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.

learn more… | top users | synonyms (1)

1
vote
0answers
87 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 ...
1
vote
0answers
19 views

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 ...
1
vote
0answers
76 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 ...
1
vote
0answers
75 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 ...
1
vote
0answers
78 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 ...
1
vote
0answers
24 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, ...
1
vote
0answers
117 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), ...
1
vote
0answers
64 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 ...
1
vote
0answers
61 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 ...
1
vote
0answers
77 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 ...
1
vote
0answers
98 views

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} ...
1
vote
0answers
80 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 ...
1
vote
0answers
86 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: ...
1
vote
0answers
64 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 ...
1
vote
0answers
42 views

Maximal development/Development of a solution

I'm having troubles to rigorously understand what a development (or maximal development) of a solution is in General Relativity. I was reading a paper by Burnett and Rendall and they write "By maximal ...
1
vote
0answers
45 views

Is a dynamical extension of non-commutative black holes feasible?

Non-commutative (sometimes called "fuzzy") black holes are solutions of Einstein's equations obtained with a previous basic assumption of non-commutativity of the coordinates $[x^{\mu},x^{\nu}]=i\, ...
1
vote
0answers
84 views

Null vector fields given Bondi metric

I'm trying to understand how to compute the null future-directed vector fields if I have a given (Bondi) metric $g=-e^{2\nu}du^{2}-2e^{\nu+\lambda}dudr+r^{2}d\Omega$ with $d\Omega$-standard metric ...
1
vote
0answers
63 views

Singularities in Schwarzchild space-time

Can anyone explain when a co-ordinate and geometric singularity arise in Schwarzschild space-time with the element $$ ...
1
vote
0answers
75 views

When is spacetime homogenous and isotropic?

When is spacetime homogenous and isotropic? For example, some metric $g_{\mu \nu}$ is homogeneous and isotropic. We now construct effective metric $$n_{\mu \nu} ~\rightarrow~ g_{\mu \nu} + ...
1
vote
0answers
112 views

Naked singularity and null coordinates

I'm trying to understand the notion of a naked singularity on a more mathematical level (intuitively, it's a singularity "one can see and poke with a stick", but I'm having troubles on how to actually ...
1
vote
0answers
55 views

Ex 0.2.1 in Sachs and Wu's textbook

In the next attachements are: 1. Exercise 0.2.5 which I want help with. Proposition 0.2.1 and its proof. Now, basically a few things are changed in the theorem, I don't think I can use here the ...
1
vote
0answers
146 views

Dust generated static space-time implications on fluid 4-velocity

Imagine we have a perfect fluid with zero pressure (dust), which generates a solution to Einstein's equations. Show that the metric can be static only if the fluid four-velocity is parallel to the ...
1
vote
0answers
132 views

Use of Principle of Equivalence

Let $x^\mu$ be the coordinates of a reference frame, $K$, where all bodies feel the same constant and uniform acceleration $\textbf{a}=\textbf{g}=-\nabla\varphi$; let $\xi^\mu$ be the coordinates of a ...
1
vote
0answers
61 views

Trying to speak correctly of spacetime intervals and how to compare them

Is it correct to speak of "magnitude of a spacetime interval"? For instance, considering a pair of (distinct) events, $A$ and $B$, which are lightlike separated, is it correct to say that "the ...
1
vote
0answers
123 views

Einstein +Maxwell 's tensor

Why is it true that we can deduce that Einstein's GR equations coupled with Maxwell's EM equations may be written in the form $$R_{ij}=C(F_{ik}F_j^{\,\,k}-{1\over 4}g_{ij}F_{mn}F^{mn})$$ without ...
1
vote
0answers
294 views

Divergence theorem over entire space on non euclidean spaces

I'm a physics major so bear with me here on the math. This is related to a problem from the textbook General Relativity - Wald. In classical electromagnetism if we have a vector field say $V$ defined ...
1
vote
0answers
59 views

The definition of $f_{NL}$ and transfer function

To me there seems to be quite a few different definitions of $f_{NL}$ in cosmology and I would like to know if or how they are equivalent. Let me cite at least 3 such, One can see the equation 6.71 ...
1
vote
0answers
150 views

Black hole entropy from collapsed entangled pure light

Consider the following scenario, very similar to the one proposed in this question, but this time, the pure quantum radiation used for the black hole collapse, is now being split with down-converter ...
1
vote
0answers
93 views

Does quantum Zeno effect play role in astrophysics?

For example, do two galaxies situated in proximity reduce the atom decay rate in each other? What happens with decay quanta escaped to infinity? Does the radius of apparent horizon effect the ...
1
vote
0answers
49 views

Any examples of negative ADM energy solutions with WEC but not DEC satisfied?

Any examples of negative ADM energy solutions with weak energy condition (WEC) but not dominant energy condition (DEC) satisfied? Witten's proof of the positive energy theorem requires the dominant ...
1
vote
0answers
77 views

Reference request: FLRW with k>0, dust, and positive cosmological constant

The exact solution representing a FLRW universe with $k>0$ and dust (p=0), and $\Lambda=0$, is described by a cycloid. What is the exact solution for dust, in the presence of a positive ...
1
vote
0answers
349 views

Newton's Law of Gravitation, Gauss Law and GR

From One of My Unpublished Papers $$\frac{d^2 x^{\alpha}}{d\tau^2}=-\Gamma^{\alpha}_{\beta \gamma}\frac{dx^{\beta}}{d\tau}\frac{dx^{\gamma}}{d\tau} \tag{1}$$ For radial motion in Schwarzschild’s ...
1
vote
0answers
99 views

How complete is our understanding of general-relativistic solutions for extremal black holes?

Putting aside quantum mechanics (or at least putting aside the question of fermions), is our knowledge of extremal General-Relativity solutions good enough that we would be able to rule out a ...
1
vote
0answers
261 views

The structure of space-time

I came across this paper recently called The Small Scale Structure of Spacetime and the following idea occured to me: To uninformed humans the universe appears Euclidean but we know from GR that on a ...
1
vote
0answers
183 views

Trying to understand the weak gravitational field metric (3)

I've worked through Carroll's explanation of the Newtonian limit as far as $h_{00}=-2\phi$ (page 106 - Lecture Notes on General Relativity). As he's previously stated that ...
1
vote
0answers
274 views

Gravitation and the QFT vacuum

I'm asking this to get yet another lessson in the inability of QFT and GR to cohabit. Many people believe GR must yield to quantization. The question here is as to why the activity of the vacuum ...
0
votes
0answers
9 views

What does Weinberg–Witten theorem want to express?

Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ ...
0
votes
0answers
46 views

Is it possible to assign a physical radius to a black hole?

The Schwarzschild metric is given by: $$c^2d\tau^2 = \left(1-\frac{r_s}{r}\right)c^2 dt^2-\left(1-\frac{r_s}{r}\right)^{-1}dr^2 - r^2 \left(d\theta^2 + \sin^2 \theta \, d\varphi^2\right).$$ The ...
0
votes
0answers
48 views

Discontinuous momentum in relativity

I'm thinking about a fantastical scenario where the velocity of all macroscopic objects in the universe is instantaneously set to 0. In a Newtonian reference frame, this is relatively easy to ...
0
votes
0answers
25 views

Relative time dilation in Schwarzschild metric

Let's say we use the Schwarzschild metric to model the curved spacetime around a planet of mass $M$ and radius $R_0$. One clock $A$ is hovering at distance $R_A$ > $R_0$ with the help of rockets, a ...
0
votes
0answers
49 views

Coordinate Symbol confusion in general relativity

In a previous post (Finding the metric tensor from the Einstein field equation?), the equation used lambda, rho mu and nu (not sure of the names of the letters!) for the Ricci tensor and swapped to a, ...
0
votes
0answers
31 views

How does an observer in arbitrary state of motion assign numbers to events in a flat spacetime?

In a flat spacetime, there is an inertial observer, who assigns events coordinates in a usual fashion: Placing a clock everywhere and synchronize them. From his POV, the other observer is moving in ...
0
votes
0answers
137 views

Time Dilation Geometry

I was recently exploring time dilation from Gravity and from velocity and I came up with an interesting derivation that I have not seen before. I was wondering if there is a paper published showing ...
0
votes
0answers
49 views

Computing the Ricci Tensor for a Spherically Symmetric Spacetime

For a homework question, we are given the metric $$ds^2=dt^2-\frac{2m}{F}dr^2-F^2d\Omega^2\ ,$$ where F is some nasty function of $r$ and $t$. We're asked to then show that this satisfies the Field ...
0
votes
0answers
57 views

Covariant Derivative Chain rule?

I want to prove that a covariant derivative of a vector $A^{\mu}(x(z))$ at the point $x(z)$ in general would be defined as $$D_z ...
0
votes
0answers
36 views

Uniqueness of the Einstein tensor

This is related with an exercise 17.4-a in MTW Here what i want to show is the Einstein tensor $G_{\alpha\beta} = R_{\alpha\beta} - \frac{1}{2} R g_{\alpha \beta}$ is the only second-rank, symmetric ...
0
votes
0answers
41 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 ...
0
votes
0answers
31 views

Gravitational Redshift and Length Contraction

Gravitational redshift is based on the time-time component of the metric (e.g., http://en.wikipedia.org/wiki/Redshift). Why does length contraction not contribute to redshift?
0
votes
0answers
31 views

Advantage and disadvantage of weak field approximation

Many textbooks related with GR, covers weak field approximation, (also called Linearized gravity). Since so far, i have been calculated many this with this $i.e$ $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}$ ...
0
votes
0answers
31 views

Do all the spacelike curve terminate at the spatial infinity $i_0$ in the Penrose Diagram of a Schwarzchild black hole?

Let's restrict to the radial direction, so the metric can be expressed as $ds^2=-(1-r_S/r)dt^2+(1-r_S/r)^{-1}dr^2$ with $r_S$ the Schwarzchild radius. Expressed in Kruskal coordinates, the metric is ...