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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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A doubt in Modified gravity

I am new to dark matter and modified gravity so excuse and inform me if I am wrong. If changes are made in the Friedman equations then there wouldn't always be an underlying action action principle. ...
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Electric field of point charge that has circular motion

We know that moving charge in constant velocity has deformed equation of electric field. $$ E = k \frac{1-\left(\frac{v}{c}\right)^2}{\left[1-\frac{v^2 \sin^2\theta}{c^2}\right]^{3/2}} \frac{q}{R^2}$...
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How to calculate the derivative of scale factor as a function of conformal time from the solution of Friedmann equation

For the flat geometry of lamda CDM model, the solution for Friedmann equation is $$ a(t) = \left\{ \frac{Ω_{m,0}}{Ω_{Λ,0}} \sinh^2 \left[\frac{3}{2} \sqrt{Ω_{Λ,0}} H_0(t - t_0)\right] \right\}^{1/3},...
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Acceleration as the logarithmic derivative of the redshift factor $U^\sigma \nabla_\sigma U^\mu = g^{\nu\mu}\nabla_\nu \ln V$

Let $K^\mu = V(x)U^\mu$ be vector proportional to the four-velocity $U^\mu$. (e.g. $K^\mu$ is a normalized time-like Killing vector for an observer at infinity). Then, $V(x) = \sqrt{-K_\nu K^\nu}$ is ...
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Energy-momentum vs charge-current

Is there a simple intuitive way to explain why energy-momentum density requires a tensor, while charge-current density is a vector? $\partial_{\mu} J^{\mu} = 0$ is a statement, in effect, that the ...
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How is Gravity created in opposite to centrifugal force?

Wikipedia points out that Gravity is: most accurately described by the general theory of relativity (proposed by Albert Einstein in 1915) which describes gravity not as a force, but as a ...
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Nature of motion between comoving observers; What is the common time that they agree on?

This is a set of follow-up questions regarding this post. The following four queries are very closely related and needed to asked at the same place. Question 1 Is it really possible to regard the ...
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Why is $\chi_{[\mu}\nabla_\nu \chi_{\sigma ]} = 0$ at the Killing horizon?

Let $\chi$ be a Killing vector field that is null along a Killing horizon $\Sigma$ Why is $\chi_{[\mu}\nabla_\nu \chi_{\sigma ]} = 0$ at $\Sigma$?
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Does Graviton bend light?

In the weak gravitational regime where the low-energy effective action holds,(linearized) gravity can be quantized, and we can treat graviton as quantum fields on a Minkowski background. One can also ...
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Length Contraction of a rotating object

When observing an object, such as a spinning ring, what velocity is used to calculate its length contraction? I know it depends on the observer, but let's say theoretically an observer is just ...
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34 views

Einstein equations algoritms solutions [on hold]

My question is, is there an Einstein equation's calculation algorithm, and what is Einstein's 10 equation system?
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Could a trajectory around a large mass ever deflect by more than 180 degrees due to general relativistic effects?

Possible mechanisms that could be an answer to the question What natural mechanisms could lead to the unlikely case of the same rogue asteroid or planet passing through our solar system twice? include ...
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Solution of Friedmann equation in terms of conformal time

We know that for the flat geometry of lamda CDM model, the solution for Friedmann equation is $$ a(t) = \left\{ \frac{Ω_{m,0}}{Ω_{Λ,0}} \sinh^2 \left[\frac{3}{2} \sqrt{Ω_{Λ,0}} H_0(t - t_0)\right] \...
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General relativity: congruence and integral curves

I've been doing some research on GR for a assignment on the Raychaudhuri equation. To do so, I've had to pick up some math I had not learnt earlier. My university offers a really poor choice of ...
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Toy almost everywhere flat metric

I was looking into this paper from 2003 by Krasnikov - “The quantum inequalities do not forbid spacetime shortcuts” - and apart from the fact that I find it very scetchy without many details and hard ...
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Does charge affect space-time?

Okay suppose there is an hypothetical particle called Nelectron which has mass = mass of electron but is electrically neutral. It has same spin and other quantum mechanical properties. Even the same ...
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54 views

Metric for a Collapsing Disk and FLRW

I have to obtain a time-dependent metric for a disk which satisfies a simple differential equation but I am stuck with making sure that the physics is correct. To be explicit, I'll first describe a ...
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The fundamental transition problem

can anyone explain what is mentioned here https://arxiv.org/abs/1405.6091 (page 7 and 8) in simple terms: Finally, Krauss makes the very problematic claim that “the structures we can see, like ...
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Simple argument for Melia's linearly expanding Universe [on hold]

Here is a simpler version of my argument for Fulvio Melia's linearly expanding Universe. The Universe is assumed to be isotropic around every point P. Therefore, in Newtonian terms, the net ...
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Total mass-energy of a system in GR [duplicate]

the Gravitation book confirm that "for closed universe the total mass-energy and angular momentum is undefined and undefinable" why many cosmologists claim that the total energy of a closed universe ...
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Is there a scalar field that gives rise to the energy-momentum tensor of a perfect fluid?

If I understand correctly, Sean Carroll's Spacetime and Gravity says that the energy-momentum tensor for a perfect fluid $$T^{\mu\nu} = (\rho + p)U^\mu U^\nu + pg^{\mu\nu}$$ can be obtained as the ...
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Is $H$ proportional to $B$ or not?

I was reading an article saying in the cylindrical coordinates a uniform magnetic intensity $H$ along the z-axis produces a magnetic field $B$ along the z-axes given by $$B\left(r\right)=\frac{...
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Will the log of wood sink in the water?

Imagine the water in a river is flowing with speed very close to the speed of light. There is a log of wood tied to any object outside the river so that it doesn't go ahead with water and is at rest ...
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Black hole horizon states in standard derivations of Hawking Radiation

In all standard derivations of Hawking radiation given e.g. by Hawking, Parker and Wald, one has the so-called horizon states. The point is that when one is quantizing a scalar field on a black hole ...
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Question (mostly) About Relativity

Before I get into the actual question, I'd like to say that my only knowledge on Einstein's Theory of Relativity (both Special and General) have been obtained through about an hours worth of videos ...
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Doubt about energy conditions: the Time-like Convergence Condition

First of all, consider a congruence of smooth time-like geodesics parametrized by proper time $\tau$. So, a tangent vector to a time-like geodesic is indeed a four-velocity up to a factor constant; ...
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3answers
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Is there a contradiction between isotropy and the Big Bang? [duplicate]

Disclaimer: I'm not asking whether the Big Bang happened at a point. I'm asking whether the fact that the universe is isotropic and that the Big Bang happened contradict each other. To be honest I am ...
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Using intuition to understand physics concepts, how and when to let that need for intuition go? [on hold]

Those of us who grew up solving Newtonian mechanics, electrostatics, and calculus of 1-3 variables problems developed good intuition for understanding simple concepts. This helped me condition a ...
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78 views

Non-relativistic limit of Hamiltonian for a free particle in general relativity

The Hamiltonian for a particle moving in a gravitational field can be taken as $$\mathcal{H} = \frac12 \sum_{\mu,\nu=0}^3g^{\mu\nu}(x)p_\mu p_\nu\tag{1}$$ as long as the parametrization is affine. ...
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25 views

Einstein field equations solutions [on hold]

How can solve Einstein's field equations equations step by step? What are the steps? What is the mathematical form of the solutions of this equation?
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1answer
48 views

Tidal force of a black hole without using tetrad

One thing I have been somewhat curious about is computing geodesic deviation for tidal effect. Specifically, given separation vector $\xi^a$ between two nearby timelike geodesics and $V^c$ the ...
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Kinematic aspects of quantum gravity

Quantum gravity proposals at the leading perturbative order, such as the quantisation of linearized gravity, or the low-energy effective action like in string theory, provide the dynamics for the ...
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If matter comes from energy, does this mean that energy has weight?

If the matter in the Universe formed from the energy of the Big Bang, and matter has weight, does this mean that energy has weight? Moreover, as the Universe expands over time, does its overall ...
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1answer
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Derivation of Komar formulae from ADM formalism?

Is there a way to derive the Komar formulae from the ADM formulae? Both the formulae give the same answer for mass and angular momentum, so I was wondering if one can be derived from another. On an ...
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Nothing can ever go through the event horizon of a black hole [duplicate]

Nothing can ever fall into a black hole, even from the perspective of something in the process of falling through (a process I am arguing can never be completed.) Here's my argument. As seen from ...
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Can we define gravity on Calabi-Yau manifolds?

I have read about applying Hermitian geometry in general relativity in deriving holomorphic gravity. But if we take it some steps further i.e. allowing Kähler manifolds with the Ricci flatness ...
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Argument for Fulvio Melia's linear cosmology? [closed]

I would be very interested in people's opinion of my argument for Fulvio Melia's linear cosmology. The FLRW metric for an expanding universe does not have a time-like Killing vector therefore in ...
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Escape velocity of Kerr black Hole [duplicate]

Do the event horizon of Kerr black Hole have escape velocity is equal to the speed of light same Schwarzschild black hole?
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57 views

When will a person falling into a black hole be crashed by tidal forces?

Assume that a person can resist $30g\approx 300\frac m{s^2}$ (remark: the record is actually at 46.2). I want to solve for the distance $r$ at which a $1.5m$ tall slim person falling radially into a ...
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63 views

Time travel to the past via solutions of General Relativity [closed]

Are there any solutions in General Relativity which allow for time travel to the past without introducing a closed timelike curve?
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1answer
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Solving differential equation for the Schwarzschild metric with cosmological constant

How do we solve for Einstein's equation in the vacuum with a cosmological constant, in the static spherically symmetric situation? Attempt: Following Sean Carroll's Spacetime and Geometry (p.195), I ...
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Where can I find 'General relativity without coordinates ' by T.Regge? [closed]

Or any other such article, I have searched everywhere but haven't found any other coordinate free treatment of GR.
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1answer
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Reference on quantization of linearized gravity

I often see claims saying that quantization of linearized gravity can be done. Is there some standard references for it? such as original papers/ review papers / textbooks etc.
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Does the frame dragging Schiff Equation imply opposite directions of spin over the pole compared to the equator?

In reviewing the answers to Schiff Equation in a polar orbit, I see that the Schiff Equation for rotation about the z-axis (north-south pole axis) can be written as: This is integrated to give an ...
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1answer
71 views

How much kinetic energy is there in the observable universe at any given time?

I know that it fluctuates, but, what would be a good estimate for how much kinetic energy is in the universe right now? I know that things cancel it out, but, how much is there?
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1answer
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Can our universe be a true vacuum bubble?

The paper "Spontaneous creation of the universe from nothing" by Dongshan He, Dongfeng Gao and Qing-yu Cai claims that our universe was created by the quantum fluctuations in the metastable false ...
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How gravity really works in 3D and how and massive object attracts another object? [duplicate]

space is 3d then how an massive object creates curvature in 3d an how another object falls into that 3d curvature also if you are answering plese show an image of it.
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In Hawking radiation, positive particle escape from black hole [duplicate]

Why does the particle with positive mass escapes? What is the process?
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Bending of light Ray in radially varying refractive index [duplicate]

If light passes near a massive object, the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refrative index of the medium ...