# Tidal Deformability of Neutron Stars in Unimodular Gravity

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^{†}

## Abstract

**:**

## 1. Introduction

## 2. Unimodular Gravity: Action and Field Equations

## 3. Neutron Stars in UG

## 4. Static Linearized Perturbations and TLNs

#### 4.1. Even-Parity Sector

#### 4.2. Odd-Parity Sector

## 5. Conclusions and Discussions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | Actually, even imposing the conservation of the energy-momentum tensor, some new features may appear at perturbative level, see Ref. [15]. |

2 | This constraint reduces the full diffeomorphism group of spacetime to transverse diffeomorphisms subgroup satisfying ${g}_{\mu \nu}\delta {g}^{\mu \nu}=0$. |

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**Figure 1.**The relationship between dimensionless tidal deformability and the mass of a star with adiabatic index $\Gamma =2$ for different values of dimensionless non-conservation parameter $\tilde{k}$. As a comparison, the constraints from gravitational wave observations on the star are presented. The blue shaded box is drawn based on the $90\%$ confidence upper bound and the $90\%$ confidence interval on the masses of the observed neutron stars from observations given by GW170817. Meanwhile, the green and red boxes represent the same bounds for the primary and secondary components with the low-spin priors in GW190425, respectively.

**Figure 2.**The magnetic-type quadrupolar TLNs ${k}_{2}^{\mathrm{M}}$ as a function of the mass of the neutron star M for different values of the parameter $\tilde{k}$, where we choose the adiabatic index $\Gamma =2$.

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**MDPI and ACS Style**

Yang, R.-X.; Xie, F.; Liu, D.-J.
Tidal Deformability of Neutron Stars in Unimodular Gravity. *Universe* **2022**, *8*, 576.
https://doi.org/10.3390/universe8110576

**AMA Style**

Yang R-X, Xie F, Liu D-J.
Tidal Deformability of Neutron Stars in Unimodular Gravity. *Universe*. 2022; 8(11):576.
https://doi.org/10.3390/universe8110576

**Chicago/Turabian Style**

Yang, Rui-Xin, Fei Xie, and Dao-Jun Liu.
2022. "Tidal Deformability of Neutron Stars in Unimodular Gravity" *Universe* 8, no. 11: 576.
https://doi.org/10.3390/universe8110576