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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42 views

What happens to light in the middle of a BH binary?

A BH binary is a system of two black holes orbiting each other in close orbit. https://en.wikipedia.org/wiki/Binary_black_hole Now on this wiki page, there is a simulation of the merging black holes,...
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Why does relativity first slow down time for the object as it approaches lightspeed, and then reverse time for the world if it passes lightspeed?

When looking into relativity I see a lot of assumptions thrown about about the knowledge of the reader, even the primers that are supposed to help newbies like me try to learn what it's about often ...
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Derive the conversion factor for electric charge from SI to Geometric units [closed]

In the Geometrized system of units, $G = c = 1$. This directly gives us the definitions for second and kilogram in the geometric system, as $1\:s = c_0\:m$ and $1\:kg = G_0c_0^{-2}\:m$, where I have ...
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Why Einstein's GR considered perfect theory of gravity even though it has geometrical base? [closed]

In my view, GR is imaginary geometrical explanation of how gravity works and fundamental science behind why gravity works is still unknown.
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What are Connection Forms in General Relativity?

I'm trying to follow an article by H. Ellis (1973), where he developed the first ever metric of a traversable Wormhole (more info here). In pages 105-106 (the end of the 3rd page in the linked file ...
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Coordinate-independent metric implies constant metric along geodesic

I am struggling to understand a problem I was given. The problem is as follows: $ {}$ Show that if the metric does not explicitly depend upon a coordinate (e.g. $x^1$) then the term $g(\dot{x}, \...
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Machs Principle Thought Experiment

Set-up: Imagine a universe that only contains a few items: A large planet - A Dyson ring around it - and some people with baseballs. This is to say there are no other stars, galaxies, or matter ...
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Is an object accelerating if it moves at a constant velocity, but the time is warping? [closed]

I have no knowledge of relativity whatsoever, but I was wondering Is an object considered accelerating when it moves at a constant velocity, but the time is warping?
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Would this double black hole in a spherical universe metric be analytic and stable?

Consider a spherically closed Universe with spacial-topology $S_3$. Put a black hole on both "poles" of this universe. This seems like it should be in equilibrium. But then again maybe the Universe ...
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Why do people say that there are no dynamic solutions to Einstein's equations?

I don't have a clear understanding of what a dynamical solution of the Einstein equations would look like. So maybe my first question is “what is a dynamical solution of the Einstein equations?” And ...
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What is common between all the equations in physics that involve harmonic maps?

Harmonic maps $\phi$ are minimizers of the energy $\int_\Omega |\nabla \phi(x)|^2 \ dx$. They arise in several equations in physics, such as the Einstein equations and the Ginzberg-Landau equations. ...
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Is there any meaning to the object $\partial_{\mu} \Gamma^{\rho}_{\ \nu\sigma} + \Gamma^{\rho}_{\ \mu\lambda} \Gamma^{\lambda}_{\ \nu\sigma}$?

In a calculation I am encountering the object $$ O^{\rho}_{\ \mu\nu\sigma} \ := \ \partial_{\mu} \Gamma^{\rho}_{\ \nu\sigma} + \Gamma^{\rho}_{\ \mu\lambda} \Gamma^{\lambda}_{\ \nu\sigma} \ , \tag{1}$...
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Harmonic maps in the Ginzberg-Landau and Einstein equations

A harmonic map $u$ is a vector-valued function that is a minimizer of the energy $E[u] =\int_\Omega |\nabla u|^2 \ dx$ such that $|u|\equiv 1$ (i.e. $u$ takes values on the sphere). I have read that ...
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Conservation of signs of eigenvalues of metric tensor

The metric of an arbitrary spacetime can be transformed into the Minkowski metric because $$g_{\mu \nu } = J_{\mu }^{\alpha } J_{\nu }^{\beta} \eta_{\alpha \beta }\tag{1}.$$ Gives ten equation for ...
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When gravity bends light, does the light still propagate orthogonally to its $\vec E$ and $\vec B$ fields?

An ordinary photon travels perpendicularly to the direction of its oscillating E & B vector fields (i.e. $\vec{v} \propto \vec{E} \times \vec{B}$). Let's say $\vec{E}$ is oscillating "in-out" of ...
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Friedmann equations and different types of universes

I'm currently reading a book (in Danish) about the Friedmann equations and I have stumbled upon a third degree polynomial: $$ \Omega_\Lambda = \frac{4K_0^3}{27\Omega_0^2} = \frac{4(\Omega_0 + \Omega_\...
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After Cartan: is Newtonian gravity potential a hint to a spacetime metric?

There are claims made here to the reasonability of seeing the existence of the potential, due to its unusual properties, as a hint that given Newtonian spacetime's connection and curvature (as per ...
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Force on a particle from geodesic equation

Say I had an action for a scalar field where the matter action is $$S_m=\int d^4x \sqrt{-\tilde{g}}\mathcal{L}_m(\psi,\tilde{g}_{\mu\nu})\tag{1}$$ such that matter will follow geodesics according to $\...
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Past boundary of $\mathcal{I}^+$ and future boundary of the hyperboloid resolving $i^0$?

Let us consider Minkowski spacetime. Let $(u,r,x^A)$ be retarded coordinates with $x^A$ coordinates on the sphere. Future null infinity is described here as the $r\to \infty$ limit with $(u,x^A)$ ...
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Is there anything wrong with this modified Einstein-Hilbert action of first order?

The Einstein-Hilbert Action: $$S_{EH}=\frac{1}{2\kappa}\int \sqrt{-g}g^{ab} \left({\Gamma^c}_{ab,c} - {\Gamma^c}_{ac,b} + {\Gamma^d}_{ab}{\Gamma^c}_{cd} - {\Gamma^d}_{ac}{\Gamma^c}_{bd}\right) d^4x$$ ...
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Linearised Gravity and Motion of Particles in Background Metric

Let's say we have two point particles as our matter source. Suppose we want to solve Einstein Equation Perturbatively and obtain the gravitational wave at the linear order. Let us expand around ...
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Concept of parallel transport and its physical intuition

I am currently reading Foster and Nightingale and when it comes to the concept of parallel transport, the authors don't go very deep in explaining it except just stating that if a vector is subject to ...
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An identity with the second covariant derivative [closed]

My question is simple and is placed in the context of GR. Let $X^{\mu\nu}$ be any rank-2 tensor, and $\nabla_\mu$ be the metric compatible, torsion-free, covariant derivative. Does the following ...
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Is Space-time compression a better explanation than warping? [closed]

Has anyone else come to the conclusion that Mass shrinks (compresses) space-time and that is what we perceive as gravity.
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Finite computational power of universe vs continuous nature of unbounded particles

I am not a physicist, but I've worked to make this an intelligible question for SE. What information is exactly and how it is stored in the universe is still being studied, but here Seth Lloyd gives ...
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Is the Cross Product of two vectors in General Relativity on a 3-Space the same as in “Non-Relativistic” Physics?

Considering the covariant tensor $$C = e_{ijk}A^j B^k = A \times B $$ in a 3 spherical-space diagonal metric $$ds^2 = g_{i,i}dx^{i}\cdot dx^i$$ Isn't $C$ the same as "Classical/Newtonian" physics? (...
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Is this an alternative Dirac Equation in curved space?

The usual covariant derivative for the Dirac equation in curved space is: $$D_\mu \psi = (\partial_\mu - {i \over 4} {\omega_\mu}^{ab} \sigma_{ab}) \psi$$ However, I think I found another ...
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Doesn't spin-spin interactions in gravity disobey Galilean relativity?

In gravity (GR) apparently there are forces which occur which are related to the spin of two masses. For example if we had a rotating gravitational source and dropped, say, some particles into it ...
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How is Schwarzschild metric asymptotically flat for large $r$?

The Schwarzschild line element is: $$ds^2 = -\left(1-\frac{2M}{r}\right)dt^2 + \left(1-\frac{2M}{r}\right)^{-1}dr^2 +r^2(d\theta^2 +\sin^2\theta d\phi^2). $$ As $r \to \infty$, this is supposed to ...
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Could gravitons be dimensionless?

If the metric $g_{\mu\nu}$ is dimensionless (i.e. does not have associated dimensional units) and gravitons are quantum excitations of the metric does that mean that gravitons themselves are ...
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Landau-Lifschitz pseudotensor from Einstein equations

In Landau-Lifschitz (Volume II): Actually, it is not difficult to bring $T^{ik}$ to this form. To do this we start from the field equation $$T^{ik}=\frac{1}{8\pi\kappa}\left(R^{ik}-\frac{1}{2}g^{ik}...
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Path of a curve

Consider $\textbf{R}^3$ as a manifold with the flat Euclidean metric, and coordinates {$x,y,z$}. Introduce spherical polar coordinates {$r,\theta,\phi$} related to {$x,y,z$} by $x = rsin(\theta)cos(\...
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Why the imaginary constant on the spin-connection?

I have been studying the spin-connection for the Dirac equation. The covariant derivative is defined as: $$D_\mu \psi = (\partial_\mu - {i \over 4} {\omega_\mu}^{ab} \sigma_{ab}) \psi$$ where $\...
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Apparent coincidence of spin-connection term and Higgs field?

In curved space time, there is a spin-connection term $\overline{\psi}\gamma^\mu\sigma^{ab}\omega^{ab}_\mu\psi$. Here's my apparent problem. If there were no Higgs field and no gravity, all particles ...
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Gravity creating other dimensions [duplicate]

It is a well known fact that gravity can bend space, kind of like a rock placed on a sheet of paper, bending the paper. But, doing this will make another third dimension, that the marble actually ...
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Does General Relativity actually satisfy the General Principle of Relativity?

The “General Principle of Relativity” being “All systems of reference are equivalent with respect to the formulation of the fundamental laws of physics”. To my knowledge, this is related historically ...
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Why is Schwarzschild metric taught at all?

It seems like the Schwarzschild metric only has historical relevance. Since other coordinates like the (ingoing) Eddington-Finkelstein coordinates are far superior. It seems like the condition on the ...
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In Eddington–Finkelstein coordinates how do we show a projectile appears to slow down near the horizon?

In the Schwarzschild coordinates it is stated that it is clear that an object appears to slow down near the horizon form the perspective of an outside observer. How do we do this calculation in in ...
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Differential of a metric determinant

In Landau Lifschitz (Volume II): We now derive an expression for the contracted Christoffel symbol $\Gamma_{ik}$ which will be important later on. To do this we calculate the differential $dg$ of the ...
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Can anyone refer me to a good study material to study Petrov Classification from?

I am currently trying to study Petrov Classification so I may start my research in the summer. I have completed a year of GR course at the level of sean Carroll.
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Would the nightsky be bright (filled with starlight) without accelerating space expansion?

As I currently understand, if a photon was emitted from a far away point in the Universe, beyond the event/particle horizon, so that the space inbetween the emitter and us is expanding faster then ...
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Are the spacelike foliations of a non-static spacetime topologically equivalent?

Assuming a stationary, globally hyperbolic spacetime, I can imagine that all spacelike foliations are topologically equivalent though not all will be identical since the spacetime is not static. Is ...
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Does Birkhoff's theorem generalize to higher dimensions without additional assumptions?

In the Newtonian theory of gravity, the shell theorem says that the gravitational field inside a massive and spherically symmetric shell is zero. The conclusion is the same in general relativity, as ...
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Is the reason of relativity circular? [closed]

I would like to ask a question related the stages of a star's life and relativity. We know that times runs slower in regions where the gravitational potential is high, if we apply this to a star it ...
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About variation of Ricci tensor

I have been doing some calculation on variation of Ricci's tensor with respect to the metric, that, according with S. Carroll (An Introduction to General Relativity: Spacetime and Geometry, equation 4....
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Does light have gravity or Gravitomagnetism?

We all agree that light has no mass yet it is affected by gravity. According to accepted theories I have seen light itself is also said to bend space meaning that it causes gravitation. This would ...
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Can a wormhole be created if it has not always existed?

I know there are solutions to Einstein's field equations that give a wormhole geometry. But they are time independent. They are static. Is there a process where empty flat spacetime can evolve into a ...
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Do planets orbiting stars emit gravitational waves?

I have heard it said that charged planets could not orbit a massless (low mass) oppositely-charged star based on electromagnetic attraction the same way they can with gravitational attraction, because ...
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Deduction of the action of $f(R)$ gravity

From $$S=\int{d^4}x\sqrt{-g}f(R)$$ I want to deduce the $f(R)$ field equations which are: $$f'(R)R_{\mu\nu}-\frac{1}{2}f(R)g_{\mu\nu}-[\nabla_{\mu}\nabla_{\nu}-g_{\mu\nu}\Box]f'(R)=\kappa T_{\mu\nu} ,$...
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How can I show the Einstein Tensor using second Identity of Bianchi? [closed]

The Einstein tensor given by: $$G_{\mu\nu}=R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}$$ Can be shown using Bianchi identity?

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