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Register a new userStringy Newton Gravity with $H$-flux
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A Symmetry Principle has been shown to augment unambiguously the Einstein Field Equations, promoting the whole closed-string massless NS-NS sector to stringy graviton fields. Here we consider its weak field approximation, take a non-relativistic limit, and derive the stringy augmentation of Newton Gravity: [ begin{array}{lll} {bf{ abla}^{2}Phi}=4pi G rho+bf{H}{bf{cdot}}bf{H},, quad&qquadbf{ abla}bf{cdot}bf{H}=0,, quad&qquad {bf{ abla}bf{times}bf{H}}=4pi G, bf{K},. end{array} ] Not only the mass density $rho$ but also the current density $mathbf{K}$ is intrinsic to matter. Sourcing $mathbf{H}$ which is of NS-NS $H$-flux origin, $mathbf{K}$ is nontrivial if the matter is `stringy. $mathbf{H}$ contributes quadratically to the Newton potential, but otherwise is decoupled from the point particle dynamics, i.e. $bf{ddot{x}}=-bf{ abla}Phi$. We define `stringization analogous to magnetization and discuss regular as well as monopole-like singular solutions.
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We consider the branch of the projectable Horava-Lifshitz model which exhibits ghost instabilities in the low energy limit. It turns out that, due to the Lorentz violating structure of the model and to the presence of a finite strong coupling scale, the vacuum decay rate into photons is tiny in a wide range of phenomenologically acceptable parameters. The strong coupling scale, understood as a cutoff on ghosts spatial momenta, can be raised up to $Lambda sim 10$ TeV. At lower momenta, the projectable Horava-Lifshitz gravity is equivalent to General Relativity supplemented by a fluid with a small positive sound speed squared ($10^{-42}lesssim$) $c^2_s lesssim 10^{-20}$, that could be a promising candidate for the Dark Matter. Despite these advantages, the unavoidable presence of the strong coupling obscures the implementation of the original Horavas proposal on quantum gravity. Apart from the Horava-Lifshitz model, conclusions of the present work hold also for the mimetic matter scenario, where the analogue of the projectability condition is achieved by a non-invertible conformal transformation of the metric.
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