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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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Is inflation a possible explanation for what started the expansion?

Alan Guth stated in this article But let me start the story further back. Inflationary theory itself is a twist on the conventional Big Bang theory. The shortcoming that inflation is intended to ...
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Is the space-time curvature linearly additive?

Could someone please show using equations if space-time curvature due to two bodies being linearly additive or not in general.
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Can universe still expand without energy and matter?

I heard dark energy is the intrinsic property of space and it cannot be particle because particle's density dilute when volume increase, I do not know how nothingness can have property and Einstein ...
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Why exactly are singularities avoided or “deleted” in physics?

What is the real reason that make us reject singularities everytime we see them in a theory/model? For example, in GR, it is predicted that black holes singularities have infinite density. This makes ...
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Four velocity, acceleration, momentum and force in general relativity

I am getting slightly confused regarding the formal definitions of different four vectors in General Relativity. Many texts on relativity begin with four vectors and dynamics in Minkowski space, and ...
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How correct is Randell Mill's “The grand unifed theory of classical quantum mechanics”? [on hold]

In https://doi.org/10.1016/S0360-3199(01)00144-6 , the author has claimed to have unified Maxwell’s equations, Planck’s equation, the de Broglie equation, Newton’s laws, and special, and general ...
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deSitter spacetime metric and curvature

I have to compute the metric of an hyperboloid given by $-(X^0)^2+(X^1)^2+(X^2)^2+(X^3)^2=H^{-2}$ in 5D Minkowski spacetime using the following coordinates: $$X^0=H^{-1}\sinh(Ht)\sqrt{1-H^2r^2}$$ $$X^...
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Index position when varying an action with respect to the metric

I'm confused about where we should put tensor indices when we vary an action wrt the metric. For example, if I have in the Lagrangian a term such as $$ A_{\mu\nu}B^{\mu\nu}, $$ do I necessarily have ...
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Big Bang, Entropy, Electromagnetic Radiation, Energy/Mass Equivalence, Gravity, General Relativity [on hold]

If the photon in electromagnetic radiation does not have mass then does this mean that electromagnetic radiation is not subject to gravitational forces. Therefore it would continue at the speed of ...
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Relativity- In a given Scenario, is FTL communication possible? [on hold]

Take a black hole singularity of sufficient size that a planet could be placed in a stable orbit with a high amount of time dilation observed from the outside. Let’s assume it’s a pretty big black ...
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Falling electric dipole contradicts equivalence principle?

Consider an electric dipole consisting of charges $q$ and $-q$, both of mass $m$, separated by a distance $d$. If the dipole is given an acceleration $a$ perpendicular to its moment the total ...
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There are a component proportional to speed in gravitional force?

Reading some introductory texts to general theory of relativity (GR), I understand that the gravitational force between two objects has, in addition to the component in the direction of the vector ...
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What is torsion physically in the Einstein-Cartan theory?

In Einsteins theory of gravity the metric gives a unique torsion free connection called the Levi-Civita connection. In the Einstein-Cartan theory we allow any connection compatible with the metric ...
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Where does the factor of one half come from in the delta-vector equation involving the Riemann Curvature Tensor?

In Einstein's Theory, A Rigorous Introduction for the Mathematically Untrained, by Grøn and Næss: The change of the covariant components a vector by parallel transport around an indefinitely small ...
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2answers
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Can the future affect the past in general relativity? [on hold]

Hypothetically, let us suppose that a black hole were to suddenly appear at time $t=1$ at position $x$. Can the effect of the black hole be felt at time $t = 1-\epsilon$ near $x$ due to the bending of ...
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Free particle in Rindler metric

I have to discuss the motion of a free particle in Minkowski using the Rindler metric $$ds^2=e^{2ap}(-d\tau^2+dp^2)$$ So it has to satisfy the geodesic condition $\frac{d^2x^\mu}{d\tau^2}+\Gamma_{\rho\...
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2answers
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Is a stable orbit possible inside the ergosphere of a Kerr (spinning) black hole?

I have heard that it's "impossible to hover" inside of an ergosphere, but everywhere I read this seemed to be speaking in the context of "relative to a stationary observer outside of the ergosphere". ...
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Black holes with different pulls?

Would a relatively small black hole attract objects in a different way than supermassive ones?
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5answers
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Varying constants in special relativity [on hold]

The first thing you learn in special relativity is: All "inertial" frames of reference are equivalent. There is a frame - invariant speed limit, usually called speed of "light." So, geometry is a ...
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How is four-velocity automatically normalized?

This is a page from Sean Carroll's Spacetime and Geometry.There is a line in this page which says that the four velocity is automatically normalized.This absolute normalization is a reflection of the ...
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3answers
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Did the rapid inflationary expansion slow down a lot because the inflaton field had decayed, or because of gravity from matter/radiation?

What happened to the rate of expansion right after inflation ended? Did the rapid inflationary expansion slow down a lot because the inflaton field had decayed, or because gravity from matter/...
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1answer
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Refraction of matter waves

My question is a bit messy, so here is the background: Normally the trajectory of a massive particle in the presence of a gravitational field is described in the context of general relativity. ...
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4answers
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What does the 'cosmological constant' represent?

Newtons theory of gravity involves a gravitational constant $G$, however one does not refer to it directly, we speak instead of gravity or the force of gravity. Now Einsteins introduced a ...
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How to find Ricci tensor?

I'm trying to find the Ricci tensor in question 3. Here $u=r/R .$ http://imgur.com/gallery/qSAknvz I found the Christoffel symbols but I can't find the Ricci tensors. On the link, there is also my ...
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Are all 4D Ricci flat manifolds locally Euclidean? [closed]

If a 4D manifold with metric signature (++++) is Ricci flat. Does this mean that locally the space is Euclidean? Does this mean that the only difference between these manifolds is there global ...
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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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1answer
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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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1answer
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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
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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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0answers
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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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0answers
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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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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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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? [closed]

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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1answer
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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
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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
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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 [closed]

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
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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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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
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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
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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
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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
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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. ...