Tagged Questions

A theory that describes how matter produces and responds to 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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64 views

Parity invariance of Einstein-Hilbert Lagrangian

How can we show that the Einstein-Hilbert action is Parity invariant? $$ S_{EH}=\int \sqrt{-g}R d^4x $$
3
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0answers
59 views

The universe could have created itself? [duplicate]

So in this Youtube video http://youtu.be/ZjaaSUHG7Xo The guy says, around 6:15, that the total energy of the universe is zero because of gravitational potential (or something like that i dont ...
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1answer
96 views

Calculating Hubble's constant at earlier times [duplicate]

I want to calculate Hubble's constant at some redshift $z$. I have found the following formula: $$H^2=H_0^2\left(\Omega_m\left(1+z\right)^3+\Omega_{\Lambda}\right)$$ Now it's obvious that at higher ...
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1answer
74 views

Deflection of light by the Sun

Can you give details of a recent experiment of deflection of light by the Sun? What is the distance from the surface of the Sun and what is the exact value of the angle of deflection?
3
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1answer
192 views

Light Deflection by a Black Hole

I think I've come across a paradox while studying general relativity. Wikipedia states that the deflection angle of light by a point mass is $4GM/(c^2b)$. ...
3
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1answer
85 views

Why do we do partial and not covariant differentiation with $x^{\nu}$?

Why when taking the velocity vector we make $$u^{\nu}=\frac{d}{d\tau}x^{\nu}$$ and not $$u^{\nu}=\frac{\nabla}{d\tau}x^{\nu}$$ where in the last equation I meant the covariant derivative. Why?
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2answers
142 views

Huygen's principle in curved spacetimes

Does Huygen's principle hold in even dimensional (2m+1,1) curved spacetimes, or are there certain necessary conditions for it to hold? In other words, if I have Cauchy data for a field satisfying the ...
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0answers
105 views

What are the implications for the AdS/Cft program if AdS is unstable?

To my understanding recent progress in the study of the non linear stability of AdS spacetime suggest that $AdS$ might be unstable. If this is true, what are the physical and mathematical ...
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1answer
119 views

GR exercise: falling particles on earth's surface

I'm having some trouble with Exercise 5.1 in Shapiro's BH,WD&NS book, which goes as follows: Consider two particles of mass $m$ at distance $r$ and $r+h$, such that $h\ll r$, on the same ...
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0answers
46 views

“Dictionnary” between QFTs in D and D-1 dimensions?

Considering Einstein equations, suppose, for instance, that the RHS, the stress-energy tensor, is uniquely due to the electromagnetic field. Now, if we imagine a quantized version of these Einstein ...
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0answers
27 views

Is gravitational acceleration less affected by relativistic mass increase? [duplicate]

Acceleration due to mechanical force will lessen due to relativistic mass increase as kinetic energy becomes significant near c. But if acceleration is gravitational, the gain in relativistic mass ...
3
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1answer
100 views

Can an underdensity in space act as a negative matter density powering a warp drive?

Consider a homogeneous isotropic universe filled with a perfect fluid with density $\rho$ and pressure $P = \rho/w$. E.g. for $w=-1$ we get a universe equivalent to one with "vacuum energy" or with ...
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72 views

Is the “Force” of Gravity Simply Hamilton's Principle on a Curved Spacetime?

It's my understanding that General Relativity abstracts away the concept of gravity as a force, and instead describes it as a feature of spacetime by which massive objects cause curvature. Then it ...
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2answers
122 views

Inside a huge sphere, which is being converted to a black hole

Suppose the following scenario: You reside inside a huge stable spherical star with non-lethal environment at its core. The object is so huge and massive, that its radius is only slightly above its ...
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1answer
1k views

How could we travel to the nearest supermassive Black hole?

I have just watched a trailer for the upcoming movie Interstellar and started to wonder about some physics involved. In the end of the trailer, they are obviously plunging into a Black hole hoping to ...
2
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2answers
100 views

Is Moon really rotating about its axis?

Wikipedia says yes but on Newtonian arguments. From general relativistic point of view Moon is not rotating but moving along geodesic trajectory. And like parallel transport of a vector (pointing to ...
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1answer
108 views

parity invariance of Einstein, Maxwell and Dirac Lagrangians

How can we show that Einstein, Maxwell and Dirac Lagrangians are parity invariant?
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1answer
103 views

Killing Equation, trouble with tensor algebra

I'm attempting to follow a proof that the commutator of two Killing vectors is itself a Killing vector. The source that I've posted is from my course notes. I've highlighted the part I'm stuck on. ...
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2answers
144 views

The Alcubierre drive and closed timelike curves

Under what conditions would it be possible to create closed timelike curves, assuming an Alcubierre drive could exist? Would it be possible to have the latter without the former? See here for ...
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0answers
71 views

Higher-Dimensional Metrics in (Hyper)-Spherical Coordinates

I want to compute the components of the Riemann curvature tensor (for a case similar to the Schwarzschild solution) in 4 + 1 dimensions, but I want to use a higher-dimensional analogue of spherical ...
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2answers
51 views

Charge Distribution in Reissner-Nordström Black Holes

In an electrically charged black hole, such as the one described by the Reissner-Nordström metric (i.e. with no angular momentum), where would the electric charge be situated (neglecting any charged ...
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1answer
62 views

The commutator of Killing vectors

I'm going over an assignment for my general relativity course. My solution to the question below strikes me as too short, considering that it appeared in the "longer questions" section of the ...
2
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1answer
56 views

Derivation of f(R) field equations, problem with integration by parts

I am following the derivation of the field equations on the the Wikipedia page for $f(R)$ gravity. But I do not understand the following step: $$ \delta S = \int \frac{1}{2\kappa} \sqrt{-g} ...
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2answers
116 views

How can space be euclidean when light bends?

I have read people arguing that tridimensional space sections of space time continuum (whatever its number of dimensions) appears to be euclidean from empirical evidence. I cannot reconcile it with my ...
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0answers
59 views

Lagrangian for FRW metric

For the metric $$ds^2=-dt^2+a^2(t)(dx^2+dy^2+dz^2),$$ $$L= \sqrt{-g_{\alpha\beta}\frac{dx^\alpha}{dt}\frac{dx^\beta}{dt}}$$ How does this become $$L= \sqrt{1-a^2 (\frac{dx}{dt})^2}~? $$ I guess ...
3
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1answer
149 views

Negative energy/mass bounds on de-Sitter spacetime

There exists a Positive Energy theorem for General Relativity in Anti-de Sitter and asymptotically flat spacetimes, but there is no equivalent theorem for de Sitter spacetimes Question: Is there ...
4
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1answer
179 views

The Aharonov-Bohm effect is purely classical, right?

Every discussion I've ever seen of the Aharonov-Bohm effect makes a big deal of its being a quantum effect with no classical analogue. But as far as I can tell it is present already at the classical ...
3
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1answer
66 views

Time Energy symmetry in General Relativity (not asking about energy conservation)

In General Relativity is there a TE symmetry similar to CPT symmetry in the Standard Model ? It's pretty easy to understand that by flipping charge and parity you merely get a time reversed equivalent ...
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5answers
204 views

On the coordinate independence of general relativity

I've been having a bit of trouble with the idea of coordinate independence in general relativity. Let me start with a simple example that I think illustrates my question conceptually: Say you have ...
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0answers
16 views

Is there some other name used for “ping rigidity”?

In MTW, p. 398, "Box 16.4 (continued)", there's an interesting sketch (which can also be seen on p. 15 of this excerpt (www.pma.caltech.edu/~ph236/yr2008/readings/MTW_Chapter16.pdf). (It's not the ...
0
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1answer
90 views

Why point mass leaves it's own gravitational well? [closed]

I suppose that point mass has its own gravitational well. Why this point mass is still attracted by other gravitational waves. I expect that this point mass is surrounded by "gravitational hills". Why ...
2
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0answers
70 views

How to calculate the 2-point function of gravitons?

I'm curious about how to calculate the 2-point function of graviton, but there are no textbooks of general relativity covering this problem. So how to calculate it? In which book can I find the ...
4
votes
1answer
74 views

Geodesics in Kerr

I'm interested in plotting the trajectories of null geodesics near an uncharged rotating black hole (described by the Kerr solution) which involves a system of first order differential equations. Kerr ...
0
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1answer
34 views

Given two events such that either one of them is 'on the light cone' of the other, do they constitute a 'null interval'?

One basic part of determining a metric (or applicable generalization) of a given set $\cal S$ of events (up to an arbitrary non-zero constant) is to determine to which pairs among those events, ...
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0answers
51 views

Ghosts in theories of gravity and holographic theories

I want to understand when a theory leads to ghosts in gravity. Is there any relation between ghosts and non-linear higher order theories? Ghost is a clasical or quantum field concept?
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1answer
53 views

Are there more distinctive names of “null curves” with certain additional properties (absence of “chord curves”)?

In this answer (to the question "In general relativity, are light-like curves light-like geodesics?", PSE/q/76170) a particular example of a curve is discussed whose "tangent is everywhere null" and ...
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0answers
89 views

How should a math undergrad student prepare himself to study GR and QM? [duplicate]

I'm quite sure that similar questions like this have been asked for more than thousands of times on here but since each person's background and interests are unique I believe questions like this ...
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3answers
1k views

Is topology of universe observable?

There is an idea that the geometry of physical space is not observable(i.e. it can't be fixed by mere observation). It was introduced by H. Poincare. In brief it says that we can formulate our ...
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3answers
198 views

Space-time curvature creates gravity or is it (could it be) vice-versa too?

Mass (Energy) creates space-time curvature and thus it forms the reason for gravity. Can it be vice-versa too? Like, mass created gravitational field, gravitational field created space-time curvature? ...
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3answers
114 views

Do massless particles follow the curved spacetime or not?

I am assuming that zero (rest) mass particles don't interact gravitationally with each other and other particles. Does that mean they experience a "flat" spacetime instead of a curved one? I find it a ...
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2answers
222 views

Why “light cones” have different shapes near black holes?

There is theory that light cone shape does not depend on the reference frame in which it is viewed. So why we draw light cones near black hole differently? I thought that if I am observing (from the ...
4
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2answers
231 views

Metric tensor in special and general relativity

I'm having trouble understanding the metric tensor in general relativity. What I've understood so far has come from my course lecture notes used in conjunction with "The Road to Reality" by Roger ...
3
votes
2answers
124 views

Frame dragging — is there a “non-tiny” example?

Now. As I understand it, in fact, the earth (10^25 kg) creates a very small, very tiny, frame dragging effect. Indeed, we have measured this using satellite experiments. So, the Earth (10^25 kg) ...
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0answers
53 views

Avoiding Pseudo-tensors when addressing global conservation of energy in GR

Discussions about global conservation of energy in GR often invoke the use of the stress-energy-momentum pseudo-tensor to offer up a sort of generalization of the concept of energy defined in a way ...
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0answers
45 views

Laplacian in tensor [closed]

Find $\vec \nabla^2\phi $ when $$ds^{2}=-dt^{2}+a^{2}(t)[dx^{2}+dy^{2}+dz^{2}] $$ or $$g_{ij}=\begin{bmatrix} -1 & 0 &0 &0 \\ 0 &a^{2}(t) &0 &0 \\ 0&0 ...
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0answers
55 views

Are there any known (closed form even if approximate) solutions to problems in relativistic elasticity?

There are several useful known solutions to the EFE with relatively simple / trivial stress-energy-momentum tensor, such as the Schwarzschild solution. Despite the idealizations made therein they are ...
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0answers
65 views

Gravitational atraction of fast object [duplicate]

Let's imagine a asteroid that travels with 0.99999999999999999c. (I know it's impossible). Anyway... Relativistic mass of such object would be almost equal to earth's stationary mass. Now let's ...
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1answer
65 views

How has the age of the Universe been derived from the observations made by the Planck mission?

The parameters of $\rm\Lambda CDM$ model have been determined to an amazing high precision from the measurements made by the Planck mission. In particular, the Hubble "constant" (the value of Hubble ...
3
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3answers
115 views

The Hole Argument

I have read explanations of this but haven't really understood. Given a spacetime $(M,g)$ I have read that if I represent the metric in some coordinates $(x,y,z,t)$ as $g(x,y,z,t)$ and then in another ...
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1answer
145 views

Finding the metric tensor from the Einstein field equation?

I have have set my self a challenge to learn all the maths behind the Einstein field equation (EFE), and from reading it seems that the Metric tensor is the thing we are trying to find (from the 10 ...