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Results tagged with spacetime
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user 265247
Within relativity (both special and general), changes of reference frames can change both the notions of space and of time, with one depending on the other as well. As a consequence, it is necessary to treat both concepts in a unified manner. Hence the term spacetime.
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Understanding this spacetime diagram
That is a conformal diagram representing the Haggard-Rovelli spacetime. The thick line represents the collapsing/bouncing null shell. …
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Does an expanding universe naturally induce a Lorentzian metric in local nonexpanding coordi...
What you are referring to its a known fact, which is that you can see a Lorentzian metric as a Riemannian metric with the addition of a causal structure given by an everywhere nonzero line field. The …
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How to relate Riemannian and Lorentzian tetrad fields on the same manifold/spacetime?
Why are you assuming that $\eta_{ab} = (\mathbb{I}_{ab}-2l_{a}l_{b})$?
The quantity $\mathbb{I}_{ab}-2l_{a}l_{b}$ gives you a Lorentzian metric, but could be different from Minkowski. For example, you …
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5
votes
Accepted
Why in physics we work with metric without defining topology/smooth structure first?
Here $\mathbb{R}^3_0$ is $\mathbb{R}^3$ minus the origin and $\mathbb{R}^{+}$ the positive real numbers.The topology can be chosen to be the manifold topology defined by the atlas or (because the spacetime … However, there are other cases where details matter: if topological and, therefore, global aspects of spacetime are discussed, as in singularity theorems, the roles are reversed, and the metric plays a …
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0
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Junction Conditions: In what cases is matching the extrinsic curvature at a boundary tantamo...
If $x^{\mu}$ are the spacetime coordinates and $y^{a}$ the hypersurface coordinates it could happen that (especially in symmetric situations)
\begin{equation}
K_{ab} =n_{\alpha} \left( \frac{\partial^{ …
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0
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Non-Compactness in Penrose Singularity
For example, in any spacetime that is asymptotic at spatial infinity to Minkowski space, a Cauchy hypersurface (if there is one) is not compact. …
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2
votes
Accepted
A question on the causal hierarchy/ladder and the existence of CTC
A strongly causal spacetime do not contains CTCs. …
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2
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Accepted
Derivation of the Schwarzschild metric: why are $g_{22}$ and $g_{33}$ the same as for flat s...
The Schwarzschild solution is a spherically symmetric solution produced by a central source. This means that at $t = \mathrm{const}$ the metric should be invariant under rotations.
\begin{equation}
d …
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2
votes
Accepted
A question about the topology of spacetime and the existence of CTCs
You have already noticed that the two topologies coincide if and only if the spacetime is strongly causal. … Moreover in the case where spacetime is not strongly causal the Alexandrov topology ceases to be Hausdorff. …
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Why do we defer to GR when describing black holes rather than rely on QM?
When we say that general relativity and quantum mechanics are not compatible, we mean a number of different circumstances. For example, by linearizing the Einstein-Hilbert action, one can obtain a leg …
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