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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123 views

A question about motion and time dilation

I was thinking that if you are in empty space with another person (with no other objects around), and from a distance you see that the other person is approaching you a constant speed, you wouldn't ...
3
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0answers
17 views

Are closed timelike curves generic feature of ANEC-violating stress-energy tensor?

Kip Thorne has shown that in order to create closed timelike curves (CTCs), one needs stress-energy tensor $T^{\mu\nu}$ that violates averaged null energy condition (ANEC). Will $T^{\mu\nu}$ with ...
2
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1answer
98 views

Wave Packet in Curved Spacetime

It is known that the classical equation of motion for a scalar field wave packet on a curved spacetime background gives the geodesic trajectory (the e.o.m. is $(\nabla_\mu \nabla^\mu + m^2) \Phi=0$). ...
3
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2answers
59 views

Gravitational Length Contraction

General Relativity predicts that a clock at rest in a gravitational field will run slower than a clock in free fall. Similarly, will a vertical ruler on the earth's surface be shorter than a ruler in ...
3
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2answers
331 views

Another faster-than-light question

Imagine we have something very heavy (i.e supermassive black hole) and some object that we can throw with 0.999999 speed of light (i.e proton). We are throwing our particle in the direction of hole. ...
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1answer
75 views

At what speed will objects hit a singularity? [duplicate]

I have read in numerous places like here that an object in free fall into a black hole will be travelling the speed of light when it passes the event horizon. How is it possible to go this fast? ...
2
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0answers
42 views

In KK theory, is proper time defined using the 5 dimensional or the 4 dimensional line element?

Let's consider five dimensional KK theory. This is Klein's metric $\hat{g}_{AB}= \begin{pmatrix} g_{00}+A_{0}A_{0}&g_{01}+A_{0}A_{1}&g_{02}+A_{0}A_{2}&g_{03}+A_{0}A_{3}&A_ 0\\ ...
16
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2answers
471 views

Is general relativity holonomic?

Is it meaningful to ask whether general relativity is holonomic or nonholonomic, and if so, which is it? If not, then does the question become meaningful if, rather than the full dynamics of the ...
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0answers
45 views

Radial Null Geodesics in Static Maximally Symmetric DeSitter Space

Given a DeSitter-space metric from the line element: $$ ds^2=\left(1-\frac{r^2}{R^2}\right)dt^2-\left(1-\frac{r^2}{R^2}\right)^{-1}dr^2-r^2d\Omega^2 $$ Where $R=\sqrt{\frac{3}{\Lambda}}$, and ...
2
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4answers
116 views

What experiment would disprove Friedmann model of cosmology?

What experiment would disprove Friedmann model of cosmology? As a layman, I have read a lot of articles and threads in specialized forums. I am probably wrong, but I developed an impression that that ...
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1answer
1k views

Do residents of the Hudson Bay area have more time?

Apparently there is a gravity anomaly in the Hudson Bay Area in Canada: gravity is "missing" or it is slightly less than it is in the rest of the world. Does that mean that things in the Hudson Bay ...
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4answers
3k views

Why does a flat universe imply an infinite universe?

This article claims that because the universe appears to be flat, it must be infinite. I've heard this idea mentioned in a few other places, but they never explain the reasoning at all.
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0answers
113 views

What is the state-of-the-art on spacelike singularities in string theory?

What lessons do we have from string theory regarding the fate of singularities in general relativity? What happens to black hole singularities? What happens to cosmological singularities? Which ...
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2answers
2k views

Can a light be bent by a magnetic field?

I'm struck with two competing ideas on the question in the title. Listing #1: http://van.physics.illinois.edu/qa/listing.php?id=2009 Q: "How far can a magnetic field bend light?" A: "Unfortunately, ...
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2answers
234 views

Does a 4-current J determine a unique maxwell-faraday F tensor up to isometry?

Maxwell's equations on a pseudo-Riemannian manifold $(M,g_{ab})$ say, $$d_a F_{bc} = \nabla_{[a}F_{bc]} = 0,$$ $$\nabla_a F^{ab} = J^b,$$ where $d_a$ is the exterior derivative, $\nabla_a$ is the ...
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2answers
36 views

Spin of anti-particles

Pretty simple question (I think), probably stemming from my lack of formal background in physics. I've been reading questions like this one related to attraction with respect to spin (a term I'm not ...
6
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0answers
95 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 ...
2
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2answers
312 views

Weight of a tensor density

Is there any freedom in choosing the weight of a tensor density? I have seen in some papers that they introduce a tensor density made from metric with a special weight. There is a tensor density with ...
5
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0answers
53 views

BTZ Black Hole Central Charge and Conformal Weight

I have been trying to reproduce a calculation (equation 4.12) in this paper http://arxiv.org/pdf/1107.2678v1.pdf by Carlip reviewing the derivation of the effective central charge of the BTZ Black ...
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0answers
42 views

Unknown Function in the Tolman-Bondi-de Sitter Metric

I've been working with some dust solutions in General Relativity, practicing calculating the Riemann curvature tensor, and I came across an odd metric: the Tolman-Bondi-de Sitter metric. A quick ...
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1answer
56 views

Misner String Singularity

In correspondence to AdS black hole solutions, what does it mean by Misner string singularities? And when there are no Misner string singularities, what does this mean in terms of curvature ...
2
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0answers
46 views

Irreducible representation for the massless particle with helicity 2 and the Weyl tensor

As it can be shown, the equations for the irrep with zero mass and helicity 2, -2 respectively can be given in a form $$ \tag 1 \partial^{\dot {b}a}C_{abcd} = 0, \quad ...
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4answers
109 views

Can the equivalence principle be shown to follow from special relativity?

Einstein showed in various papers that the energy content of a body was a measure of its inertial mass. If you increase the kinetic energy of a system while keeping the center of energy at rest, its ...
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5answers
2k views

Does a charged particle accelerating in a gravitational field radiate?

A charged particle undergoing an acceleration radiates photons. Let's consider a charge in a freely falling frame of reference. In such a frame, the local gravitational field is necessarily zero, ...
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0answers
34 views

Can you explain the rationale of FLRW cosmology and the expansion of space? [duplicate]

I have read here and there about Friedman equations and that they interpret/simplify GR cosmology. The main idea is that mass curves spacetime, then there are the stress/energy tensor and the density ...
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1answer
96 views

Regarding Non-renormalizatibility of GR

I've been doing some reading trying to get to a better understanding of some renormalization issues with the Einstein-Hilbert action. But, something odd came into mind that I'm hoping some users may ...
2
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1answer
144 views

Energy-Momentum Tensor under Lorentz Transformation

In relativity, the symmetric energy-momentum tensor is given by $$ T^{ij}, $$ where $T^{00}$ is the energy density and $\frac{1}{c}T^{10}$ is the momentum density. Thus: $$ \left(\frac{1}{c}T^{00}dV, ...
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0answers
27 views

Caustic and Singularities in General Relativity

What is the relation between the formation of caustics of a family of null geodesics and the existence of an incomplete null geodesic?
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1answer
91 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 ...
3
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1answer
190 views

What is the equation for the scale factor of the universe, a(t), for the best fit of data to the $\Lambda CDM$ Model of Cosmology?

Ideally I like a single formula or multiple formulas for different time ranges that would cover the time from the end of inflation through 100+ billion years after the big bang using the $\Lambda ...
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1answer
48 views

Quantum uncertainty of a singularity: A Black Hole Problem

A black hole in GR seems to have a sharply defined radius. Of zero, that is since all the mass has been compressed into the infinitely dense center point. However, shouldn't the fuzziness of quantum ...
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2answers
65 views

Static geodesics in GR

Can we find static geodesics of the type $$x^{\nu}=x_0^{\nu}+\delta_0^{\nu}\tau$$ in some space-time other than Minkowski's?
5
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2answers
129 views

Why does the second law of thermodynmics only occur in the time dimension?

If I break an egg, how broken it is depends on "when" I am not "where" I am. Why is the time dimension special?
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 ...
3
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0answers
60 views

Parity invariance of Einstein-Hilbert Lagrangian

How can we show that the Einstein-Hilbert action is Parity invariant? $$ S_{EH}=\int \sqrt{-g}R d^4x $$
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1answer
81 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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1answer
107 views

Trajectory of a photon around a Schwarzschild black hole?

Consider a photon coming from the infinity in a unbounded orbit to a Schwarzschild black hole (Schwarzschild radius $r_{s}$) (see this for illustration). Its impact parameter is $b$ and its distance ...
3
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1answer
80 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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1answer
63 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?
2
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1answer
45 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} ...
3
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1answer
184 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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2answers
134 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 ...
1
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0answers
42 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 ...
4
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1answer
84 views

Pressure and Density Using a General Lagrangian

Given a lagrangian of a form: \begin{equation}\mathcal{L}=f(\phi,\partial_{\mu}\phi\partial^{\mu}\phi)\end{equation} where $f$ is a function, I need to derive pressure and density in a FLRW universe ...
0
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1answer
148 views

What are the conditions around Sgr A* for a space ship trying to plunge into the central black hole?

The possible problems for a space ship near an active galactic nucleus are the following: tidal forces, hot plasma accreting into the black hole and "jetting" out, radiation, and magnetic fields. If I ...
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0answers
26 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 ...
26
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7answers
8k views

Why does GPS depend on relativity?

I am reading A Brief History of Time by Stephen Hawking, and in it he mentions that without compensating for relativity, GPS devices would be out by miles. Why is this? (I am not sure which relativity ...
3
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1answer
94 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 ...
3
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0answers
63 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 ...
2
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2answers
97 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 ...