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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255 views

How is the poincare conjecture(and perelman proof) helpful in studying the properties of the universe?

Can someone tell me how the poincare's famous conjecture or its proof by perelmen can be helpful in deciding some properties like the shape of the universe?
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272 views

composition of space expansion and movement as a gauge invariance

suppose i have a space-time where we have one point-like object* which we will call movement space probe or $\mathbf{M}_{A}$ for short, and it will be moving with constant velocity $V^A_{\mu}$ in ...
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357 views

Calculation of the non-Gaussity parameter for primordial cosmological perturbations by the ADM Formalism

Maldacena has used the ADM Formalism in one of his papers (http://arxiv.org/abs/astro-ph/0210603) in computing the the three point correlation function (i.e the non-Gaussianity) parameter for ...
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298 views

net displacement and path dependence

reading the paper about spacetime swimming by Wisdom (something related to this has been previously asked here) can't help but think that there is more to this than what is on the paper. Basically ...
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224 views

Singularities in Bianchi models in general relativity ( physical science)

what are the conditions to check point type singularity in a bianchi type model ? bianchi type model are of Type I,II,III,IX,IV or u can say we use different Bianchi type models having some specific ...
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25 views

Tangent Vector Field from Metric

Question: Starting from an arbitrary spacetime metric, how does one obtain a tangent vector field? (We might need to assume certain geodesic congruences but my understanding is very limited.) Build ...
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41 views

Momentum conservation in FRW spacetime

The spatially flat FRW metric in Cartesian co-ordinates is given by: $$ds^2 = -dt^2 + a^2(t)(dx^2 + dy^2 + dz^2)$$ As I understand it, since the metric does not depend on the spatial co-moving ...
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21 views

Is macroscopic causality an issue in the context of certain quantum experiments?

In order to formulate my question properly I need to explain a few things. Cramer_Herbert Zych_Brukner Reference 1. - John Cramer, Nick Herbert, "An Inquiry into the Possibility of Nonlocal Quantum ...
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59 views

How does a rotating black hole look like? How would it be to descend into one?

This image from Wikipedia shows how a black hole would look like: A black circle that acts as a gravitational lens for light rays coming from behind. How would a rotating black hole look like? How ...
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41 views

What are the zero point energy densities of the individual quantum fields?

I'm reading through "General Relativity - An Introduction for Physicists", by Hobson, Efstathiou, and Lasenby, and I have a question regarding one of the statements related to the cosmological ...
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77 views

Phenomena in the intersection of general relativity and quantum mechanics

I am looking for physical phenomena that have aspects involving both general relativity and quantum mechanics. The only example I know is Hawking radiation. While black holes are objects that cannot ...
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25 views

Accretion disks on neutron star binaries

Why does hydrogen gas from accretion disks not constantly get sucked onto/into a neutron star or into a black hole? I understand that some gets sucked into the black hole and some may come down and ...
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23 views

FRW Metric maximally symmetric, derivation, $R=3K$ or $R=6K$ confusion, two different texts

I'm looking at Tod and Hughston Introduction to GR and writing the metric in the two forms; [1]$$ ds^{2}=dt^{2}-R^{2}(t)(\frac{dr^{2}}{1-kr^{2}}+r^{2}(d\theta^{2}+sin^{2}\theta d\phi^{2})) $$ [2] $$ ...
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54 views

Is the Weyl Postulate correct?

The Weyl postulate in cosmology states that worldlines do not intersect but it can be shown in GR that using Raychaudhuri equation that geodesics can intersect if there is curvature so I'm really ...
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42 views

Problem on finding the spatial components of canonical momenta in Fierz-Pauli Lagrangian

My problem is about finding the spatial components of canonical momenta $\pi_{i j}=\frac{\partial \mathcal{L}}{\partial \dot{h}_{i j}}$ corresponding to the Fierz-Pauli Lagrangian. I am using the ...
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32 views

Name for the transformation into an accelerated frame?

A transformation into a frame that looks at an experiment from a rotated perspective is called a rotation. A transformation into a frame that moves with a different constant velocity is called a ...
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44 views

Ricci tensor of Metric black holes with nils and solv geometries of Horizon

The metric of black holes with nils and solv geometries of the horizon is generically represented by $$\mathrm{d}s^2=-r^{2z}\mathrm{d}t^2+\frac{\mathrm{d}r^2}{r^2}+\sum_{I=1}^3 r^{2q_I}(w^I)^2$$ How ...
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41 views

Super-luminal separation

Suppose there are are 5 bodies separating in space (due to it's expansion), and let us consider that they can emit light. 1st body moves in the -x direction, at the speed of light. 2nd body moves ...
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40 views

Light rays in linearized General Relativity

In General Relativity, particles follow geodesics in space-time, obeying $$\ddot x^a + \Gamma^a_{bc}\dot x^b\dot x^c=0,$$ where $\Gamma^a_{bc}$ are the Christoffel symbols, expressed in terms of the ...
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24 views

Free Components of the Riemann Tensor

Knowing the symmetries of the Riemann tensor, it is known that in 4-dimensional space we would have only 20 free components. My question is: How one can decide which components are necessary to ...
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53 views

Are there experimentally verified differences between general relativity and Lorentz invariant “newtonian” gravity?

I used to have (I lost it) a historical article about how Eintein's general relativity theory "won" over a Lorentz invariant generalization of Newton's gravity (I cannot remember the author). This is ...
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81 views

Boyer–Lindquist coordinates

In the Kerr solution to the vacuum Einstein Equation written in Boyer–Lindquist coordinates. Because it is not spherical polar coordinates, $r$ ranges from 0 to infinity does not cover all the space, ...
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37 views

For gravitational wave from twin stars, how was the tidal effect counted?

As the primary indirect evidence, the work on calculating the rotational slow down earned the 1993 Nobel prize. However, I cannot find any where mention how the work deal with the tidal effect. Are ...
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59 views

What is static mass increase effect predicted by General relativity?

According to wikipedia, static mass increase is predicted by Einstein's General Relativity. In the book 'The Meaning of Relativity' by Einstein, inertia will increase when the object is near a ...
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29 views

Is energy-momentum of curvature a boundary/holographic density?

Since the beginnings of General Relativity, we have had this awkward, unholy separation of the universe in marble versus wood. divergence of the stress-energy momentum holds at all points of ...
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49 views

Does the curvature of spacetime by gravity affect homogeneity and isotropy of the space of the universe?

The FLRW metric starts with the assumption of homogeneity and isotropy of space.(Wikipedia) FLRW metrics of the universe have no or only very weak curvature - It is curved space. In contrast, ...
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31 views

Assigning an asymptotic power to the volume form?

I was reading about the covariant theory of asymptotic symmetries in this review: http://arxiv.org/abs/hep-th/0111246 I have a question about eq. (1.8), but before I ask I should describe what the ...
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80 views

Spin connection and covariant derivative

How to prove explicitly (i.e., to don't postulate it) that by including Lorentz indices $a$ the covariant derivative $D_{\mu}$ looks like $$ D_{\mu}A^{\nu a} = \partial_{\mu}A^{\nu a} + ...
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54 views

On GR with perturbation

Could anyone explain to me what I have misunderstood/missed when trying to understand this paper on GR perturbation? The paper is http://arxiv.org/pdf/0704.0299v1.pdf In equation 25 for $R_{00}$, ...
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119 views

Energy-momentum tensor

I need to show that: \begin{align} \mathcal h_i^a \, T_{ab} \, h_i^b=(\nabla_i \phi)^2-\frac{h_{ii}}{2}[\dot{\phi}^2-(\nabla \phi)^2-m^2 \phi^2] \end{align} where i) $T_{ab}=\nabla_a \phi ...
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56 views

What is the relationship between the formal definition of a tensor and the frequently discussed notion of a “higher order matrix”?

I've been doing some self study on the principles of tensors & manifolds in preparation for a first course in general relativity. I tend to learn better when presented with the full mathematical ...
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94 views

Will relativistic glider cause lower gravitational force in Newtonian gravitation?

In the articles The relativistic glider and The relativistic glider revisited, the relativistic glider is proposed where a quasi-rigid body can slow down its fall under gravity without any reaction ...
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53 views

What's the physical or mathematical meaning of considering non-minimal coupling?

Why we still consider the case of non-minimal coupling? And I don't really understand the motivation of coupling. In general relativity, the non-minimal coupling violates the principle of ...
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61 views

General Relativity: impact of acceleration on time, experimental setup

In What is relativity by Jeffrey Bennett (Amazon link), the author explains how acceleration/gravity impact time and causes time dilation. For this he takes an example of an accelerating space-ship ...
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79 views

Manifold for Schwarzschild and Bertotti-Robinson

In short: what is the manifold in discussion for Schwarzschild metric $$ ds^2 = -(1-\frac {2M}r)dt^2 + \frac1{1-\frac{2M}r} dr^2 + r^2 (d\theta^2 + \sin^2 \theta d\phi^2)$$ and Bertotti-Robinson ...
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97 views

Free fall coordinates/Fermi (normal) coordinates

It makes sense intuitively given the equivalent principle, and I've seen many times it stated, that for a free fall (geodesic) path in an arbitrary spacetime, we can choose our coordinate system to ...
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37 views

Can a quark irreversibly pass though an event horizon?

This is an attempt to transform a question I asked about a year ago into a binary yes-or-no question: Since a quark has electrical charge, can it irreversibly pass though an event horizon? The ...
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73 views

(Scalar) Ricci flatness of a metric

What is the physical meaning to vanishing Ricci scalar $R=0$ of a metric in general relativity? Note that this is not the same questions as the geometric meaning of $R_{\mu\nu}=0$ which has been asked ...
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83 views

Relation between $f(R)$ gravity and Tensor–vector–scalar (TeVeS) gravity

We know that there is a relation between f(R) gravity and scalar-tensor gravity. By applying the Legendre-Weyl transform, we can receive brans-dicke gravity from $f(R)$ gravity. If we start with the ...
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68 views

Gravity's effects on photons moving away from source

As a photon has no mass and must always have velocity c, if I were to shine a laser straight up (so Earth's gravity would be pulling straight back on it), what would the effect be on the photon? It ...
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94 views

Applying Weak Energy Condition for a specific energy-momentum tensor

So, I have a particular energy-momentum tensor, for a specific line element, and I want to check if this obeys the weak energy condition ($T_{ \mu \nu} U^\mu U^\nu \geq 0$ where $U^\mu$ and $U^\nu$ ...
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63 views

Conditions for a diagonal induced metric?

Let $M$ be a manifold of dimension $n$ with a (say Lorentzian) metric $g$, that is diagonal in some choice of local coordinates. Let $S$ be manifold of dimension $k<n$ , embedded in $M$ by some ...
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80 views

Metric with 5D signature: +---+

From a paper that a friend sent to me (on inflation theory which I am still in learner mode) a 5D signature +---+ was specified with the 5th dimension being a velocity dimension. I didn't know that ...
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107 views

Forward's frame-dragging accelerator

On 1962, Robert Forward studied the possibility of using General Relativity Frame-Dragging effects to accelerate probes inertially (that is, without feeling any internal G-forces) One of the ideas is ...
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145 views

Textbook disagreement on geodesic deviation on a 2-sphere

Apologies if I have this completely wrong (and for the general long-windedness). I've searched online but can't find anything helpful/relevant. I'm trying to use the geodesic equation ...
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86 views

How to test that a flat metric represents a global three-torus geometry

When introducing Robertson-Walker metrics, Carroll's suggests that we consider our spacetime to be $R \times \Sigma$, where $R$ represents the time direction and $\Sigma$ is a maximally symmetric ...
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73 views

In an Evolving Block Universe, does the growth rate of the universe give the value of C

In an Evolving Block Universe (http://arxiv.org/abs/0912.0808, http://arxiv.org/abs/1407.7243) the future does not exist. The present moment is the bounding edge of the universe in the time dimension. ...
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52 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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83 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 ...
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62 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?