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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Breakdown of correspondence principle: null dust case

In both quantum and general relativity theories we are used to provide results in the "limited" conditions to demonstrate a correspondence between new and old formalism. For instance deflection of ...
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Guesses from a Rindler observer

Suppose an observer travels through Minkowski space $M=\mathbb{R}^4=\left\{x_0,x_1,x_2,x_3\right\}$ on a uniformly accelerated path: \begin{equation} \begin{cases} x_0= R \sinh(\frac{\tau}{R}) \\ x_1= ...
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51 views

Transforming to the Transverse-Traceless gauge

I have a certain Ansatz for a gravitational wave perturbation of the metric $h_{\mu \nu}$ that is nonzero in a compact set of background flat Minkowski spacetime But the Ansatz field does not satisfy ...
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35 views

Spherically Symmetric Metric in Nordstrom gravity

Nordstrom's theory of gravity postulates that the metric is of the form $g_{\mu \nu} = \phi ^2 (x) \eta_{\mu \nu}.$ The field equations, in vacuum are of the form $R=0$, where $R$ is the Ricci ...
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55 views

Is there something similar to Gauss's Law For Gravity in General Relativity?

In Newtonian Physics there is an equation that for the Gravitational Flux of an object known as Gauss's Law For Gravity. Gauss's Law for Gravity describes the number of Gravitational Field Lines ...
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String spreading?

What is 'string spreading' (in the context of string theory)? Does it have implications for the observability of post-classical effective field theory of gravity terms near macroscopic black hole ...
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48 views

Questions arising from the presentation of “Schild's ladder” in “Gravitation” (Misner, Thorne, Wheeler)

MTW, p. 248, presents a description of "Schild's ladder" construction which I quote here extensively enough for referencing some subsequent questions. A. Transport any sufficiently short stretch ...
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40 views

Bending of light in a gravitational field & the principle of equivalence

I have a few conceptual issues following a standard thought experiment to argue why light bends in a gravitational field and I'm hoping I can clear them up here. Consider an observer in a lift in ...
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28 views

Dark Energy Density Paramater For Unlimited Expansion

Suppose that the universe is dominated by matter and dark energy. Let $\Omega_m$ and $\Omega_\Lambda$ denote the respective relative density parameters. Given $\Omega_m$, what does $\Omega_\Lambda$ ...
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27 views

Are only measurements registered as events?

When we measure an electron or some other system behaving quantum mechanically, we observe something. Now, this can be called as an event in relativity terms meaning if we live in 1-D spacetime, only ...
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32 views

Gibbons-Hawking Variation

I know there already exist some questions about this and some very good answers. However, I am still having trouble understanding one part of the calculation. The GHY term is given by ...
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57 views

Which property do the word Pressure refer to in General Theory of Relativity?

In this course by MIT Alan Guth while delivering the lecture stated " Both Pressure and Energy densities can produce gravitational fields. Negative pressure creates repulsive gravity and positive ...
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DGP model, minus one dimension

Is there a name for a theory like the DGP model, but with one fewer dimension? That is, a theory whose action consists of the 4D Einstein Hilbert action at long distances, and the 3D one at small ...
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32 views

Expression for the energy in the limit case of weak gravitational field

I'm trying to solve the following problem of General Relativity. Consider a particle of mass $m$ which moves following a geodesic in a space-time with metric $$ ds^2 = - ...
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80 views

Gravity's force on space

Here is a quote from Brian Greene, The Fabric of the Cosmos: Space, Time, and the Texture of Reality, p. 273: “The early universe provided an arena in which gravity exerted its repulsive side with ...
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70 views

Does rest mass increase in the FRW metric?

The flat FRW metric can be written in conformal co-ordinates: $$ds^2=a^2(\eta)(d\eta^2-dx^2-dy^2-dz^2)$$ where $\eta$ is conformal time. Let us assume that $a(\eta_0)=1$ when $\eta_0$ is the present ...
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Definition of Energy in Friedmann equations?

The first Friedmann equation for a flat Universe is given by: $$\bigg(\frac{\dot{a}(t)}{a(t)}\bigg)^2 = \frac{8 \pi G}{3} \rho(t)$$ The energy density $\rho(t)$ is given by: $$\rho(t) \propto ...
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How to derive the relation satisfied by “gravitational magnetic field” from an equation of the Weyl tensor?

Let us call the spacetime $M$ with a metric $g_{ab}$. There is a unit spacelike vector field $\eta^a$ orthogonal to a hypersurface. So that we can define the so-called gravitational electric and ...
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Why is special relativity still in use, if general relativity is more broad?

I always thought special relativity is only there because it is the building block for "The General theory of Relativity", until recently I encountered a text from my course book given below. A ...
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Local Translation of frame field- Geometric Picture

In order to phrase my question I review my geometrical picture of the first order formulation of gravity: Given some d-dimensional manifold $\mathcal{M}$ one constructs the Frame bundle $FM$, a ...
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31 views

Solving the Stress-energy-momentum tensor with metric

Let's say I want to find an expression for $T_{00}$ in Einstein field equations given a particular metric. I need to find first $g_{00}$, which is not complicated to find, and $R_{00}$ which is ...
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38 views

Calculating propagation time along the path of a photon

In this paper $\tau(t) := \int_{t}^{t_d}ds$ is defined as "the propagation time between the detection time, $t_d$, and $t$, as incrementally measured by a set of local observers along the light path". ...
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de Sitter reviews?

I'm very interested in learning more about de Sitter and anti-de Sitter spaces and their applications in GR and cosmology. Can anyone recommend favorite review articles -- or, more likely, a series ...
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Is the curvature formed due to mass/volume of spactime convex or concave?

I am really confused about the curvature of space-time. Does it bends in a concave shape in presence of mass/volume as shown by the example of rubber sheet and ball or does it bends in a convex shape? ...
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Anti de Sitter Motion without matter

I've read that a non zero cosmological constant can lead to "motion without matter" in vacuum spacetimes such as AdS. Initially I didn't understand what the significance of this statement was since I ...
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66 views

Topology of Anti-de Sitter manifold with black hole

I'm interested in understanding the topology of space-time with a black hole. In other words how does having a black hole affect quantities such as the fundamental group, de-Rham cohomologies, Euler ...
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61 views

3D-representation of space-time

When I read something about GR, I nearly always see some pictures that look like trampolines, like this one. I know that the curvature of space-time is described by the Riemann-Tensor $R$. I was ...
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Hilbert Stress Energy Tensor for fermions + EM field and Yang-Mills theory (fermions + gluons)

@Qmechanic or anyone else who knows the reference. I am trying to find a references to the work(s) where thorough derivation of Hilbert Stress Energy Tensor for fermions + EM fields and Yang-Mills ...
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37 views

Variable $r$ in Dirac equation

Solutions of Dirac equation for an electron in orbit of an atom are usually expressed in terms of spherical coordinates $r,\theta$ and $\phi$. For a point ($r,\theta,\phi$) the variable $r$ represents ...
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Variation of a tensor quantity

How does one go about in finding a variation of a tensor quantity say, with respect to the variation in the metric tensor? I've gone through calculus of variations but I can't figure out how one ...
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41 views

Is it true that GR waves can interfere if and only if the change to the metric can take negative values?

This appears to be a unique question compared to other topics about electromagnetic waves or quantum mechanics already on Stack Exchange. The topic on resonance doesn't really answer this question. ...
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88 views

How to calculate photons/light trajectory under gravity

I'm aware many questions are out there asking similar questions about photons and gravity and I got the basic concept by searching through them. I will just call it light although it may not be the ...
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37 views

Bulk action - Can a brane velocity be defined?

a) If a brane action in a bulk is defined, in that case, that a brane is modelwise moving through a bulk, how is this ratio defined? Is this a regular "velocity" in that meaning, that space is being ...
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Can the curvature of space be measured using a swimming pool?

I read somewhere that if the center of mass of two twelve ton elephants was one meter apart then the space they curve would be one nanometer longer. (Though I doubt elephants come that dense) This ...
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Derivation of stress-energy tensor in curved space-time

I've a problem about calculating the components of the stress-energy tensor in general relativity. I've learned that if we have an action of the form : $$ S=\int (R+\mathcal L_{m})\sqrt{-g}d^4x $$ ...
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What is the degrees of freedom of metric tensor?

As $g_{\mu\nu}$ can be taken to be symmetric, it contains 10 functions of spacetime in 4 dimensions. But, why we call these 10 functions as the degrees of freedom of the metric while they are the ...
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Expanding Electric Field, Magnetic Field in post-Newtonian Gravitational Potential

I've cross-posted this question from Mathematics since Physics is probably better suited for the nature of the question. I've ...
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38 views

What is the scale factor of a hyperbolic universe?

I wanted to derive the solution to this question from the Friedmann equations myself but I ran into some trouble. I was working in natural units where $c=G=1$, then, for brevity, I defined ...
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Clarification of Type D space-time

I've asked this question on MathOverflow but received no feedback, so I thought I'd try better luck here. I've read the following formulation of the Goldberg-Sachs theorem in Chandrasekhar's ...
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Any applications of kinetic physics on cosmological scales?

On galaxy cluster scales, one is usually forced to use approximate theories such as hydrodynamics or magnetohydrodynamics for modelling cosmological phenomena. I wanted to ask if kinetic theory is ...
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68 views

Particle energy in conformal FRW spacetime?

Let us start with the flat-space FRW metric in Cartesian co-ordinates for simplicity: $$ds^2=-dt^2+a(t)^2(dx^2+dy^2+dz^2).$$ In GR the energy of a particle is given by: \begin{eqnarray*} ...
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What is the status of the area theorem in AdS?

The area theorem, by Hawking (in "Gravitational Radiation from Colliding Black Holes", also found in Wald), states that the area of an event horizon cannot decrease with time. As I understand, there ...
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51 views

Gravitomagnetic railgun

Would a gravitomagnetic analogue of a railgun work as expected, in theory? Consider replacing the electric currents on each rail with mass currents. Then place a mass between the rails, moving with ...
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Radius of apparent event horizon for accelerating observer

This question is related to my last question on the Unruh effect, which can be found here. First, recall the quote from the Wikipedia article on the Unruh effect: An accelerating observer will ...
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Was the impossibility of the second degree perpetuum mobile in the General Relativity ever proven?

Somewhere I've heard, that gravity often likes to work against the entropy. For example, the surprisingly low temperature of the black holes. Or see the gravitational separation of different elements ...
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Does a graviton impart negative momentum?

Picture a massive system on an axis. If a graviton is generated and emitted by a system in the positive direction, will that system also be accelerated in the positive direction? Another system ...
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Are there any $f(R, T)$ models of gravity?

For the past few months I have been studying $f(R)$ models of gravity. Recently I came cross $f(R, T)$ modified models of gravity. For the past few days I have tried to work out the difference between ...
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About spin 2, graviton, in the context of attractive force.

excerpt from Introduction to Black hole physics, Valeri P. Frolov and Andrei Zelnikov In this textbook, there is comment about spin of gravitons as follows For gravitating bodies the gravitational ...
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Relativity… Twin paradox

Sorry, but I have another stupid question about relativity. In the twin paradox: Let's say the travelling twin went to Proxima Centauri and back at 0,99c. However, he did not slow down to stop on ...
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Which is the corrispondent of the Lorentz's transformation in general relativity?

The Lorentz's transformations tell us how space and time change in a flat case? There are a more general and powerfull transformation for general relativity?