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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“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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69 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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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 ...
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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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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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92 views

Is inertia actually a property of the force rather than the mass?

I ask this because it occurred to me that the inertial property of mass only actually arises in the context of forces (such as the EM force) as a resistance to their accelerating effect. Inertia plays ...
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27 views

Difference between Gravitational and Matter Scalar Fields

In the context of Scalar-Tensor theories of gravity (for example in Brans-Dicke) what is the difference between gravitational and matter scalar Fields? My doubt comes from "The scalar-tensor Theory ...
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76 views

Maybe photon energy is constant as the Universe expands?

This is a question following on from my previous post Time-like Killing vector in FRW metric? For simplicity I take the spatially flat FRW metric in cartesian co-ordinates given by: $$ds^2 = -dt^2 + ...
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18 views

Lee Yang force and cosmology

The text I am reading (Stars and Relativity by Ya. B. Zel'dovich) discusses the possible existence of a repulsive force proportional to total baryon number. At the time of the book's publication it ...
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64 views

Variation of the purely covariant Riemann tensor

I need to find the variation of the purely covariant Riemann tensor with respect to the metric $g^{\mu \nu}$, i.e. $\delta R_{\rho \sigma \mu \nu}$. I know that, $R_{\rho \sigma \mu \nu} = g_{\rho ...
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38 views

How to prove this auxiliary lemma to Hawking's singularity theorem?

This theorem is number 44 of chapter 14 in Barret O'Neil's book "Semi-Riemannian Geometry (with applications to relativity)". The proof given, in particular the use of another theorem to justify the ...
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87 views

Are standard and isotropic forms of Schwarzschild metric truly equivalent?

My admittedly rudimentary understanding of physical meaning of conformal flatness - as pertaining to a stationary observer exterior to a spherically symmetric static gravitating mass $M$: Locally ...
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22 views

4-acceleration of rotating frame

Consider the 3-dimensional Minkowski space $$ ds^2=dt'^2-dr'^2-r'^2d\phi'^2 $$ Now we transform it into a rotating frame: $$ t'=t,r'=r,\phi'=\phi+\omega t $$ Then the metric becomes $$ ...
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65 views

Stationary and Static

I have some confusion about the concept of stationary and static. A metric $g$ is called stationary if there is a time like Killing vector $K$. $g$ is called static is further HSO (hyper surface ...
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74 views

About the proof of the second Bianchi Identity

The second Bianchi Identity is $$ \nabla_{[a}R_{bc]de}=0 $$ As far as I know, the proof (say, Walfram Mathword) start by stating the representation of Riemann tensor in local inertial coordinates $$ ...
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77 views

'hypersurface orthogonal' component of covariant derivative of normal vector

I believe that answer to my question is rather trivial but I can't seem to get my head around it. In context of ADM formulation of gravity (or any other differential geometry context, I guess) the ...
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21 views

Instabilities in the CDMT

Could anyone explain or refer to references on why the CDMT f(R) gravity model suffers from Instabilities any why the sign of ${\mu}^{4}$ matters.
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71 views

What if UV behaviour of gravity was perturbative?

I understand that the UV behaviour of gravity ought to be dominated by black hole production and that graviton-graviton scattering ought to blow up above the Planck scale. Suppose, however, that ...
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61 views

Are there 'special' cases for when special relativity can be applied for accelerating bodies?

I have the following theoretical situation: A space station modeled as a ring in free space is rotating about its centre point at a high speed. I am trying to work out where time flows slower. From ...
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52 views

General Relativity representations

General relativity is said to be essentially unique. What is the equivalence relation that links the different constructions? In other words, is the equivalence relation called isomorphism or ...
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67 views

Wave equation for de Sitter invariant Green's functions

In several papers on QFT in de Sitter space (curvature set to $1$) it is asserted that the Klein-Gordon equation obeyed by the two point function of the free fields: $$(\square-m^2)G(x_1,x_2)=0 $$ can ...
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61 views

Schwarzschild diagram in Einstein Cartan theory

I'm a very visual learner and I would like to know if the diagram representing the Schwarzschild solution is altered at all when the torsion tensor is non zero. Of particular interest - what is the ...
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110 views

Tetrad formalism: getting back to coordinate basis

Let $\omega^{\hat{a}}$ be an orthonormal basis, and $\theta^{\hat{a}}_{\hat{b}}$ be the associated connections. From Cartan's second structure equation, we may compute the curvature 2-form, i.e. ...
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59 views

Topology of spacetime in 2+1 dimension

In the book Quantum Gravity in 2+1 dimension by S. Carlip, in the second chapter (section 2.1), he comments that a compact 3-manifold with a flat time orientable Lorentzian metric and a purely ...
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108 views

Covariant Derivative with a Torsion Free Metric

Where $\triangledown$ is the covariant derivative and we are to assume that the connection is torsion free (that is, we can exchange the lower indices of the connection coefficients), how can I prove ...
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126 views

Induced metric on the boundary of a manifold

The Gibbons-Hawking-York term which supplements the Einstein-Hilbert action is, $$S_{GH} = \frac{1}{8\pi G} \int_{\partial M} d^3 x\sqrt{-h} \, K$$ where $\partial M$ is the boundary of the manifold ...
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40 views

How to calculate the minimum number of extrinsic dimensions of a metric tensor?

The Question How does one calculate the minimum number of dimensions of an extrinsic space that can be used to define the metric tensor \begin{align} g_{mn} = \dfrac{\partial y^k}{\partial x^m} ...
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80 views

Reissner-Nordström Black Holes

The Reissner-Nordström black holes are described by the metric, \begin{align} ds^2 = -\left(1-\frac{2M}{r}+\frac{Q^2}{r^2}\right)dt^2 + \frac{1}{1-\frac{2M}{r}+\frac{Q^2}{r^2}}+r^2d\Omega^2 ...
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43 views

Information paradox and spacelike slices

I'm reading S. Mathur's paper on the information paradox and I can't seem to understand the reason why we choose spacelike slices. Is it because we want to have a global timelike vector so that we ...
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48 views

Meaning of $k$ in Sachs-Wolfe formula for angular power spectrum

I've seen the formula for the angular power spectrum of the CMB written as $$C_\ell = \frac2\pi \int\left|\Theta_\ell(k) \right|^2 k^2dk, $$ where $\Theta_\ell(k)$ is the temperature contrast at a ...
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87 views

Wald General Relativity, Chap 7.1

On page 166 of Wald's General Relativity book, he claims that the equation (7.1.20), $$ 0 = R^t{}_t + R^\phi{}_\phi = (\nabla_a t) R^a{}_b \xi^b + (\nabla_a \phi) R^a{}_b \psi^b, $$ yields (7.1.21), ...
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74 views

Moment of Inertia in SR/GR & Calculating it in General

In classical mechanics you want to calculate the moment of inertia for hollow & solid: lines, triangles, squares/rectangles, polygons, planes, pyramids, cubes/parallelepiped's, circles, ellipses, ...
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82 views

Modelling a matter dominated universe collapsing into a black hole

With the FLRW equations we can get solutions for a matter dominated closed universe in which the finale is an ultimate collapse, but this is only in terms of $a$ (the scale factor) and $t$ (time) and ...
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55 views

Do wormholes have a side to their path through space?

In theory do wormholes have a side to their path through space? What is there at a point in line with the entry and exit, would anything look different at that point in space? Could a space ant get ...
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139 views

Understanding spherically symmetric metric

In these lecture notes the static isotropic metric is treated as follows (p. 71): Take a spherically symmetric, bounded, static distribution of matter, then we will have a spherically symmetric ...
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79 views

Ricci scalar higher dimensions

I was wondering if there is a straightforward way to compute the Ricci curvature of a metric that has the form (à la Kaluza-Klein): $g_{MM}\equiv\begin{pmatrix}g_{\mu\nu}&g_{\mu ...
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Is it possible to express “free”-ness of a time-like world line without referring to “tangent space” (but only directly to causal relations )?

I don't know much about tangent spaces, or tangent vectors, "as such"; nor about affine parametrization (which seems to be closely related to the notion of tangent vectors, as far as I understand for ...
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69 views

The time dilation in an oscillating elevator

Suppose you are in an elevator which oscillates vertically with a frequency $\nu$. How will we find the time dilation in this oscillating reference frame ? If the lift is accelerating upward or ...
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71 views

4 of Einstein equations without 2nd order time derivative

This question is related to my previous one and it was a homework problem and was due two weeks ago. Problem:prove that four of Einsteins' equations $$ G_{0\nu} = 8\pi T_{0\nu} $$ have to 2nd order ...
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76 views

Weak gravitational lensing multispectral, multibackground correlations

My understanding of weak gravitational lensing is that it assumes random alignment distribution of galaxies in order to estimate statistical shear and convergences, which are used to estimate matter ...
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23 views

If the absolute horizon were exclusionary of matter, what supernova behaviors would that predict?

Kip S Thorne's "Black Holes & Time Warps", 1994 paperback, p.415, Box 12.1: ... The absolute horizon is just a point when created, but it then expands smoothly, like a balloon being blown up, ...
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53 views

Is there a matching material interior for the Kerr solution of Einstein's equations?

Is there a matching material interior for the Kerr solution of Einstein's equations? I can only find informal and conflicting information about this. Some time ago, I've heard that it was expected to ...
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105 views

Linearized gravity and symmetries

I have naive question. When we analyzing weak gravity field we introduce expression for metric tensor as $$ g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}, \quad \eta_{\mu \nu} = diag(1, -1, -1, -1), ...
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61 views

River model of spacetime for arbitrary situations

This paper describes black holes as space flowing inward (the rotating hole also twists in a weird way): http://arxiv.org/abs/gr-qc/0411060 The proper time given by the objects is the same as ...
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57 views

Present experimental status of Moffat's Modified theory of Gravity

Modified theories of Gravity have been discussed before in this 2-year old question, Are modified theories of gravity credible? I was going through Moffat's modified gravity, given in ...
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76 views

Preservation of a scalar along geodesic trajectory

Let $u^\mu$ be the velocity of a particle , and $\xi^\mu$ be a killing vector. would taking a contravariant derivative of to scalar product $\xi_\mu u^\mu$ , and showing that it equals to 0 shows that ...
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Thermal radiation in the Unruh Effect

The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator): $$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} ...
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79 views

Would a closed field of gravity neccesarily lead to paradoxes?

I've asked wether artificial gravity, as seen in some SF-Movies, would violate known laws of physics. To recap, my idea of an Artificial Gravity (AG) system was like this: A Device that creates an ...
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80 views

Superradiance of electromagnetic waves

I have to do a calculation (problem 5 of chapter 12 in Wald) verifying the super-radiance of electromagnetic waves incident on Kerr black holes and have a few preliminary questions. As background: ...
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62 views

What do the components of light velocity look like in polar coordinates?

The Schwarzschild solution makes use of polar coordinates, and I'm wondering how the different components of velocity of light change with the position. Might I get some examples of light velocity ...