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The formal definition of a naked singularity can be found in standard GR books (Wald, Hawking & Ellis, probably others). However, here's a slightly crude, rule of thumb way of checking whether your sp …

What is the speed of a wave in a non-linear theory? Answering before considering your question is important, because that answer will tell you where to look for your answer. A useful notion is that o …

An infinitesimal diffeomorphism, generated by $\xi^a$, acts on the metric as $g_{ab} \mapsto g_{ab} + 2 \nabla_{(a} \xi_{b)}$. The last term is zero precisely when $\nabla_{(a} \xi_{b)} = 0$, that is, …

I will add here some more details to expand my comment. Any two functions $Y_1(x^3,x^4)$ and $Y_2(x^3,x^4)$ give local coordinates on any open domain of the $(x^3,x^4)$-plane where their Jacobian dete …

I will add a pessimistic answer. You are right that Choque-Bruhat's (and any related local-in-time) existence result only guarantees that the solution metric exists and is sufficiently regular (includ …

In the case of a globally hyperbolic spacetime, what you want is a smooth Cauchy temporal function (the gradient is everywhere timelike, not just causal, and each level set is a Cauchy surface that is …

Although the focus of the original question was on conformal compactification, a necessary step along the way is an introduction of double-null coordinates that are regular on the horizons and bifurca …

I'm going to guess that your interest in Wick rotation comes from the role it plays in the formulation of quantum field theories (QFTs) on Miknowski spacetime and some other curved spacetimes, like th …

My answer will be a bit more charitable than Willie's. There is an algorithm (sort of) to compute the dimension of the solution space of the Killing equation. Whether it is simple or not, you can deci …

The answer is Yes, at least under the reasonable conditions that (i) the number of conformal Killing vectors locally admitted by $(M,g)$ is constant and that (ii) the de Rham cohomology $H^{n-1}(M)=0$ …

Trying to recover as much of the topology/geometry from the causal order as possible has been studied quit a bit since the early paper of Hawking et al that you cite. A quick summary of my understandi …

I presume the formula you are asking about is the long one highlighed by $*$ $*$ in your question, while the standard "contracted Bianchi identity" $\delta \operatorname{Ein}\left({ }^{(4)} g\right)=0 …

If I understood your question correctly, the answer indeed is due to Lovelock. I think it's important to state all the hypotheses clearly, because they are not always reported accurately. Theorem. (Lo …

The dependence on AC through the use of Zorn's lemma in the proof of the Choquet-Bruhat–Geroch theorem on the existence of a maximal globally hyperbolic development for solutions of the Einstein equat …

Here is an argument whose conclusion is that it is unlikely that exotic 4d manifolds are physically important in general relativity. For physical reasons (mainly causality, stability, and determinism) …