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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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 ...
3
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1answer
348 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
47 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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12 views

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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69 views

Possible theory of everything? [on hold]

Tell me if there is anything that sounds immediately incorrect about this possibility or if it's already been considered. We know that the universe can be in infinite different quantum states, but we ...
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122 views
+100

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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0answers
18 views

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
33 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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60 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 ...
7
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84 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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57 views
+50

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
42 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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27 views

How comes, that for Gravitational Waves H-atom size we need energy of a neutron star, but for the warp-drive only negative mass of jupiter? [closed]

Gravitational Waves and the Warp-Drive - both have a kind of wave form. However for GW's you need at least neutron star merger to create an amplitude of H atom size. Comparing that to the ...
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56 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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73 views

Could gravitational pressure act as dark energy? [closed]

The Newtonian hydrostatic equation, which is normally applied to compact objects in gravitational equilibrium like stars, is given by: $$\frac{dP}{dr}=-\frac{GM(r)\rho(r)}{r^2}$$ where $P(r)$ is the ...
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1answer
41 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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64 views

Schroedinger wave equation [closed]

Has there been any work on how the Schroedinger wave equation is affected in the stretched spacetime of a strong gravitational field in General relativity?. Rather than being a 'broad' question this ...
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1answer
44 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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36 views

What is the current expansion velocity in the standard model of cosmology (Big bang, Lamda CDM model)? [closed]

There are roughly four phases of expansion: inflation, radiation (red) , matter (blue), dark energy (green/yellow). What is the current velocity according to that model? Ps.: I am not interested in ...
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1answer
39 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
17 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
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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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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 ...
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47 views

Hodge dual on dx example [closed]

If I have equation (1) $$*dx = \frac{1}{1!} \epsilon^1_idx^i $$ where $$*$$ is the hodge dual on $$dx$$, can I lower the 1 from the epsilon? If so why? Please note: Edit dx is basis of a 1-form ...
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1answer
79 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 ...
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2answers
158 views
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4
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40 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. ...
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50 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
116 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
30 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 ...
3
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0answers
38 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 ...
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251 views

A Theorem Due to Hodge: Hawking/Ellis

This is probably quite an obscure question but hopefully somebody has a simple answer. I'm studying the proof of the topology theorem on black holes due to Hawking and Ellis (Proposition 9.3.2, p. 335 ...
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2answers
75 views

Newtonian potential defines size of Universe?

As I understand it the Newtonian potential $\Phi$ at the position of an observer in space is approximately given by: $$\Phi \sim \frac{G M}{R},$$ where $R$ is the radius of a sphere centered at the ...
3
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1answer
56 views

Riemannian curvature tensor [closed]

In Einstein's field equations, it includes only energy momentum tensor of the matter alone. However, it doesn't include the energy momentum tensor of the field. In Professor Hamber lectures on General ...
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27 views

Relation between the curvature of a manifold and the number of covariantly constant vector fields that it admits

Suppose that on a four dimensional manifold we are able to explicitly construct four linearly independent covariantly constant vector fields $K^a_{\mu}$: $$D_{\mu}K^a_{\nu}=0,$$ $a=1,2,3,4$ then it ...
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33 views

Problem about Schwarzschild Radius [closed]

I'm a high school student in korea. Could you help me solve this problem? I should express theta as schwarzschild Radius (=Rs) and b when v_0 → c(=3x10^8m/s) help me......
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3answers
79 views

Generators of the Diffeomorphism Group

So what are the generators of a Diffeomorphism Group? For simplicity, let's consider $ Diff(R^2) $ (diffeomorphisms of the euclidean plane.) Diffeomorphisms are differentiable, invertible ...
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1answer
128 views

Does accelerating generate gravitons?

If gravity and acceleration are indistinguishable, then does that mean converting potential energy to kinetic energy generates gravitons... but only temporarily until you stop accelerating?
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1answer
62 views

Ricci Scalar of the five-dimensiional Reissner–Nordström metric is different to zero?

The Ricci scalar of the four-dimensional Reissner–Nordström metric is equal to zero. In the case of the five-dimensional Reissner–Nordström metric, the Ricci scalar is different to zero?
1
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2answers
51 views

Conserved quantity of Spactime Diffeomorphism Group

So it's my understanding that the underlying symmetry of GR is the Diffeomorphism Group of 3+1 spacetime. It's also my understanding that a symmetry implies a corresponding conserved quantity in a ...
6
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1answer
73 views

Does nature of singularity in black hole depend on material that fell in?

Electromagnetic waves have a tracesless stress energy tensor, and therefore if they are the only fields in a region of spacetime, the Ricci curvature scalar $R=0$ according to GR. However $R^{\mu\nu} ...
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1answer
70 views

How does gravity's space time distortion access energy to induce freefall? [closed]

An observer, standing on top of a building, has a gravity switch (use your imagination) which allows him to turn gravity on and off. He turns the switch off, then releases a pool ball over the edge ...
4
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2answers
137 views

FRW metric and its validity througout the age of the universe

Why do we think that the FRW metric should be valid throughout the entire history of the universe?
4
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2answers
76 views

Can time be interacted with? [duplicate]

Astronauts come back to Earth younger than they would have been had they stayed on Earth for that same period of time. They are traveling so fast relative to the Earth that time slows down for them. ...
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1answer
77 views

Variational principle for a point particle (massive or massless) in curved space

We know that for a point particle, the action is $$ S[x,e] ~=~ \frac{1}{2}\int_{\lambda_A}^{\lambda_B} d\lambda\left[e^{-1}(\lambda)~g_{\mu\nu}(x(\lambda))~\dot{x}^\mu(\lambda)~\dot{x}^\nu(\lambda) ...
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207 views

Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory

In Einstein-Cartan gravity, the action is the usual Einstein-Hilbert action but now the Torsion tensor is allowed to vary as well (in usual GR, it is just set to zero). Variation with respect to the ...
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Forward's frame-dragging accelerator

On 1962, Robert Forward studied the possibility of using General Relativity Frame-Dragging effects to accelerate probes inertially (that is, without feeling any internal G-forces) One of the ideas is ...
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2answers
104 views

When does a singularity start to exist during a black hole formation?

Excuse me if the question is naïve. I am not a physicist. Let's imagine formation of a black hole from a homogeneous collapsing star. At certain moment when enough of matter is inside of a small ...