Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2112.04116

Geometric origin of the galaxies' dark side

Leonardo Modesto·Tian Zhou·Qiang Li
View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that Einstein's conformal gravity is able to explain simply on the geometric ground the galactic rotation curves without need to introduce any modification in both the gravitational as well as in the matter sector of the theory. The geometry of each galaxy is described by a metric obtained making a singular rescaling of the Schwarzschild's spacetime. The new exact solution, which is asymptotically Anti-de Sitter, manifests an unattainable singularity at infinity that can not be reached in finite proper time, namely, the spacetime is geodetically complete. It deserves to be notice that we here think different from the usual. Indeed, instead of making the metric singularity-free, we make it apparently but harmlessly even more singular then the Schwarzschild's one. Finally, it is crucial to point that the Weyl's conformal symmetry is spontaneously broken to the new singular vacuum rather then the asymptotically flat Schwarzschild's one. The metric, is unique according to: the null energy condition, the zero acceleration for photons in the Newtonian regime, and the homogeneity of the Universe at large scales. Once the matter is conformally coupled to gravity, the orbital velocity for a probe star in the galaxy turns out to be asymptotically constant consistently with the observations and the Tully-Fisher relation. Therefore, we compare our model with a sample of 175 galaxies and we show that our velocity profile very well interpolates the galactic rotation-curves for a proper choice of the only free parameter in the metric and the the mass to luminosity ratios, which turn out to be close to 1 consistently with the absence of dark matter.

Explore related subjects

gr-qcastro-ph.GAhep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Leonardo Modesto, Tian Zhou, Qiang Li. 2021-12-08. Geometric origin of the galaxies' dark side. https://arxiv.org/abs/2112.04116

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

An upper bound on the minimum orbital period of black holes

Previous research has focused on establishing lower bounds on the minimum orbital period of black holes. In this work, we explore the complementary question of whether an upper bound exists for the minimum orbital period of black holes. We investigate the minimum orbital periods of three types of black holes: Schwarzschild, Reissner-Nordström and Kerr-Newman black holes. We find that the minimum orbital period of these black holes is bounded by an upper limit $T_{min} \leqslant 6\sqrt{3}πM$, where $M$ is the black hole mass. Our results suggest that this upper bound on the minimum orbital period may be a general property in black hole spacetimes.

gr-qc↗
arXiv2026

Dirac Observables for Gowdy Cosmologies regular at the Big Bang

Gowdy cosmologies are exact, spatially inhomogeneous solutions of the vacuum Einstein equations which describe nonlinear gravitational waves coalescing at the Big Bang singularity. With toroidal spatial sections they provenly have the Asymptotic Velocity Domination property, in that close to the Big Bang dynamical spatial gradients fade out and the dynamics is governed by a Carroll-type gravity theory. Here we construct an infinite set of Dirac observables for Gowdy cosmologies, valid off-shell, strongly, and without gauge fixing. These observables stay regular at the Big Bang and can be matched to much simpler Dirac observables of the Carroll-type gravity theory. Conversely, in an adapted foliation there is a systematic anti-Newtonian expansion (in inverse powers of the reduced Newton constant) of the full Dirac observables whose leading terms are the Carroll ones. In particular, this provides an off-shell generalization of the Asymptotic Velocity Domination property.

gr-qc↗
arXiv2026

Global causality constraints in rotating scalar-tensor spacetimes

Modified gravity is often formulated as an effective field theory (EFT), where higher-order corrections parametrize departures from General Relativity. We argue that such corrections should be constrained by the global causal structure of curved spacetime, in addition to the usual flat-space requirements such as positivity and unitarity. We propose that within the domain of validity of the EFT, the onset of closed timelike curves should not happen in a parametrically more accessible region than in the corresponding GR background. We test this diagnostic in the quadratic k-essence sector of scalar-tensor gravity. For stationary and axisymmetric spacetimes, the invariant test for closed axial orbits is the sign of the azimuthal component of the metric \(g_{φφ}\). We supplement this test by requiring a local time function in the space of Killing vectors. We apply these conditions to quadratic k-essence on Kerr--(A)dS backgrounds, with and without scalar charge. The zero-charge branch is exact Kerr--(A)dS, and we treat the charged branch perturbatively in scalar charge and in Hartle--Thorne slow rotation. Expanding for small spin \(χ=a/(GM)\ll1\), frame dragging begins at \(\mathcal O(χ)\), while the quadrupolar backreaction relevant for circular closed timelike curves enters at second order in both rotation and charge. We find that, in the truncation used here, any occurrence of \(g_{φφ}<0\) also lies outside EFT control. A higher-order calculation or a fully nonlinear treatment is therefore needed. Finally, we discuss how quasinormal modes and black-hole echoes could probe such causal structure.

gr-qc↗