Galactic dark matter halos: From anisotropic fluids in general relativity to Horava-Lifshitz gravity

Abstract

We 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 in this reduced phenomenological toy model. We then turn to HL gravity, where the absence of a local Hamiltonian constraint leaves a non-vanishing local Hamiltonian density, giving a controlled nonconservation law for the 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 with the continuous $\lambda \to 1$ limit, in which the effective dust amplitude vanishes together with the deviation from GR. 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.