# Null Geodesics and Repulsive Behavior of Gravity in (2+1)-dimensional Massive Gravity

## TL;DR

This paper analyzes null geodesics in a (2+1)-dimensional black hole spacetime within BHT massive gravity, revealing how the gravitational hair parameter influences deflection angles and exhibits repulsive gravity effects.

## Contribution

It provides explicit analytic solutions for null geodesics and deflection angles in BHT massive gravity black holes, highlighting the role of the gravitational hair parameter in repulsive gravity behavior.

## Key findings

- Deflection angles can be positive, negative, or zero depending on impact parameter.
- Negative deflection angles indicate repulsive gravity effects.
- The gravitational hair parameter significantly influences geodesic behavior.

## Abstract

We study the null geodesics in a static circularly symmetric (SCS) black hole spacetime which is a solution in the $(2+1)$-dimensional massive gravity proposed by Bergshoeff, Hohm and Townsend (BHT massive gravity). We obtain analytic solutions for the null geodesic equation in the SCS black hole background and find the explicit form of deflection angles. We see that for various values of the impact parameter, the deflection angle can be positive, negative or even zero in this black hole spacetime. The negative deflection angle indicates the repulsive behavior of the gravity which comes from the gravitational hair parameter that is the most characteristic quantity of the BHT massive gravity.