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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$\pi$ and the Curvature of Space

If one draws a circle on a sphere and measures the ratio of the diameter to the circumference, that value varies depending on the diameter of the circle compared to the diameter of the sphere it is ...
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313 views

Is a black hole's surface area invariant for distant intertial observers?

Let's imagine I'm very far from any massive objects, so my local space-time is Minkowskian. Off in the distance is a black hole, far enough away that it doesn't noticeably curve space-time near me, ...
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245 views

Will a black hole increase the speed of sound above the speed of light in this medium

For the sake of this question we are inside the EH and a sound wave enters from our perspective as the sound moves closer to us at the EH would it speed up. Specifically how would the extreme ...
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355 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From One of My Unpublished Papers $$\frac{d^2 x^{\alpha}}{d\tau^2}=-\Gamma^{\alpha}_{\beta \gamma}\frac{dx^{\beta}}{d\tau}\frac{dx^{\gamma}}{d\tau} \tag{1}$$ For radial motion in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 ...
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145 views

Pseudo-Superluminal Motion and the Synchronization of Clocks

Let's consider two points A an B separated by a finite distance in curved space time. A light ray flashes across an infinitesimally small spatial interval at B. Metric: ...
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753 views

Curvature of spacetime in only required to explain tidal forces?

I'm a bit confused about the equivalence principle in GR. I'm quoting from Wikipedia: An observer in an accelerated reference frame must introduce what physicists call fictitious forces to ...
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3answers
228 views

Apparent non-aberration of gravity waves

Since GR assumes that gravity waves travel at speed c, we expect we would be able to some day detect an aberration effect similar the that of light. Of course, gravity waves are so tiny in magnitude, ...
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840 views

Zero divergence of energy-momentum tensor and gravitational energy

Trying to teach myself general relativity and have just hit yet another confusion. I'm reading that in curved spacetime the energy-momentum tensor has zero divergence, ie ...
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1answer
488 views

Geocentric Model in General Relativity

In classical mechanics, if I want to view the Earth as the fixed center of the solar system, I must accelerate my reference frame to keep it centered on the Earth. That accelerated reference frame ...
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152 views

Effect of gravity at near-lightspeeds

Let's say I'm in a space station, hurtling towards our galaxy nearly close to the speed of light. From my reference frame, I see the galaxy coming towards my ship at the same speed. I pass the Sun, ...
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448 views

General Relativity - Einstein field equation and quantum field theory

Einstein field equation has many solutions. Out of them, is there any solution that is incompatible with quantum field theory? Also, what solutions of Einstein field equation would be incompatible ...
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189 views

Comparing Lagrangian in Special Relativity vs General Relativity for a weak gravitational field

This is a sequel to this question. Who knows a difference between the Lagrangian in SR and GR for a weak gravitational field in non-relativistic case? What is the reason of this difference?
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409 views

Does the current acceleration of universe imply that our universe is open?

Does the current acceleration of universe imply that our universe is open? If the universe is closed, from the Friedmann's equation, the acceleration of universe wouldn't be possible, would it be? (Of ...
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How is Big Bang related to theory of relativity?

I'm not someone with good scientific knowledge, so if my question are weird, correct me. I was reading about big bang and I came by the theory of relativity. Can someone explain the relation between ...
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284 views

The Light Cone in GR-----A Flickering One?

Events in relativity[SR or GR]are marked by coordinate values and not by physical values.We write a metric for motion along the x-axis: $$ds^2=g_{00}dt^2-g_{11}dx^2$$ ----------- (1) For physical ...
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806 views

metric signature explanation

Can anyone explain what metric signature is? I have a basic knowledge regarding tensors, btw. Also, how is it related to fundamental understanding of general relativity? Thanks.
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299 views

Confusion regarding geodesic of thrown ball - curved or Cartesian coordinates?

I'm confused trying to understand what's happening in terms of spacetime geodesics when a ball is thrown and its trajectory plotted, height against time to give a parabola. I read (from more than ...
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Why do objects follow geodesics in spacetime?

Trying to teach myself general relativity. I sort of understand the derivation of the geodesic equation ...
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556 views

spacetime expansion and universe expansion?

First of all, does the expansion of spacetime solely cause the expansion of universe? Secondly, if spacetime is the sole cause, do objects(matter with mass) themselves expand? Thirdly, by spacetime ...
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Will free-fall object into black hole exceed speed of light $c$ before hitting black hole surface?

In Newtonian mechanics, if we throw an object in against direction of gravity with speed $v$ and it achieve max height of $h$. Now if we allow object to fall from that height $h$, it will eventually ...
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462 views

Interpretation of the Einstein-Hilbert action

Everyone knows the famous Einstein-Hilbert action $S_{EH} = \int d^4x \sqrt{-g} R$. I'd like to know if, after we first explicit the Ricci scalar in terms of the metric, it could be possible to ...
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2answers
335 views

How does gravitation propagate along curved spacetime?

In this wikipedia article it is described how a beam of light, with its locally constant speed, can travel "faster than light". That is to say it travels a distance, which, from a special relativistic ...
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517 views

shouldn't gravity travel at light speed immediately

if gravity travels at c(light speed), why aren't objects pulled to earth at that speed? Since the velocity of gravity is 9.8 meters per second squared, will it eventually accelerate until it maxes ...
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How does the string worldsheet affect the space-time in which they live?

I don't understand much about string theory and never really got much further past the Nambu-Goto action and very basic supersymmetry (SUSY) lectures in my undergraduate courses, but the only thing ...
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2answers
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Are neutrinos affected by gravity?

Layman here, but EE and BS physics. I know that light is affected by gravity. But are neutrinos? During the collapse of a star into a neutron star, as the electrons join protons to form neutrons ...
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778 views

A dictionary of string - standard physics correspondences

Motivated by the (for me very useful) remark ''Standard model generations in string theory are the Euler number of the Calabi Yau, and it is actually reasonably doable to get 4,6,8, or 3 ...
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799 views

Derivation of the Gauss-Codazzi equation

I'm interested in the derivation of the Gauss equation (Gauss-Codazzi). Usually we consider the definition of the Riemann tensor on the hypersurface. $$^{(n-1)}R_{abc}^{~~~~~~~d}~w_d=[D_a,D_b]w_c$$ ...
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212 views

Clarification on Wald's book

I have a question concerning the Wald's book: General Relativity. In the appendix E, he derived the Einstein equation by considering the surface term (GHY). I do not understand what he said after the ...
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4answers
453 views

What does the equivalence principle mean in quantum cases?

We know that electron trapped by nuclear, like the hydrogen system, is described by quantum state,and never fall to the nuclear. So is there any similar situation in the case of electron near the ...
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1answer
360 views

What is the fate of a 3-Torus universe?

Since it is flat, will it expand forever like a flat and open universe or collapse like a closed and curved universe?
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2answers
249 views

How can we model intrinsic curvature?

Can it only be done in Euclidean space? Doesn't Euclidean space only model extrinsic curvature?
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434 views

Why is the universe described in terms of Euclidean space and not Minkowski spacetime?

The universe is described as an infinite Euclidean space in cosmology. Why isn't it treated as Minkowski spacetime?
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296 views

How to deal with the product of distributions by Renormalization or similar?

how can we deal for example with the product of distributions in physics ?? is there any mean to define with physics $ \delta ^{2}(x) $ or to treat a product of two distributions within the ...
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3answers
296 views

Twin paradox - observers counter orbiting Earth

Imagine three observers - one (A) stationary on the surface of Earth (latitude 0 deg) and two others orbiting the planet in the same circular equatorial orbit just in the opposite direction. When the ...
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1answer
191 views

Simulating a black hole binary system

As part of a project for my degree I am writing code to simulate N-body gravitational interactions, however I have to then use this code to investigate something. Struggling to think of ideas I ...
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What makes the stars that are farther from the nucleus of the galaxy go faster than those in the middle?

It has no sense that stars that have a bigger radius and apparently less angular speed($\omega$) goes faster than the ones near the center.
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Faster-than-light communication using Alcubierre warp drive metric around a single qubit?

The Alcubierre warp drive metric has been criticized on the points of requiring a large amount of exotic matter with negative energy, and conditions deadly for human travellers inside the bubble. What ...
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2answers
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How do we determine the temperature of a Black Hole?

How do we determine the temperature of a Black Hole? Since we cannot see a Black Hole, which I presume, is because it absorbs light, would it not also prevent radiation from escaping, making ...
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1answer
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Why is light described by a null geodesic?

I'm trying to wrap my head around how geodesics describe trajectories at the moment. I get that for events to be causally connected, they must be connected by a timelike curve, so free objects must ...
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330 views

Computing the path of photons near a black hole

For a simulation, I want to compute the path that light follows near a black hole. Non-relativistically, a massive point particle in a central newtonian gravitational field follows either an ellipse, ...
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1answer
408 views

Do spacelike junctions in the Thin-Shell Formalism imply energy nonconservation and counterintuitive wormholes?

The Thin Shell Formalism (MTW 1973 p.551ff) is used to properly paste together different vacuum solutions to the Einstein equations. At the junction of the two solutions is a hypersurface of matter – ...
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The relativistic mechanics of a battery that is being charged and accelerated at the same time

This might be an interesting question: Let's attach a battery into one end of an electric cable. Then we rotate the battery around, with accelerating speed, using 100 Watts of power, while the ...
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Does a photon exert a gravitational pull?

I know a photon has zero rest mass, but it does have plenty of energy. Since energy and mass are equivalent does this mean that a photon (or more practically, a light beam) exerts a gravitational pull ...
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Abstract Algebra in Relativity and Cosmology?

Is Abstract Algebra useful in theoretical Relativity and/or Cosmology? If so can anyone give me some examples or point me towards a good book with that emphasis if it is one? Thanks in advance.
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647 views

Why does large curvature of spacetime imply high temperature?

I`ve just stumbled about a sentence which says that high curvature of spacetime implies that any matter present is at high temperature. This somehow confuses me, so my probably dumb question(s) are: ...
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2answers
247 views

Are we going to be able to travel trough space deforming the space-time?

I'm not talking about the speed of the spaceship. If we can deform space-time we needn't any type of propulsion. And how can the travel affect to it's pilots? Can they survive?
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Equivalence of definitions of ADM Mass

ADM Mass is a useful measure of a system. It is often defined (Wald 293) $$M_{ADM}=\frac{1}{16\pi} \lim_{r \to \infty} \oint_{s_r} (h_{\mu\nu,\mu}-h_{\mu\mu,\nu})N^{\nu} dA$$ Where $s_r$ is two ...
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3answers
267 views

Tension on a cable in a gravitational field

Consider a mass 'm' suspended in the gravitational field of a massive star. Assuming the Schwarzschild metric it is easy to calculate the gravitational acceleration at the location of the mass and ...
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604 views

Does spacetime in general relativity contain holes?

Are there physical models of spacetimes, which have bounded (four dimensional) holes in them? And do the Einstein equations give restrictions to such phenomena? Here by holes I mean ...
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347 views

Evidence that “space exists rather than just particles”

What is (theoretical) evidence that you need to define all of space with properties rather than just stating where all particles are? I mean, does every single coordinate x, y, z have a meaning or ...