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Sub-Lorentzian Geometry of Curves and Surfaces in a Lorentzian Lie Group
Advances in Mathematical Physics, 2022 We consider the sub-Lorentzian geometry of curves and surfaces in the Lie group E1,1. Firstly, as an application of Riemannian approximants scheme, we give the definition of Lorentzian approximants scheme for E1,1 which is a sequence of Lorentzian ...
Haiming Liu, Jianyun Guan
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Functors in Lorentzian geometry: three variations on a theme
General Relativity and Gravitation, 2023 AbstractWe consider three examples of functors from Lorentzian categories and their applications in finiteness results, singularity theorems and boundary constructions. The third example is a novel functor from the category of ordered measure spaces to the category of Lorentzian pre-length spaces in the sense of Kunzinger–Sämann.
Olaf Müller, Müller Olaf
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A Lorentzian quantum geometry [PDF]
Advances in Theoretical and Mathematical Physics, 2012 We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry:
Finster, Felix, Grotz, Andreas
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Journal of High Energy Physics, 2022 The analytic continuation of the general signature (1, 3) Lorentzian Kerr-Taub-NUT black holes to signature (2, 2) Kleinian black holes is studied.
Erin Crawley +3 more
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Lorentzian spectral geometry with causal sets [PDF]
Classical and Quantum Gravity, 2020 Abstract We study discrete Lorentzian spectral geometry by investigating to what extent causal sets can be identified through a set of geometric invariants such as spectra. We build on previous work where it was shown that the spectra of certain operators derived from the causal matrix possess considerable but not complete power to ...
Yasaman K Yazdi +2 more
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Journal of Inequalities and Applications, 2018 Given a null hypersurface of a Lorentzian manifold, we isometrically immerse a null hypersurface equipped with the Riemannian metric (induced on it by the rigging) into a Riemannian manifold suitably constructed on the Lorentzian manifold.
Karimumuryango Ménédore
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Spaces of Lorentzian and real stable polynomials are Euclidean balls
Forum of Mathematics, Sigma, 2021 We prove that projective spaces of Lorentzian and real stable polynomials are homeomorphic to Euclidean balls. This solves a conjecture of June Huh and the author.
Petter Brändén
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An Invitation to Lorentzian Geometry [PDF]
Jahresbericht der Deutschen Mathematiker-Vereinigung, 2013 The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of 'Cauchy hypersurfaces': (1) structure of globally hyperbolic spacetimes, (2) the relativistic initial value problem, (3) constant mean curvature surfaces, (4) singularity ...
Müller, Olaf, Sánchez, Miguel
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Pseudo-Slant submaniolds of nearly δ- Lorentzian trans Sasakian manifolds [PDF]
Journal of HyperstructuresOur focus is on the existence of certain structures and similarities between pseudo slant submanifolds and nearly δ- Lorentzian trans Sasakian manifolds.
Shamsur Rahman
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Bra-ket wormholes in gravitationally prepared states
Journal of High Energy Physics, 2021 We consider two dimensional CFT states that are produced by a gravitational path integral. As a first case, we consider a state produced by Euclidean AdS2 evolution followed by flat space evolution.
Yiming Chen +2 more
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