Gravitational emissions and light curves of quasi-periodic orbits in Schwarzschild spacetime embedded in a Dehnen-type dark matter halo

TL;DR

This paper studies closed timelike orbits in Schwarzschild spacetime with a dark matter halo, analyzing their gravitational wave and light curve signatures to explore dark matter effects.

Contribution

It identifies how dark matter parameters influence orbit morphology and signals, highlighting multi-messenger signatures for dark matter detection.

Findings

Dark matter parameters significantly amplify orbital scales.

Phase lag in gravitational waves correlates with dark matter properties.

Light curve peaks reveal orbital structure signatures.

Abstract

Timelike orbits in curved spacetimes encode intrinsic information about the background geometry and serve as critical probes for investigating gravitational theories and source distributions. In this study, we investigate strictly closed timelike orbits within a Schwarzschild spacetime embedded in a Dehnen-type dark matter halo. By solving the geodesic equations, we identify various configurations of these closed orbits and simulate their corresponding gravitational waves and electromagnetic light curves. Our findings reveal that the morphology of closed orbits is primarily governed by the ratio of the azimuthal period to the radial period. Notably, dark matter halo parameters such as the core scale and density parameters exert a significant amplification effect on the orbital scale, which further induces a discernible phase lag in the gravitational wave signals. Furthermore, although certain orbital structures including the number of leaves remain challenging to distinguish via gravitational wave signals alone, they exhibit identifiable signatures in the characteristic peaks of light curves. These findings reveal the multi-messenger potential of closed orbits in bridging black hole environments and dark matter properties, providing theoretical guidance for future dark matter searches.