nLab Lorentzian orbifold

Idea

A Lorentzian orbifold is an orbifold with Lorentzian structure, hence like a Lorentzian manifold but possibly with singularities modeled on fixed points of local actions of finite groups by Lorentz transformations.

Related concepts

• Riemannian orbifold

• symplectic orbifold

• complex orbifold

References

Discussion of Lorentzian orbifolds as target spacetimes in string theory:

• Gary Horowitz, Alan R. Steif, Singular string solutions with nonsingular initial data, Physics Letters B Volume 258, Issues 1–2, 4 April 1991, Pages 91-96 (doi:10.1016/0370-2693(91)91214-G)

• Nikita Nekrasov, Milne Universe, Tachyons, and Quantum Group, Surveys High Energ. Phys. 17 (2002) 115-124 (arXiv:hep-th/0203112)

• Hong Liu, Gregory Moore, Nathan Seiberg, Strings in a Time-Dependent Orbifold, JHEP 0206:045, 2002 (arXiv:hep-th/0204168)

• Hong Liu, Gregory Moore, Nathan Seiberg, Strings in Time-Dependent Orbifolds, JHEP 0210:031, 2002 (arXiv:hep-th/0206182)

• Boris Pioline, Aspects de la théorie des cordes enchamp de fond dépendant du temps, LPTHE, Paris 2003 (pdf)

• Micha Berkooz, Dori Reichmann, A Short Review of Time Dependent Solutions and Space-like Singularities in String Theory, Nucl. Phys. Proc. Suppl. 171:69-87, 2007 (arXiv:0705.2146)

Classification of compact 2d Lorentzian orbifolds:

• N. I. Zhukova, E. A. Rogozhina, Classification of compact lorentzian 2-orbifolds with noncompact full isometry groups, Sib Math J 53, 1037–1050 (2012) (doi:10.1134/S0037446612060080)

conformal maps between Lorentzian orbifolds:

• N. I. Zhukova, The influence of stratification on the groups of conformal transformations of pseudo-Riemannian orbifolds, Ufa Mathematical Journal Volume 10, Number 2 (2018) pp. 44-57 (doi:10.13108/2018-10-2-44)