Spacetime backreaction on particle trajectory could source flat rotation curve

Abstract

The point-particle approximation is foundational to modelling clustering of matter in the universe, but is fundamentally inconsistent within General Relativity due to associated spacetime singularities. This bottleneck has historically restricted the study of matter clustering to linear scales. We resolve this by utilising the recent observation that a matter horizon precedes the formation of caustics in expanding spacetimes. This allows for the isolation of singularities via spacetime surgery. By glueing distinct spacetime sheets related by a discrete transformation across the shared boundary, we derive a covariant backreaction term that contributes to the effective energy-momentum tensor. We demonstrate that the spacetime backreaction contribution modifies local particle trajectories, naturally producing flat galaxy rotation curves in the outskirts without the need for dark matter particles.

Figures (3)

• Figure 1: We illustrate the matching of spacetimes at a common hypersurface. The timelike boundaries $B_\pm$ enclose the spatial region, while the spacelike boundaries denote where the initial data is defined.
• Figure 2: The figure illustrates a nested sequence of sub-regions across cosmic time. Clusters evolve on longer timescales, while galaxies and stars have shorter timescales. The key point is the hierarchical separation of characteristic timescales: $\tau_{ \rm{H}} < \tau_{ \rm{star}} < \tau_{ \rm{gal}} < \tau_{ \rm{clus}}$, which highlights the multi-scale nature of gravitational clustering in an expanding universe.
• Figure 3: The galaxy rotation curves of a typical galaxy with Hernquist density profile for the baryon density with parameters set to $a_{\pm} = 0.2$ Mpc, and $M =1.5\times10^{12} M_{\otimes}$. The velocity dispersion is set to $\sigma_{T\hat{\rho}_{\pm}1D}^2= \sigma_{\hat{\rho}_{\pm}1D}^2 = 20$[km/s]. The NFW prediction is added for comparison Navarro:1995iw.