• Corpus ID: 250264632

Causal bubbles in globally hyperbolic spacetimes

@inproceedings{GarciaHeveling2022CausalBI,
  title={Causal bubbles in globally hyperbolic spacetimes},
  author={Leonardo Garc'ia-Heveling and Elefterios Soultanis},
  year={2022}
}
. We give an example of a spacetime with a continuous metric which is globally hyperbolic and exhibits causal bubbling. The metric moreover splits orthogonally into a timelike and a spacelike part. We discuss our example in the context of energy conditions and the recently introduced synthetic timelike curvature-dimension (TCD) condition. In particular we observe that the TCD-condition does not, by itself, prevent causal bubbling. 

Figures from this paper

On the asymptotic assumptions for Milne-like spacetimes

Milne-like spacetimes are a class of hyperbolic FLRW spacetimes which admit continuous spacetime extensions through the big bang, τ = 0. The existence of the extension follows from writing the metric

Uniqueness and non-uniqueness results for spacetime extensions

Given a function f : A → R n of a certain regularity defined on some open subset A ⊆ R m , it is a classical problem of analysis to investigate whether the function can be extended to all of R m in a

References

SHOWING 1-10 OF 24 REFERENCES

Global Hyperbolicity for Spacetimes with Continuous Metrics

We show that the definition of global hyperbolicity in terms of the compactness of the causal diamonds and non-total imprisonment can be extended to spacetimes with continuous metrics, while

Smoothness of Time Functions and the Metric Splitting of Globally Hyperbolic Spacetimes

The folk questions in Lorentzian Geometry which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic

On Lorentzian causality with continuous metrics

We present a systematic study of causality theory on Lorentzian manifolds with continuous metrics. Examples are given which show that some standard facts in smooth Lorentzian geometry, such as

The $C^0$-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian Geometry

The maximal analytic Schwarzschild spacetime is manifestly inextendible as a Lorentzian manifold with a twice continuously differentiable metric. In this paper, we prove the stronger statement that

Causality theory of spacetimes with continuous Lorentzian metrics revisited

We consider the usual causal structure (I +, J +) on a spacetime, and a number of alternatives based on Minguzzi’s D + and Sorkin and Woolgar’s K +, in the case where the spacetime metric is

Good geodesics satisfying the timelike curvature-dimension condition

. Let ( M, d , m , ≪ , ≤ ,τ ) be a locally causally closed, K -globally hyperbolic, regular measured Lorentzian geodesic space obeying the weak time- like curvature-dimension condition wTCD ep ( K,N

A review of Lorentzian synthetic theory of timelike Ricci curvature bounds

The scope of this survey is to give a self-contained introduction to synthetic timelike Ricci curvature bounds for (possibly non-smooth) Lorentzian spaces via optimal transport & entropy tools,

The future is not always open

TLDR
The phenomena described here are relevant for recent synthetic approaches to low-regularity Lorentzian geometry where, in the absence of a differentiable structure, causality has to be based on locally Lipschitz curves.

Lorentzian length spaces

TLDR
A main focus of this work is the introduction of synthetic curvature bounds, akin to the theory of Alexandrov and CAT(k)-spaces, based on triangle comparison, for Lorentzian manifolds with metrics of low regularity, closed cone structures, and certain approaches to quantum gravity.