# Tag Info

### Can light be somehow confined to create a kugelblitz?

At high enough intensities light forms particle-antiparticle pairs which carry energy away from the region in which you're trying to form a black hole: https://arxiv.org/abs/2405.02389 This constrains ...
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### A study on the speed of gravity

It is well known that General Relativity predicts that gravitational waves exist [1] and that they travel at the speed of light. But, until the construction of LIGO, these were not experimental facts. ...
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### Can perfectly stable orbits exist in GR?

In the literature, the orbits you are looking for a called “floating orbits”. Floating orbits are not possible in plain GR (See e.g. 1302.1016).
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### What's the relevance of geometric rigidity/flexibility to physics?

Well, rigid structures (such as e.g. affine manifolds; think SR) and flexible structures (such as e.g. differential manifolds; think GR) both appear in physics. Canonical transformations on a ...
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### Can perfectly stable orbits exist in GR?

As you say, GR implies that all orbits lose energy (very slowly) over time, due to gravitational waves. Also the vacuum of space is not true vacuum and there is some drag from the intergalactic medium ...
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### Can perfectly stable orbits exist in GR?

In the 1979 paper "Time without end", Freeman Dyson calculates a time in the order of 1020 years until the earth would fall into the sun due to gravitational decay alone, based on the ...
• 365

Accepted

### Wormholes in general relativity

There are solutions to the Einstein Field equations that describe a wormhole (i.e. a black hole connected to a white hole). But there is no evidence that these objects actually exist.
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### What specific renormalized Lagrangian is used for quantum gravity of GR?

You can use the same Lagrangian as classical GR: the Einstein–Hilbert action. The trick is that this action is not renormalizable, meaning you need infinitely many terms to control the infinities that ...
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### Necessity of Singularity in General Relativity

Well the famous singularity theorems show (very very roughly speaking) that in the theory of classical GR, collapse beyond horizon implies a singularity. Classical GR is not the true theory of physics,...
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Accepted

### Proof of Bianchi identity with the use of Riemann normal coordinate

I’ll let you fill in all the indices, but the Riemann tensor is related to the Christoffel symbols by a formula like $R^{a}_{\,bcd}=\partial\Gamma-\partial\Gamma+\Gamma\Gamma-\Gamma\Gamma$, with ...
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### GW luminosity depends on the 3rd time derivative but quadrupole formula depends on the 2nd time derivative?

The quadrupole formula is an approximate result which is valid at distances $r \gg c \tau \gg d$, where $\tau$ is the timescale of variation and $d$ is the size of the system. So, it works when you're ...
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### "A coordinate transformation changes components, but not one-forms themselves"

I think all he means is that coordinate transformations do not change the vector per se, but it's coordinates. A 1-form is of course also a vector in the space of linear maps, i.e. the dual space. But ...
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Accepted

### Dirac sign flip in matter tensor

This sign is indeed a convention. It actually has to do with how you define the Ricci tensor. Some authors define it as $R_{ab} = R_{acb}{}^{c}$, but some as $R_{ab} = -R_{acb}{}^{c}$. Flipping the ...
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### Reformulate Einstein equations to make them linear

Good question. In principle, every nonlinear ODE can locally be recast by a suitable, nonlinear, choice of variables into a linear system. I even think that you can reduce every such system to a ...
• 31

### Is rotation invariant under gravitational time dilation?

is vertical rotation an invariant in general relativity or not? If we consider the general case of rotation in any orientation, the answer is no. The large vertical case is difficult to analyse ...
• 6,691
Accepted

### Two contradictory derivations of Killing equation

As an overall comment, I stress that conservation of $Q$ is valid for the Killing vector $\xi$ if the considered curve is a geodesic. Let us come to the issue. First of all, generally speaking, the ...
• 74.8k
Both approaches are fine. In the first approach, the analysis is done at the coordinate/component level of the equations. Simply asking the question how does $Q$ very with $\tau$ if we write ...