationary, then we ...
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1answer
22 views

Stress-Energy Content

I think that the Einstein Field Equation relates the pseudo metric to the the distribution of matter-energy as represented by the stress-energy tensor. Are the stress entries in the stress-energy ...
3
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1answer
71 views

Is there high ring-down frequencies in LIGO's recent discovery?

This question is from Physics overflow: question in physicsoverflow. I am reading LIGO's new discovery of gravitational waves by black hole merger. During the merger, two phases are not hard to ...
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0answers
58 views

(Causal) Set notation round brackets vs square brackets? [closed]

In many (quite old) papers & books I have been reading recently in the causal theory of general relativity (e.g. On the structure of causal spaces, Kronheimer & Penrose, 1967) I find sets ...
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2answers
93 views

Can there exist an observer able to observe a collapse of a star into a black hole?

We know that an observer at infinity cannot see a star forming into a black hole as the matter will take progressively longer and longer time to compress (from this observer's point of view). Is ...
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2answers
113 views

Is this video's notion of general relativity correct? [duplicate]

In this video it explains the path of the apple in the general relativity version of gravity as being a straight line on a curved surface. Is this valid? Edit: this isn't a duplicate of the supposed ...
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3answers
122 views

Two Robertson-Walker observers, at what time will a light signal be received?

Here is a question I have that is inspired by this question here. The spacetime metric of a radiation-filled, spatially flat ($k = 0$) Robertson-Walker universe is given by$$ds^2 = - dT^2 + T[dx^2 + ...
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1answer
64 views

Cosmic Rest Frame

Cosmic Rest Frame is defined in the paper "Adventures in Friedmann cosmology :A detailed expansion of cosmological Friedmann equations" by R Nemiroff and B Patla as the frame at a point where average ...
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36 views

How does Einstein's curved space time produce acceleration in a free falling object? [duplicate]

I never really thought much about all of this before so I'm definitely a newbie. Please excuse my ignorance. If I understand what I have read so far: if spacetime is curved time would click by at a ...
2
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1answer
47 views

An example of a theory that respects the Weak Equivalence Principle but violates the Einstein Equivalence Principle

The Weak Equivalence Principle has any one of the following forms: the inertial mass is equal to the gravitational mass there exists a preferred class of trajectories through spacetime, known as ...
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1answer
137 views

Torsion-free, symmetric connection and non-coordinate basis

The torsion tensor is defined as (Hawking p.34) \begin{equation} \mathbf{T}(\mathbf{X},\mathbf{Y}) = \nabla_{\mathbf{X}}\mathbf{Y} - \nabla_{\mathbf{Y}}\mathbf{X} - [\mathbf{X},\mathbf{Y}]. \end{...
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1answer
51 views

About periodicity of coordinates given a metric

If I am given a metric how do I decide which coordinate is periodic? Eg. can I look at metric in plane polar coordinates and tell that θ direction is periodic. Also How do I calculate the period of ...
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1answer
57 views

Questions about null geodesic [closed]

Show for the null geodesic in 3D flat spacetime using polar coordinates so the line element is $ds^2=-dt^2+dr^2+r^2d\phi^2$. Do light rays move on straight lines? My question is that I only learned ...
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1answer
50 views

Energy conservation around a black hole

In the Schwarzschild black hole, the Killing vector "time translation" $k^a$, so that the following quantity is conserved along a geodesic: $$E = -g_{ab}k^au^b = (1 - \frac{2GM}{r})\frac{dt}{d\tau}.$$...
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1answer
94 views

Indicating that indices are equal in Einstein notation

tl;dr: I have an expression like this: (dramatization) $$ R_{\mu\nu} = \begin{pmatrix} B^{00}C_{00} & 0 & 0 & 0 \\ 0 & B^{11}C_{10} & 0 & 0 \\ 0 & 0 & B^{22}C_{20} &...
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1answer
51 views

Difference between Fermi and Riemann normal coordinates

What is the difference between Fermi normal coordinates and Riemann normal coordinates? Which one of them is related to the vanishing of the Christoffel symbols?
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2answers
83 views

What is more fundamental: Geometry and Topology or physical matter? [closed]

Since, there is always an interplay between gravity and the fabric of spacetime. I wonder which is more fundamental: Geometry and Topology or physical matter?
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0answers
24 views

Does a black hole ever fully form to an outside observer? [duplicate]

According to general relativity, I had understood that time appears to slow down when looking into high gravitational fields from afar, so that as a black hole forms, the light from a collapsing star ...
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0answers
28 views

Relative motion in particle measurements

I was thinking about measurement of particles at almost-zero energies/temperatures and the movement associated with it. Compared to an observer next to the particle who sees the particle moving at ...
3
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1answer
75 views

What happens if I slowly lower a dangling object into a black hole?

I could've sworn I've seen this question before, but I couldn't find it. Suppose I have an object on the end of a really long string. I can slowly lower it near the event horizon of a black hole, ...
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0answers
32 views

Doubts about Chern-Simons state as a solution of the Hamiltonian constraint in quantum gravity

I've been doing some work with both Baez's Knots, gauge fields and gravity (1) and Gambini, Pullin's Loops, knots, gauge Theories and quantum gravity (2), lately. I have basically two problems: I ...
2
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2answers
95 views

Using $\sqrt{-g}$ in integrals of proper volume

I am a little confused over integration using proper volume element. When do we use $\sqrt{-g}$ in calculations? For example, in many calculations involving stars, say when using TOV equation, this ...
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0answers
36 views

Interpreting meaning of coordinates given a metric

I was working problem 3.6 in Carroll's GR textbook and was given the following metric, which is a good approximation to the metric outside the surface of the Earth. $ds^2=-(1+2 \Phi(r))dt^2 + (...
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0answers
36 views

The derivation of the Mass-Energy(including mechanical energy) equivalence principle [duplicate]

(Not duplication! I couldn't find the answer for the general case, instead of the special case that I've already seen in Youtube I hyperlinked.) I will fully satisfy with not only a mathematically ...
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0answers
23 views

The mass-energy equivalence is a principle which can not be derived from anything? [duplicate]

Not duplication) I couldn't find the answer for the general case, instead of the special case that I already seen in Youtube I hyperlinked. I will fully satisfy with not only a mathematically ...
1
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1answer
86 views

Simulation of relativistic probe passing through an external solar system

I recently read about the Breakthrough Initiative to launch "StarShot", a nano-probe that is designed to travel to Alpha Centauri at $0.2c$. One of the challenges to be solved involves the precise ...
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2answers
54 views

Does the constancy of the speed of light in vacuum hold for any observer in GR as well?

From SR, we know that the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source. But in GR, does it still hold for all observers? I mean the constancy ...
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2answers
133 views

Why would a modern smartphone not work if the theory of general relativity hadn't been discoverd? [closed]

My teacher told me that todays smartphones wouldn't work if the theory of relativity hadn't been discovered, but he didn't explained why.