An introduction to Gravitational Lensing in TeVeS gravity

TL;DR

This paper provides a tutorial on calculating gravitational lensing effects in TeVeS gravity, highlighting differences from dark matter models and addressing common misconceptions.

Contribution

It introduces methods to compute lensing phenomena in TeVeS-like theories, clarifying how to adapt dark matter-based intuitions to modified gravity frameworks.

Findings

Demonstrates how to compute lensing convergence and time delays in TeVeS.

Highlights caveats when applying dark matter intuitions to TeVeS.

Provides practical examples illustrating the differences from standard dark matter models.

Abstract

Bekenstein's (2004) TeVeS theory has added an interesting twist to the search for dark matter and dark energy, modifying the landscape of gravity-related astronomy day by day. Built bottom-up rather than top-down as most gravity theories, TeVeS-like theories are healthily rooted on empirical facts, hence immediately passing sanity checks on galaxy rotation curves, solar system constraints, even bullet cluster of galaxies and cosmology with the help of 2eV neutrinos. Nonetheless, empirical checks are far from perfect and complete, and groups of different expertises are rapidly increasing the number of falsifiable properties of the theory. The theory has also been made much simpler and more general thanks to the work of Zlosnik, Ferreira, Starkman (gr-qc/0606039, astro-ph/0607411). Here I attempt a tutorial of how to compute lensing convergence, time delays etc in TeVeS-like theories for non-spherical lenses. I gave examples to illustrate a few common caveats of Dark-Matter-guided intuitions.