# Questions tagged [lorentzian-geometry]

Lorentzian geometry is the geometry of Minkowski spacetime, hence essentially of a Euclidean space, but equipped not with the standard Euclidean Riemannian metric of signature $(+,+,+,…,+)$ (which yields Euclidean geometry) but with the pseudo-Riemannian metric of signature $(−,+,+,…,+).$

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### Conformal changes of metric and Ricci curvature

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### Topology on Minkowski space $\mathbb{R}^{4}$ and Lorentz invariant measure

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### On intersection of null geodesics

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### conformal changes of Lorentzian metrics

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### Proving Hawking area Theorem without cosmic censorship

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### stability of two-sided sectional curvature bounds in Lorentzian geometry

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### Arbitrary sectional curvatures at a point

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### Homotopy types of causal / chronological pathspaces in Lorentzian manifolds?

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### Geometric interpretation of the Weyl tensor?

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### On thinking of spacetime as a local Scott domain

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### Outer Minimizing Horizon for a Perturbed Metric

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### A pseudo-Riemannian version of a theorem by Fubini

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### Globally hyperbolic spacetimes and future Cauchy developement

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### Perturbation of a spacetime in general relativity

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### conformal changes to Lorentzian curvature

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### Lorentzian manifolds of negative spacelike sectional curvature

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### Distance function and Hessian in Lorentzian geometries with positive curvature

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### Lower bound for domain of exponential map on Lorentzian manifolds

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### Fourier transform on Minkowski space

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### A Riemannian manifold with a non-degenerate metric and an inner product $u_{\beta} u^{\beta}=1$

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### Is it possible for null geodesics to suddenly “stop”?

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### What's the “actual” shape of a black hole accretion disk?

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### Literature Request: Berger Spheres and their Construction

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### Definition of twisted geometries and existence of coordinate transformation for twisted $AdS_2 \times S^2$

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### Explanation for “Squashing” and “Stretching” (Lorentzian Analogue of Berger Spheres)

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### Transformation Poincaré-coordinates to global coordinates in $\mathrm{AdS}_2$

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### Example of a Lorentz-invariant probability measure?

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### Do (3+1)-dimensional Lorentzian manifolds admit unique smoothings?

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### Existence of transverse null vector bundle in a degenerate Lorentzian hypersurface

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### maximal surface, parametric approach

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### Harmonic maps into de Sitter Space

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### $(M,g)$ is complete iff $(\tilde{M},\tilde{g})$ is complete (non-Riemannian version)

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### Are there Lorentzian complex manifolds?

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### Decomposition of a Jacobi field along a lightlike geodesic

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### Lorentzian analogue to Thurston geometries

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### Is the set of Lorentzian metrics metrizable?

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### Closed Semi-Riemannian manifolds with non-compact isometry group

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### Canonical Metrics on 3- and 4-Manifolds

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### Support of functions on Minkowski space and their Fourier transform

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### Find the fixed geodesic of an orientation-preserving isometry of the $3D$ hyperboloid model

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### Distributional PDE solutions as topological linear duals of PDE solutions

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### Continuous dependence on initial data for (null) geodesics in Lorentzian manifolds

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### On the topology induced by a Lorentzian metric

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### On the causal structure of spacetimes: piecewise $C^1$, $C^k$ or $C^\infty$?

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### Tensor Field Decomposition in Space time

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### Conformal Transformations that are Ricci Positive Invariant

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### Induced connection on null hypersurfaces

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### Decay estimates for wave and Klein-Gordon equation in “generic” curved backgrounds

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### Reference for Bonnet Fundamental theorem of surfaces in Lorentzian spaces

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