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Affine linking number estimates for the number of times an observer sees a star

Vladimir Chernov, Ryan Maguire

Abstract

Affine linking numbers are the generalization of linking numbers to the case of nonzero homologous linked submanifolds. They were introduced by Rudyak and the first author who used them to study causality in globally hyperbolic spacetimes. In this paper we use affine linking numbers to estimate the number of times an observer sees light from a star, that is how many copies of the star do they see on the sky due to gravitational lensing.

Affine linking number estimates for the number of times an observer sees a star

Abstract

Affine linking numbers are the generalization of linking numbers to the case of nonzero homologous linked submanifolds. They were introduced by Rudyak and the first author who used them to study causality in globally hyperbolic spacetimes. In this paper we use affine linking numbers to estimate the number of times an observer sees light from a star, that is how many copies of the star do they see on the sky due to gravitational lensing.
Paper Structure (2 sections, 2 theorems)

This paper contains 2 sections, 2 theorems.

Table of Contents

  1. Lorentz geometry: conventions and definitions
  2. Affine linking numbers and their application

Key Result

Theorem 2.1

Assume $({X}, g)$ is globally hyperbolic and Cauchy surface of it is not an odd dimensional rational homology sphere. Let $\gamma:(-\epsilon, \epsilon)\to {X}$ be a small timelike curve that passes through $p$ at time moment $0.$ Assume that $\bigl (\mathop{\mathrm{alk}}\nolimits( S_{\gamma(\epsilo

Theorems & Definitions (5)

  • Theorem 2.1
  • proof
  • Theorem 2.2
  • Remark 2.3
  • Remark 2.4