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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32 views

Maxwell equations in curved spacetime with cosmological constant

I am aware of Maxwell Equations in Curved Spacetime. But how do these equations change if the cosmological constant is not assumed to vanish?
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Why isn't the De-Broglie wavelength of massive particles redshifted in an expanding universe

It is pretty straight forward how light is redshifted in an expanding universe, yet I still can't understand why the De'Broglie wavelength of a massive particle isn't redshifted in an expanding ...
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Why is the Christoffel symbol in the geodesic equation for a test particle negative?

The geodesic equation is $$ {d^2 x^\mu \over {ds}^2}+\Gamma^\mu {}_{\alpha \beta}{d x^\alpha \over ds}{d x^\beta \over ds}=0\ $$ for some scalar parameter of motion s and connection coefficients of ...
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Dark matter's effect in 2+1 GR?

In the appendix to The Planiverse, it is acknowledged that GR in 2 dimensional space implies no gravitational forces between separated masses--only in the interior of extended massive bodies. The ...
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Diffeomorphism in static spherically symmetric space-time

In a static, spherically symmetric space time we can choose the coordinates so that the metric takes the form: $$ds^2=-A(r)dt^2+\frac{dr^2}{B(r)}+C(r)\,[d\theta^2+\sin^2\theta\,d\varphi^2]$$ Sometimes ...
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What would happen if somebody dropped a small black hole into the Earth?

Suppose we drop a small black hole, but large enough that it accumulates mass more quickly than it radiates it, into the Earth. What happens? This question has already been asked here and here, but ...
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Relativistic rigid motion

In Bryce DeWitt's Lectures on Gravitation, in eq. 2.7 on page 25 when he describes the rigid motion of a continuum he states $$x^\mu(\xi,\tau)=x^\mu(0,\sigma)+\xi^in^\mu_i(\sigma)\,\,\,(i=1,2,3) \, .$$...
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Could tilted light cones lead to causal paradoxes?

For an observer at a given point in spacetime,  we find a spacelike region of spacetime that is  informationally inaccessible to the observer (no signal possible to or from this region from/to the ...
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Cylindrical universe cosmology in general relativity

Is there a compact cylindrical universe solution to the Einstein equation, with space homogeneity, without using "artificial" periodic boundaries? I'm expecting a metric of the following shape: \...
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How to construct the $r$ coordinate near $\mathcal{I}^+$ in asymptotically flat spacetimes?

Asymptotically flat spacetimes can be defined in an abstract manner. For example, Ashtekar defines it as: A space-time $(\hat{M},\hat{g})$ is said to be asymptotically flat at null infinity if ...
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Angular momentum in relativistic hydrodynamics

When we study particle dynamics in General Relativity, the angular momentum is written as $$\mathscr{L}=-u_\phi$$ Whereas, the fluid angular momentum is expressed in terms of the 'enthalpy density' $h$...
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Timelike and spacelike projections in General Relativity and associated conservation laws

For any timelike curve $p_\mu$ in General Relativity (section 3 of this review), we can project this into its timelike and spacelike components. Further, these projections are associated with ...
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Reference systems in Special and General Relativity

I am enthralled by the notion of placing observers along with standard identical clocks in a line spaced from one another according to rods of standard length when place next to one another at the ...
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Are there any known (closed form even if approximate) solutions to problems in relativistic elasticity?

There are several useful known solutions to the EFE with relatively simple / trivial stress-energy-momentum tensor, such as the Schwarzschild solution. Despite the idealizations made therein they are ...
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How does spatial curvature apply to the planets' orbits?

We all know that in the presence of large, massive objects, spacetime is positively curved, more so the more massive it is. This means that the path of an object without any forces on it is a straight ...
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Gauss-Bonnet contact interaction

Can anyone please point me to a paper in which the tree level contact interaction has been systematically computed for the Gauss Bonnet Lagrangian, in D >= 5?
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Unlimited energy storage using relativistic flywheel?

Theoretically, is it possible to store huge amount of energy using a flywheel that spins at speeds that approach light speed? Can the amount of energy be higher than the mass equivalence of the wheel?
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Does light curve at the speed of the g force of a particular star? If not why not? [on hold]

For example if you have a star with a g Force of 100ms/ms at a distance of 1 million kilometers, will a beam of light travelling tangent of the G force at 1 million kilometers curve toward the star at ...
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Are photons affected by SR time dilation (velocity) or not?

Photons are massless particles. Time dilation is caused between two observers either by the relative speed of the observers or by the observers being in different gravitational zones (stress-energy ...
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Is gravity a force given that it derives from curved massless space-time?

One of the answers to a similar question regarding gravity concluded that gravity is an "observed effect" of the curvature of space-time. I read this (and other answers) to imply that gravity results ...
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Do the Earth and I apply the same gravitational force on each other in GR?

Our high-school teacher told us that the Earth pulls us with some force $F$ and we pull the Earth with the same force $F$. Within Newtonian physics this is true because of Newton's 3rd law, but let’s ...
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What does it mean to go from a co-variant vector to a contravariant vector?

In most presentations of general-relativity I see the following statement, We can change from a covariant vector to a contravariant vector by using the metric as follows, ${ A }^{ \mu }={ g }^{ \...
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What is the relation between “projective geometry” and “Projective geometry of paths”?

this is my first time posting so please point out if I am doing it wrong. So as the title says my question is, What is the relation between "projective geometry" and "projective geometry of paths"? ...
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Pictogram extrinsic time variable

In Gravitation, it is said that the extrinsic time variable can be represented by a pictogram: Gravitation page 551 but I didn't find much data on it. How is that pictogram called? Is it equivalent ...
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Curvature and length contraction paradox

I was thinking about the Flat-Earth model and I confronted with the following issue. Consider a sphere and an observer who is leaving the sphere. Using length contraction principle from special ...
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A question about accelerating motion [closed]

When we are talking about motion in relativity is it possible for a specific motion that has a specific acceleration in all three dimensions simultaneously? designating an acceleration of A to all ...
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Can gravitational waves be used to investigate the inside of black holes?

I do understand that nothing, no particles and no information can escape a BH. Gravitational waves are real, they have been observed. Gravitational waves are disturbances in the curvature of ...
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Metric tensor and dependence on parameter

In "Tensors" by A. Das on p166 the author derives the first integral (5.202) of the geodesic equation. To achieve this, he uses the chain rule $$\frac{dg_{jk}}{d\tau} = \frac{\partial g_{jk}}{\...
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How to obtain Einstein Equations for empty space [on hold]

Based on Einstein tensor: $G^i_j=R^i_j-\delta^i_j\frac{R}{2}$ How can i show that the einstein equations are reduced to $R_{ij}=0$ if $G^i_j=0$
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How to Change Coordinate Systems in General Relativity

Let me preface by stating that I have no experience with General Relativity. I am working on a project for school that requires a little knowledge of it, so I am hoping to find some help. I do have ...
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Why isn't an infinite, flat, nonexpanding universe filled with a uniform matter distribution a solution to Einstein's equation?

In Newtonian gravity, an infinite volume filled with a uniform distribution of mass would be in perfect equilibrium. At every point, the gravitational forces contributed by masses in one direction ...
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Confused about the gauge transformation of the amplitude tensor for gravitational waves

Far away from the field sources, where the energy-momentum tensor $$T_{mn}=0 \tag{m,n=0,1,2,3}$$ The linearized EFE becomes $$\Box \bar h_{mn}=0 \tag{1}$$ where $\bar h_{mn}$ is the trace-reverse ...
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Coupling a spinor field to a preexisting scalar field?

So I'm not a physicist, but I'm thinking about a mathematical problem where I think physical insight might be useful. We're working on a Riemannian manifold $(M,g)$ (positive definite metric) with a ...
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(Anti-) De Sitter Algebra

In the (Anti) De Sitter Algebra, the "momenta" commute the following way $$[P_{\mu}, P_{\nu}] = \mp \frac{M_{\mu\nu}}{4L^2}.\tag{12.16}$$ This is taken from Page 251, Section 12.6.1, Equation 12.16 ...
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How to define *dynamical* dimensions?

I'm considering a simple toy model. The spacetime is flat with $d$ space dimensions. Using cartesian coordinates, the spacetime metric is Minkowskian : $$\tag{1} ds^2 = dt^2 - dx_1^2 - dx_2^2 - dx_3^...
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lemaitre big bang article? [on hold]

Is the article which made Lemaitre postulate Big bang "Expansion of the universe, A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic ...
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Zero mass Kerr metric

When mass in Kerr metric is put to zero we have $$ds^{2}=-dt^{2}+\frac{r^{2}+a^{2}\cos^{2}\theta}{r^{2}+a^{2}}dr^{2}+\left(r^{2}+a^{2}\cos^{2}\theta\right)d\theta^{2}+\left(r^{2}+a^{2}\right)\sin^{2}\...
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Angular momentum of a cylindrical system in general relativity

The definition of energy and enegry flux of a cylindrical symmetric system in general relativity is given by Kip Throne in Phys. Rev. 138, B251 and generalized by Chandrasekhar in Proc. Roy. Soc. Lond....
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In Bondi gauge/coordinate, how to obtain covariant derivative of the 2-dimemsional sphere using null projection operators?

In Bondi coordinate , the Bondi-Sachs metric is written as $$ ds^2=-\frac{V}{r}e^{2\beta}du^2-2e^{2\beta}dudr+r^2h_{AB}(dx^A-U^Adu)(dx^B-U^Bdu) $$ Before any decomposition, the covariant derivative $...
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How is spacetime warped by a massive object?

I was going through this question (Why don't planets have Circular orbits?) related to planetary orbits. In the accepted answer it is stated that orbits are actually conic sections. Given this ...
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Prove that colliding celestial bodies produce perturbations in the fabric of space-time

So I was recently asked this question by one of my professors, it really is confusing for me at the moment since I only have a basic grasp of and the ideas Einstein proposed. P.S: I was wondering if ...
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What are Connections in physics?

This question arises from a personal misunderstanding about a conversation with a friend of mine. He asked me a question about the "truly nature" of spinors, i.e., he asked a question to me about what ...
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Motivation for the abandonment of inertial frames in general relativity [closed]

Inertial frames are at the core of special relativity. The laws of physics are supposed to be the same among them and free particles follow rectilinear paths in spacetime or simply stay at rest. Just ...
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Christoffel symbol derivation in book by Wald

In chapter 3 of Wald's General Relativity he starts by defining a covariant derivative $\nabla$ as a map on a manifold M from tensor fields $\mathscr{T}(k,l) \to \mathscr{T}(k,l+1)$ plus some required ...
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Evaporation of large charged black holes

Black holes evaporate (Hawking Radiation) acting as black bodies with the temperature inversely proportional to the mass. No physical process, be it evaporation or any other "trick", can make a black ...
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Graviton propagator, and Gauss-Bonnet gravity

Let's say we consider Einstein's Lagrangian from GR. In linearized gravity, we would expand the Ricci scalar to quadratic order in the perturbation parameter to find the propagator. My question is as ...
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Does gravity emerge from general coordinates transformations? [closed]

In a inertial reference frame, a particle at rest is defined its acceleration equals 0. By a general coordinate transformation, we end up with a similar equation but now there is a term which under ...
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What is the difference between Einstein aether theory and general relativity?

I'm currently doing some research on the various aether theories and I stumbled upon Einstein aether theory. It appears to be much different from Luminiferous aether and be more closely related to ...
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Do orbiting masses accelerate or decelerate (relative to us) near black holes? [duplicate]

Apologies if this question seems stupid; I was just curious after watching a documentary, and I am not a trained astrophysicist. Simply put, I cannot reconcile the (perhaps misunderstood) facts that ...
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What are the characteristics of space-time? [duplicate]

How does distortions in space-time caused by earth make us attracted towards the earth?