The motion of twisted particles in a stellar gravitational field

Abstract In this work, we explore the motion of a twisted particle possessing intrinsic orbital angular momentum (OAM) as it traverses a weak stellar gravitational field, which we approximate using a polytropic model. We disregard the spin characteristic of the twisted particle, modeling it as a massless complex twisted scalar wave packet to simplify its interaction with gravitational fields. Building on this simplification, we determine the trajectory of this twisted particle by using the center of its energy density and investigate the gravitational birefringence induced by its OAM. In a weak field approximation, we find the gravitational birefringence-OAM relationship parallels that with spin, as described by the Mathisson-Papapetrou-Dixon equations. This indicates that the gravitational birefringence induced by OAM can potentially exceed that induced by spin by several orders of magnitude, significantly enhancing its detectability. To broaden our analysis, we introduce a nonminimal coupling term, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mi>R</mml:mi> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>ϕ</mml:mi> <mml:msup> <mml:mo stretchy="false">|</mml:mo> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> , into the Lagrangian, resulting in the modified expression <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">L</mml:mi> </mml:mrow> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:msub> <mml:mi mathvariant="normal">∇</mml:mi> <mml:mi>ρ</mml:mi> </mml:msub> <mml:mi>ϕ</mml:mi> <mml:msup> <mml:mi mathvariant="normal">∇</mml:mi> <mml:mi>ρ</mml:mi> </mml:msup> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mi>λ</mml:mi> <mml:mi>R</mml:mi> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>ϕ</mml:mi> <mml:msup> <mml:mo stretchy="false">|</mml:mo> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> . This adjustment is necessitated by the quantization of the scalar field in curved spacetime. We then explore the effects of this term on the motion of the twisted particle. Our findings show that the trajectory of the twisted particle under nonminimal coupling ( λ ≠ 0) differs from that in the minimal coupling scenario ( λ = 0). Specifically, for a positive nonminimal coupling constant λ , the trajectory of the twisted particle is expected to deviate away from the stellar center, compared to the minimal coupling scenario.