Anisotropy Strikes Back: Modified Gravity and Dark Matter Halos

TL;DR

This work investigates whether dark-matter-like halos can emerge from modifications of gravity rather than new particle components, focusing on a spherically symmetric LTB minisuperspace. In a GR setting, adding a weight-$+1$ density to the potential yields an effective anisotropic fluid with ρ_h ∝ 1/A^2 and p_r = -ρ_h, which preserves the Dirac algebra but cannot produce truly flat rotation curves due to anisotropic stress. In Horava-Lifshitz gravity, a deformed hypersurface-deformation algebra leads to a controlled nonconservation of a would-be dust component, and on a restricted class of LTB backgrounds this can generate a positive ρ_DM ∝ 1/A^2 that can produce flat rotation curves in the quasi-static limit, albeit with strong parameter degeneracies and without a fully backreacted solution. The results delineate a clear contrast between GR-like deformations (anisotropic fluids) and HL-induced nonconservation (dust-like scaling), and outline the key next steps toward fully self-consistent, backreacted spacetimes and observational tests such as lensing.

Abstract

We explore dark matter like fluids in a spherically symmetric Lemaitre Tolman Bondi (LTB) minisuperspace, tracking how symmetry properties of the Hamiltonian constraint control the emergence of effective dark sources in General Relativity (GR) and Horava Lifshitz (HL) gravity. We first deform the GR Hamiltonian by adding an extra weight $+1$ density to the potential. We show that potential deformations of this type leave the (reduced) Dirac algebra unchanged and the modification is naturally reinterpreted as an effective anisotropic stress energy contribution. While the fluid reproduces an isothermal-like mass scaling, its pressure anisotropy prevents it from giving flat rotation curves. We then turn to HL gravity, where the deformed Dirac algebra induces a controlled nonconservation law for an emergent dust component. Generalizing earlier results, we identify a restricted class of LTB backgrounds for which the HL source term yields a positive scaling dark matter density, consistent with ghost-freedom, and recovery of GR in the infrared. The analysis is conditional on a prescribed background: obtaining a fully backreacted areal radius solution consistent with the HL field equations is left as a natural direction for future work.