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arXiv · 2601.18079

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

Edwin J. Son·Kyungmin Kim·John J. Oh
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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.

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Edwin J. Son, Kyungmin Kim, John J. Oh. 2026-01-26. Vanishing Compactness Gap and Fermionic Compact Dark Matter in Ho\v{r}ava-Lifshitz Gravity. https://doi.org/10.1103/zcwn-hq7g

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