Particle and light motion in Lyra–Schwarzschild spacetime

Abstract

Abstract In this paper we recall the static and spherically symmetric solution derived within LyST gravity. LyST stands for ‘Lyra Scalar-Tensor’ and is a scalar-tensor proposal for the gravitational interaction modifying general relativity by adopting Lyra manifold as the spacetime substrate. Lyra manifold is characterized both by the metric tensor g μ ν ( x ) and the scale ϕ ( x ) ; the latter being an integral part of the definition of reference frame. In a previous work, we have launched the formal geometrical basis of LyST, we have proposed an associated action integral for the gravitational interaction, we have derived the field equations generalizing Einstein field equation, and we have solved these equation to obtain the generalized version of Schwarzschild line element in Lyra manifold. This lead us to Lyra–Schwarzschild spacetime, which is further explored in the present paper. Herein, the trajectories of test particles is thoroughly studied. This is done for both massive particles and massless particles. The geodesic equations are built and solved. The effective potential associated to the motion of these particles around the source is determined and characterized. The possible trajectories include gravitational capture, scattering, bounded orbits, stable and unstable circular orbits, near-horizon motion. The innermost circular orbit allowed for massive particles is determined and compared to the one predicted by GR. The last photon orbit is also calculated for Lyra–Schwarzschild metric. The equation for the periastron shift in the context of Lyra–Schwarzschild solution is constructed; its application to observational data could be useful to constrain the parameters typical of LyST, telling it apart from GR.