Particle motions and gravitational lensing in de Rham-Gabadadze-Tolley massive gravity theory

Abstract

We investigate gravitational lensing and particle motions around nonasymptotically flat black hole spacetime in nonlinear, ghost-free massive gravity theory, called de Rham-Gabadadze-Tolley (dRGT) massive gravity. Deflection angle formulas 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 behavior of gravity from a linear term $\ensuremath{\gamma}$ in the dRGT black hole solution. We also find an analytically approximated formula of deflection angle in two regimes: large and small $\ensuremath{\gamma}$ term regimes which are shown to be consistent with direct numerical integration. Null and timelike geodesic motions on an equatorial plane are explored. Particle trajectories around the dRGT black hole are plotted and discussed in detail.