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Questions tagged [general-relativity]

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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How do we calculate massive particle paths from schwaschield diagram?

Given the diagram here, we can easily trace out paths of light rays. But if I imagine a stationary particle moving upwards in time going through the center of the light cone, it appears as if it doesn'...
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Gravitational redshift and Energy of a photon

Let us assume that we have a large gravitational field, then the gravitational redshift can be expressed as, $$\frac {v_{\infty}} {v_e} = (1-r_s/R_e)^{1/2}$$ In this equation $v_{\infty}$ represents ...
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All black holes no matter of their mass, will evaporate immediately? [on hold]

If general relatively are proven that time travels slower near a blackhole, As we know how to calculate black holes' lifespan due to hawking radiation, for the particles locked inside the black hole, ...
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1answer
45 views

Differentiating Scalar along a geodesic

I have been studying GR for sometime and doing exercises from Schutz and I have a question about differentiating along a geodesic. Here is what I know. The equation of geodesic in terms of four ...
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1answer
38 views

Spacetime drag and galaxies' radial velocity mismatch

We know - or theorize - that a spinning black hole drags spacetime in its surroundings, producing measurable effects on the accretion disk (the minimum stable orbit radius). What I cannot grasp is why ...
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Advanced and Retarded Coordinates for Hawking Radiation

I am trying to solve the Klein Gordon equation near the horizon of a black hole. For a more accurate result I am using the Vaidya Metric in which the mass is a function of retarded time u. When ...
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Apparent FTL speeds seen by observer

MY guestion is if I was in a ship orbiting a black hole (not very close to the event horizon) I am orbiting pretty far and I am experiencing that my time is slowing down realitive to people on earth. ...
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2answers
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Can a photon circle a black hole indefinitely?

Does a photon lose energy or redshift as it circles? Will it's wavelength be the rest wavelength with centripetal and gravitational forces exactly cancelling?
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42 views

Is “time” just a word? [duplicate]

What I mean is: Is "time" something that causes change in objects ,(i.e something that really exists physically ,like gravitational energy) OR Is it just a word that we uses to represent, the ...
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Questions about tear in spacetime [duplicate]

Sorry if there's any mistake in the language. In Einstein's General Relativity Theory gravity is described as the curvature of the spacetime fabric. So can analogous to a real fabric can this ...
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36 views

How to calculate mass from time dilation and radius?

I'm new to this site and I'm been searching the internet all over for this solution. I'm looking for an equation, that if given the time dilation at the surface of an object and its radius, it will ...
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11answers
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Is spacetime wholly a mathematical construct and not a real thing? [on hold]

Speaking of what I understood, spacetime is three dimensions of space and one of time. Now, if we look at general relativity, spacetime is generally reckoned as a 'fabric'. So my question is, whether ...
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I have a question about the gravity probe B geodectic precession formula and why it seems to be twice the planetary precession formula

Specifically, I can work out the planetary precession formula to give radians per orbit as 6*pi*GM/c^2r (and I find that on the web at places like http://farside.ph.utexas.edu/teaching/336k/...
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Mass bending spacetime: what is the mechanism? [duplicate]

What is the mechanism that causes mass to bend spacetime? Merely inferring that it does is not an answer. How it does it is the answer.
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1answer
39 views

Schwarzschild geometry for negative masses

Imagine that in a part of our universe there exists negative masses $M=-|M|<0$. The metric around this object -- say a black hole -- will be of the form $$ ds^2 = -\Big(1+\frac{2|M|}{r}\Big)dt^2 + ...
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1answer
44 views

Will I be destroying spherical symmetry if I write the mass of the body as a function of time?

Will I be destroying spherical symmetry if I write the mass of the body as a function of time? If yes, then how can I write a metric for a body with mass as a function of time?
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time dilation in zero gravity [on hold]

My guestion is if somehow someone could lower gravity in a limited field ( like a meter diameter sphere of zero gravity or near zero gravity around a clock) and let's say an observer watched the clock ...
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2answers
92 views

Non-static spherical symmetry spacetime

The Schwarzschild solution is a static spherically symmetric metric. But I wanted to know that how would the space-time interval look in a Non-Static case. I tried to work it out and got $$ds²= Bdt² -...
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Did inflationary expansion “abruptly” turn into non-inflationary, rather than gradually decelerate to non-inflationary?

From the $\Lambda$CDM model, the universe was in an expanding state and then inflation occurred which turned non-inflationary expansion into inflationary expansion. After inflation ended, did ...
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0answers
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Kaluza-Klein approach and Gauss-Cadazzi approach

Can you tell me the difference or physical application of Kaluza Klein approach and Gauss Codazzi approach? In Kaluza Klein theory, 5 dimensional theory can be dimensional reduced to 4 dimensional ...
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1answer
121 views

Spacetime has an infinite number of choices for differentiability. Coincidence?

Spacetime can be modelled using a four-dimensional topological manifold. Say we denote the manifold using $(M, \mathcal{O})$ where $\dim M =d$. The structure $(M,\mathcal{O})$ is not sufficient for ...
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1answer
78 views

Time for a photon to pass through a massive body

Suppose there is a neutron star with a hole in the middle. Through this hole, scientists shoot a laser beam in such a way that it will pass through the gravity well of the neutron star but will not ...
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1answer
67 views

Why $dS^d \cong SO(d,1)/SO(d-1,1)$?

I have found a similar question, but there they give a seemingly rigorous proof, and what I am looking for is just an intuition. I understand that $S^2 \cong SO(3)/SO(2)$: for every point in $S^2$ ...
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Windowless space station: rotation vs. gravity ring vs. frame dragging?

Imagine a windowless hollow cylinder, with an observer sitting inside on the curved wall. Something is pulling the observer against that wall. The observer can also walk easily along the inner ...
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1answer
100 views

Why Einstein's unified field theory is believed not to work?

In his later life, Albert Einstein was trying to extend his general theory of relativity to incorporate electromagnetism and other fundamental forces with it, something he himself called "The theory ...
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Is there any use of a quadratic equation of state in FLRW cosmology?

Consider standard FLRW cosmology. Usually, the relation between energy density $\rho$ and pressure $p$ of a cosmological fluid component is linear: \begin{equation}\tag{1} p = w \, \rho, \end{...
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2answers
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Hamiltonian formulation of general relativity

Why is it not possible to find a Hamiltonian formulation of general relativity as easily as in classical mechanics? There was a remark to this in my lecture but no real explanation as to why this is. ...
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1answer
63 views

Line element 1-form

It was pointed out that dual vectors of a manifold, and hence differential 1-forms, are not dependent on the metric (Intuition behind dual vectors ('Bongs of a bell' does not help)). But doesn'...
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Is general covariance operationally incomplete? [closed]

In a previous post it was noted that the principle of general covariance admits an overabundance of coordinate systems that leads to an ambiguity of physical interpretation. Although each of these ...
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1answer
60 views

Why do we impose de Donder gauge?

In the field language, a massless particle corresponds to irreducible representations of the Lorentz group. In particular, given a spin-2 massless particle, we can embed the creation and annihilation ...
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3answers
49 views

Ricci Scalar as Curvature

So I understand that the Ricci scalar represents the curvature of the space. Since any manifold can be considered locally flat, is Ricci scalar always zero locally for any manifold? On one hand it ...
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1answer
61 views

Confusion of the motion of a photon inside the photon sphere

In lecture, I am told that if a photon is initiated outside the event horizon of a black hole, from the laboratory frame of reference, it will never reach the event horizon. What is confusing is that ...
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1answer
55 views

Energy in spherically symmetric space times

In deriving the equations of motion for geodesics in spherically symmetric spacetimes through Hamiltonian formalism, we can find some constants of motion, namely, $E$ and $L$, the energy per unit of ...
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4answers
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Visualization of $ dtdx$ and $dxdy$ term in metric tensor

For the sake of simplicity, lets take a 2+1 dimensional spacetime. Lets take the metric $$ds^2 = g_{tt}dt^2 + g_{xx}dx^2 + g_{yy}dy^2 + g_{tx}dtdx + g_{xy}dxdy$$ What is the visualization or ...
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2answers
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How can the universe be dodecahedron-shaped?

Physicsworld references "Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background" by J.-P. Luminet et al., published in Nature (...
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How to go into another parallel world? [closed]

If I go into another parallel world in train, Then where is the original me in the world go? If I saw the white hair Old people in train, is she grandmother or she herself? should I talk to her? they ...
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3answers
92 views

Intuition behind dual vectors ('Bongs of a bell' does not help)

Similar to the post here (How to visualize the gradient as a one-form?), I'm wondering about an intuition behind dual vectors and differential forms (and the link in that answer to Thorne's notes is ...
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3answers
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Is spacetime-curvature relative?

Velocity is relative, which means kinetic energy is. Since, according to general relativity, energy bends spacetime around it, wouldn't this mean observers moving in different inertial frames measure ...
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Book recommendation for second look at GR [duplicate]

Between Hawking & Ellis and Wald, which one would be the better choice to follow up a graduate-level course in GR (based off of Carroll's book)? If not either of those two, does anyone have any ...
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Obtaining Brans Dicke theory scalar (wave) equation

I have trouble with obtaining d'Alambert equation for scalar field in Brans-Dicke gravity (http://www.scholarpedia.org/article/Jordan-Brans-Dicke_Theory). B-D gravity langrangian density is given by: ...
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1answer
48 views

Gravitational redshift discrepancy?

I want to compute the redshift of a signal emitted by a static observer in $r=R_1$, $\phi=\phi_1$and recieved by another static observ at $r=R_2$, $\phi=\phi_2$ with $R_2>R_1$, in Schwarzschild ...
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1answer
57 views

Modification of Gravitational force's law and related problem

I'm facing a problem which states the following: Suppose that it is discovered that Newton's law of gravitation is incorrect and that the force $F$ on test particle of mass $m$ due to a body of ...
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1answer
64 views

Why would it take so great distance for an object to have the acceleration due to gravity?

Let's suppose that in a certain reference frame, a hyperbolic coordinate is used, i.e. $(x,t)=(r\cosh \omega, r \sinh \omega)$. On each hyperbola $r=R$, where $R>0$ is a constant, the proper ...
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1answer
102 views

Why are we trying to fit GR in QFT when there's a chance that GR is incomplete?

GR explains most phenomena in our universe, but not everything.. Dark matter and Dark energy still don't fit in explanation of GR. QFT, on other hand, is almost complete. Shouldn't physicists go for ...
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Circular motion in schwarzschild metric

Hi i have an observer in circular motion in Schwatzschild metric, the velocity is described by the vector $$u^{\mu}=A(\delta_0^\mu+\Omega\delta_0^\mu)$$ and i have to fix A, compute the acceleration ...
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2answers
87 views

Role of the special linear Lie algebra in general relativity (GR)

The Lie derivative measures the difference between two paths in the timespace manifold, and hence the commutator bracket occurs naturally, as explained in the presentation What is a Tensor? Lesson 21: ...
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1answer
62 views

Direction of gravity

General Relativity explains the path a falling body makes (ex. An apple falling toward the center of the Earth) as a geodesic in curved spacetime. What explains the direction the apple falls? In other ...
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0answers
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Propagation of gravitaional waves near black holes [duplicate]

As we know near black holes light gets strongly deflected. And if the gravity of the black hole is strong enough, the light can move in circles around the black hole. How the gravitational wave ...
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1answer
56 views

Derivation of equation for geodesic deviation

I am trying to figure out the calculation which leads to the geodesic deviation on this site. So far I understood all steps until (14.7) and managed to show that (14.6) = (14.7), namely $$ \ddot\xi^\...
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1answer
85 views

Flattening a curved space

It is possible, apparently, to describe gravitational lensing as if gravitational potential induces an effective refractive index change in the vacuum, and spacetime is flat. As pointed out by @...