Tagged Questions

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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GHY boundary term

What is the simplest way to calculate Gibbons-Hawking-York boundary term for Schwarzschild metric? \begin{align} \int ...
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How does matter interact with spacetime? [on hold]

It's easy to see how matter interacts with itself but how does it interact with spacetime which is "not" matter? Einstein showed us that mass and energy cause a curvature in spacetime, which intern ...
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56 views

Ray tracing in General Relativity

I would like to find out what one would see at the Schwarzschild radius of a massive non-rotating black hole, if the black hole is surrounded by a bright ring. For that, I would place the observer at ...
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1answer
79 views

Verifying a solution to Einstein's vacuum field equations

I need to verify a solution to Einsteins vacuum field equations. I have the solution as follows $$ds^2=a\,dt^2+b\,dr^2+\cdots$$ Is the following the right approach? Einsteins equation reduces to ...
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1answer
104 views

Is General Relativity based on a Symmetry?

In short: Is there any kind of symmetry one can start with to derive general relativity (GR)? Longer: Einstein had the opinion that GR was the generalisation of special relativity, because instead of ...
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General relativity, expressing a distance in terms of the metric tensor [on hold]

My starting point is: I've been told in the question. The interval between events which belong to the same world line of light equals zero, so I think that means ds = 0. So I now have: From ...
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1answer
40 views

Circular orbit in Schwarzschild coordinates [on hold]

This was an example in a general relativity textbook which I've been trying to work through myself. A spaceship uses its rocket engine to maintain a circular orbit around a Schwarzschild black hole ...
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0answers
22 views

What is the rate at which the field of an electron spreads? [duplicate]

There are 2 steps in the creation of a force field: (1) first the object comes into existence (2) then the field appears. In the case when a photon splits into an electron and an antielectron, these 2 ...
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1answer
33 views

Can we define the effective mass or the moving mass of a photon?

I know that the rest mass of a photon is zero. but the photon can be bent by gravity (which can also be explained by the curvature of space-time due to the effect of mass), this implies that it must ...
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0answers
74 views

What is the derivation of $E=mc^2$? [duplicate]

How did Einstein derive his most famous equation: $$E=mc^2$$ Is the above equation a special case of $$E^2=m^2c^4+p^2c^2$$ Its derivation? What is the difference between them?
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Tensors and Minkowski space time [on hold]

I have a vector field $A^i$ in Minkowski space time whereby I need to determine the following: $$\nu_\mu \frac{\partial \nu^\mu}{\partial t}$$ $$\nu_\nu \nabla \nu^\mu$$ In terms of the gamma ...
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Gravitational multi instantons

I was reading "GW Gibbons and SW Hawking, Gravitational multi-instantons, Physics Letters B 78 (1978), no. 4, 430–432." I had a few questions regarding the metric they define. I was wondering how ...
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How to do averaging of the second order ricci tensor.? [on hold]

since we cannot write a covariant form of energy momentum tensor for the fields, we will take average over several wavelengths at every space points. To do the averaging for the energy momentum tensor ...
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1answer
301 views

Angular momentum in curved spacetime

It is known that the angular momentum components are also a representation of the $SU(2)$ generators. Given a non-trivial spacetime, say a black hole of some kind or AdS space, how can one define the ...
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3answers
171 views

Recommended books for a “relativity for poets” class?

I teach physics at a community college and have developed a new course titled "Relativity for Poets," which I will be teaching for the first time in spring 2015. As implied by the title, it's a ...
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1answer
68 views

What is Laplace operator of Schwarzschild-Spherical coordinates? [closed]

This is the Laplace operator of Spherical coordinates: What is the Laplace operator of Schwarzschild-Spherical coordinates? where the Differential displacement of Schwarzschild-Spherical ...
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0answers
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Some books to bridge the gap before GR [duplicate]

I am extremely interested in GR, but somehow feel that the books I read are not really enough. Frankly, I find many question on this site and elsewhere completely bewildering, which makes me think ...
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Tensor raising and lowering [closed]

Just a quick question. I know: $V^{a}V_{a} = 1$ But wondered on the following: $V^{a}_{ab}$ Is it $1*V_{b} = V_{b}$ Or would I have to re-label V as it wouldn't be the same component?? Thanks!
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1answer
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Correct tetrad index notation

There seems to be some different conventions on the indexes of the tetrad. I am wondering which is the standard, which is correct, and which is an abuse of notation. In Sean Carroll's notes and in ...
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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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3answers
135 views

Gravity - Force or Result?

I am no Physicist, but I enjoy reading about Physics. However reading about leading theories such as M-Theory and others they speculate about the existence of the Graviton. In my past reading of ...
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2answers
925 views

Is my interpretation of how a gravitational wave is formed correct?

I'm sure many here are familiar with the following image showing the 2D representation of how the fabric of spacetime is warped by the presence of mass:- Can this fabric be interpreted as an ...
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1answer
52 views

One step in deriving the Einstein-Hilbert action

In this amazing first principles derivation of the Einstein-Hilbert action there is one small manipulation needed to show $$c g_{ab,cd}\left(\eta^{ac}\eta^{bd} - \eta^{ab}\eta^{cd}\right)$$ is ...
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1answer
377 views

How quickly does gravity extend from created mass? [duplicate]

I apologize in advance if this is a stupid or off-topic question. Since Energy can be converted into matter according to $E=mc^2$, how fast does it take for the gravity of that new matter to extend ...
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1answer
52 views

Increasing matter density in the Friedman equations?

From what I understand, the Friedman equation is $H^2=\frac{8\pi G}{3} \rho$ and the $H$, the Hubble constant, is a measure of the rate of expansion of the universe. What I am confused about is that ...
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how to specify eigenfunctions(eigentensors) of Lichnerowicz operator?

Lichnerowicz operator is an operator which acts on transverse trace-free symmetric tensors. If this statement is correct, my question is that any transverse trace-free symmetric tensor is an ...
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1answer
255 views

Geodesic deviation equation - why does the ordinary second derivative give the correct answer?

I've calculated the correct answer to my problem, but don't understand one of the assumptions I made when doing so. I used the geodesic deviation equation ...
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General Relativistic Boltzmann Equation Verification

Let $(M,g)$ be a (pseudo)Riemannian manifold. Define on $TM$ the symplectic 2-form $\omega=dx^\mu\wedge dp_\mu$ and use $g$ to define the pull back $\omega_g=dx^\mu\wedge d(g_{\mu\nu}p^\nu)$. Define ...
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1answer
35 views

Cluster of Black Holes around a Central Point [duplicate]

Within the Star Wars Extended Universe, there is a science base on a small object within a near impenetrable sphere of Black Holes. These Black Holes remain in roughly the same position and, according ...
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65 views

Is there a null incomplete spacetime which is spacelike and timelike complete?

Geodesic completeness, the fact we can make the domain of the geodesic parametrized with respect an affine parameter the whole real line, is an important concept in GR. Especially, because the lack of ...
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1answer
96 views

Why is it so coincident that Palatini variation of Einstein-Hilbert action will obtain an equation that connection is Levi-Civita connection?

There are two ways to do the variation of Einstein-Hilbert action. First one is Einstein formalism which takes only metric independent. After variation of action, we get the Einstein field equation. ...
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1answer
115 views

Advanced Gravitational Waves? [closed]

Do advanced gravitational waves exist?
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1answer
95 views

Help understand article on thin shell formalism

I've been learning the Israel formalism (see original article here, although I prefer the exposition given by E. Poisson in his book A Relativist's Toolkit) for thin shells. I think I understand the ...
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1answer
49 views

Determining zero energy from $k=0$?

I'm curious as to the equations necessary for finding a total energy of 0 (or, I suppose, the energy density of empty space due to quantum fluctuations) in a flat Friedmann universe such as ours. The ...
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60 views

Why doesn't this proof change indices?

In this pdf, in the second line of the proof, $\sigma$ was plugged in where it appears as $$\frac{\partial x^\sigma}{\partial y^{\rho'}}$$ Meanwhile in converting the coordinates of $g^{\mu'\rho'}$, ...
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1answer
47 views

Tidal affect on an object and the length contraction in Relativity Theory

According to the equivalence principle in general relativity theory; If an object are in free falling in a gravitational field,the object will not detect gravitational force on it. From this ...
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1answer
46 views

Christoffell symbols manipulations [closed]

Why is it that $$\Gamma^\lambda_{\lambda\tau}\Gamma^\tau_{\mu\nu} = 0?$$ The same goes for $$\Gamma^\lambda_{\nu\tau}\Gamma^\tau_{\mu\lambda} $$which was set equal to zero by the author..
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1answer
41 views

Confused about equations for the Big Bang in general relativity ad loop quantum gravity?

I am trying to get a vague understanding of the mathematical equations for the Big Bang in GR and LQG. My understanding so far is that when the universe is assumed to be homogeneous and isotropic, ...
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1answer
22 views

Kaluza suggested metric

Is there a book or a paper that goes into the mathematical details of getting scalar curvature of the 5 dimensional metric that Kaluza wrote down? I am running into many mathematical issues for I am ...
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52 views

Non-trivial scalar quantity

Is there any scalar quantity made of only the Christoffel symbols, determinant of a metric and tensors, not derivatives? In other words, can we construct a scalar quantity which cannot be written in ...
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3answers
2k views

Does Gravity Really Exist? [closed]

As far as I understand some of the readings, Gravity does not exist in real terms. It's only a way of modeling motion as we see. Einstein for example explained the motion without having to have ...
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0answers
39 views

What topics should I develop complete concepts in before I begin the derivation of GR? [duplicate]

I had just been trying to understand GR but i just cannot understand where some of the formula of field came from. Apparently all those initial formula are from Newtonian physics so please anyone ...
3
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1answer
85 views

Modifying Newtonian gravity to fit observed precession of Mercury's orbit

The idea is to modify Newtonian gravity so that it fits measurements of orbits around the sun. For example the precession of Mercury's orbit unlike Newtonian $n$-body simulations. I'm currently not ...
3
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2answers
166 views
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0answers
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0answers
41 views

What is the status of gauged gravity [duplicate]

The Standard Model of elementary particles is a gauge theory with gauge group $SU(3)\times SU(2)\times U(1)$, which is really a successful theory. We might be able to quantize gravity similarly. ...
2
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0answers
51 views

What's the meaning when Kerr-Newman metric's mass is zero?

Kerr-Newman metric represents the spacetime of a charged and rotating black hole. If the mass parameter is zero, this metric is still not the Minkowski spacetime. What's the meaning of a charged and ...
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2answers
121 views

Geometric meaning of parallel transport

The definition of parallel transport of a vector $v^b$ along a curve $C$ with tangent field $\it{t}^a$ is given by Wald's GR as $$t^a \nabla_a v^b = 0$$ Is it correct to think of $\nabla_a v^b$ as ...
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1answer
31 views

Tensors applied to vector and dual vector fields in GR

This is a specific question about tensor manipulation in Wald's GR. I'm asking for clarification of a trivial step, because I'm working through the text outside the context of a class, without prior ...
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0answers
39 views

How to derive the cigar soliton solution to the Ricci flow equation? [closed]

I am trying to derive the cigar soliton solution to the Ricci flow equation. Such solution has the form $$ {\frac {{{\it dx}}^{2}+{{\it dy}}^{2}}{{{\rm e}^{4\,t}}+{x}^{2}+{y}^{2 }}} $$ I am ...