Revisiting Flat Rotation Curves in Chern-Simons Modified Gravity

TL;DR

This paper introduces a new slow rotating black hole solution in Chern-Simons modified gravity that accounts for frame dragging and analyzes its implications for galactic rotation curves, finding limitations in explaining flat rotation curves.

Contribution

It presents a novel perturbative black hole solution in Chern-Simons gravity that extends previous models and examines its effects on gravitational forces and galaxy rotation curves.

Findings

New black hole solution includes frame dragging effects.

Additional $1/r^3$ term in tidal force compared to Schwarzschild.

Perturbative solutions cannot fully explain flat galactic rotation curves.

Abstract

We revisit slow rotating black hole (BH) solutions in Chern-Simons modified gravity (CSMG) by considering perturbative solution about Schwarzschild BH. In particular, the case when nondynamical CSMG with noncanonical CS scalar is considered. We provide a new solution different from the previously obtained one \cite{Konno:2007ze} which we refer to as KMT model. The present solution accounts for frame dragging effect which includes not only radial dependence as in the KMT. Nevertheless, it reduces to KMT as a particular case. We show that the tidal gravitational force (Kretschmann invariant) associated to the present solution contains a term of order $1/r^3$ additional to Schwarzschild but absent from directional divergence, unlike KMT model which diverges along the axis of symmetry. We derive the corresponding circular velocity of a massive test particle in which the KMT velocity is recovered in addition to an extra term $\propto r$. We investigate possible constraints on KMT and the present solutions from the observed rotation curve of UGC11455 galaxy as an example. We show that perturbation solutions cannot physically explain the flattening of galactic rotation curves.