# Particle motions and Gravitational Lensing in de Rham-Gabadadze-Tolley Massive Gravity Theory

## TL;DR

This paper studies gravitational lensing and particle trajectories around black holes in dRGT massive gravity, revealing unique deflection behaviors including negative angles indicating repulsive gravity effects.

## Contribution

It derives new deflection angle formulas in dRGT gravity and analyzes particle motions, highlighting novel gravitational phenomena not seen in standard theories.

## Key findings

- Deflection angles can be positive, zero, or negative depending on perihelion distance.
- Negative deflection angles indicate repulsive gravity effects from the linear term.
- Analytical approximations match numerical results in different regimes.

## Abstract

We investigate gravitational lensing and particle motions around non-asymptotically flat black hole spacetime in non-linear, ghost-free massive gravity theory, called de Rham-Gabadadze-Tolley (dRGT) massive gravity. Deflection angle formulae are derived in terms of perihelion parameter. The deflection angle can be positive, zero or even negative with various perihelion distance. The negative angle reveals repulsive behaviour of gravity from a linear term $\gamma$ in the dRGT black hole solution. We also find an analytically approximated formula of deflection angle in two regimes: large and small $\gamma$ term regimes which are shown to be consistent with direct numerical integration. Null and timelike geodesic motions on equatorial plane are explored. Particle trajectories around the dRGT black hole are plotted and discussed in details.