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pro vyhledávání: '"Aazami, Amir Babak"'
Autor:
Aazami, Amir Babak
It is well known in general relativity that trajectories of Hamiltonian systems lift to geodesics of pp-wave spacetimes, an example of a more general phenomenon known as the "Eisenhart lift." We review and expand upon the benefits of this corresponde
Externí odkaz:
http://arxiv.org/abs/2408.16139
Autor:
Aazami, Amir Babak
Utilizing the covariant formulation of Penrose's plane wave limit by Blau et al., we construct for any Riemannian metric $g$ a family of "plane wave limits" of one higher dimension. These limits are taken along geodesics of $g$, yield simpler metrics
Externí odkaz:
http://arxiv.org/abs/2408.02567
Autor:
Aazami, Amir Babak
On an oriented 4-manifold, we examine the geometry that arises when the curvature operator of a Riemannian or Lorentzian metric $g$ commutes, not with its own Hodge star operator, but rather with that of another semi-Riemannian metric $h$ that is a s
Externí odkaz:
http://arxiv.org/abs/2309.13717
Autor:
Aazami, Amir Babak
Publikováno v:
Adv. Theor. Math. Phys., vol. 27, no. 7 (2023), 2219-2259
We approach the problem of finding obstructions to curvature distinguished Riemannian metrics by considering Lorentzian metrics to which they are dual in a suitable sense. Obstructions to the latter then yield obstructions to the former. This framewo
Externí odkaz:
http://arxiv.org/abs/2207.14701
We conduct a review of the basic definitions and the principal results in the study of wavelike spacetimes, that is spacetimes whose metric models massless radiation moving at the speed of light, focusing in particular on those geometries with parall
Externí odkaz:
http://arxiv.org/abs/2207.03591
The Penrose plane wave limit is a remarkable property of Lorentzian spacetimes. Here, we discuss its extension to Finsler spacetimes by introducing suitable lightlike coordinates and adapting the Lorentzian definition of pp-waves. New examples of suc
Externí odkaz:
http://arxiv.org/abs/2205.01162
Autor:
Aazami, Amir Babak, Ream, Robert
Publikováno v:
Lett. Math. Phys. 112, 84 (2022)
We establish a one-to-one correspondence between a class of strictly almost K\"ahler metrics on the one hand, and Lorentzian pp-wave spacetimes on the other; the latter metrics are well known in general relativity, where they model radiation propagat
Externí odkaz:
http://arxiv.org/abs/2203.02825
Autor:
Aazami, Amir Babak
Gravitational lensing is the study of the bending of light by gravity. In such a scenario, light rays from a background star are deflected as they pass by a foreground galaxy (the lens). If the lens is massive enough, then multiple copies of the ligh
Externí odkaz:
http://hdl.handle.net/10161/3861
Autor:
Aazami, Amir Babak, Ream, Robert
Publikováno v:
Mathematische Nachrichten, 296 (2023), 3948-3966
We give a complete local classification of all Riemannian 3-manifolds $(M,g)$ admitting a nonvanishing Killing vector field $T$. We then extend this classification to timelike Killing vector fields on Lorentzian 3-manifolds, which are automatically n
Externí odkaz:
http://arxiv.org/abs/2011.01144
Autor:
Aazami, Amir Babak
On a smooth $n$-manifold $M$ with $n \geq 3$, we study pairs $(g,T)$ consisting of a Riemannian metric $g$ and a unit length closed vector field $T$. Motivated by how Ricci solitons generalize Einstein metrics via a distinguished vector field, we pro
Externí odkaz:
http://arxiv.org/abs/2007.00071