Vanishing Compactness Gap and Fermionic Compact Dark Matter in Ho\v{r}ava-Lifshitz Gravity

TL;DR

This paper explores how Hořava-Lifshitz gravity can eliminate the traditional compactness gap between black holes and neutron stars, suggesting new possibilities for dark matter and compact objects.

Contribution

It demonstrates that in HL gravity, the compactness gap vanishes above a certain fermion mass, allowing objects to be classified differently from standard GR predictions.

Findings

Existence of a minimum fermion mass for gap vanishing.

Potential for fermionic dark matter objects of ~40 GeV mass.

Discovery of a new class of highly compact objects.

Abstract

We show that the gap in the compactness between black holes and neutron stars witnessed in general relativity may be vanishing in Ho\v{r}ava-Lifshitz (HL) gravity. Assuming a fermion equation-of-state for simplicity, and solving the Tolman-Oppenheimer-Volkoff equation within the HL gravity framework, we see that there exists a minimum fermion mass $m_f^\text{(min)}(q,y)$, above which the gap of the compactness between black hole and fermionic compact object vanishes, for a given deformation parameter $q$ of HL and interaction strength $y$ between fermions. Thus, in HL gravity, the mass and radius of an object found in the lower mass gap by LIGO-Virgo-KAGRA observations might not be able to classify it as a black hole or a neutron star. It is interesting to note that a fermion of mass $\sim 40\ \text{GeV}$ can form a highly compact object of mass $\sim 10^{-4}\ \msun$ and radius $\sim 1\ \text{m}$ that may play the role of the cold dark matter. In addition, we find the possible existence of another class of compact objects whose compactness is comparable to that of a black hole.