Correction: Godzieba, D.A.; Radice, D. High-Order Multipole and Binary Love Number Universal Relations. Universe 2021, 7, 368

The authors wish to make the following corrections to their paper [...]

High-Order Multipole and Binary Love Number Universal Relations

Using a data set of approximately 2 million phenomenological equations of state consistent with observational constraints, we construct new equation-of-state-insensitive universal relations that exist between the multipolar tidal deformability parameters of neutron stars, Λl, for several high-order multipoles (l=5,6,7,8), and we consider finite-size effects of these high-order multipoles in waveform modeling. We also confirm the existence of a universal relation between the radius of the 1.4M⊙ NS, R1.4 and the reduced tidal parameter of the binary, Λ˜, and the chirp mass. We extend this relation to a large number of chirp masses and to the radii of isolated NSs of different mass M, RM. We find that there is an optimal value of M for every M such that the uncertainty in the estimate of RM is minimized when using the relation. We discuss the utility and implications of these relations for the upcoming LIGO O4 run and third-generation detectors.

Tidal deformation of quantum black holes

The response of a gravitating object to an external tidal field is encoded in its Love numbers, which identically vanish for classical black holes (BHs). Here we show, using standard time-independent quantum perturbation theory, that for a quantum BH, generically, the Love numbers are nonvanishing and negative. We calculate the quadrupolar electric quantum Love number of slowly rotating BHs and show that it depends most strongly on the first excited level of the quantum BH. Finally, we discuss the detectability of the quadrupolar quantum Love number in future precision gravitational-wave observations and show that, under favourable circumstances, its magnitude is large enough to imprint an observable signature on the gravitational waves emitted during the inspiral. Phase of two moderately spinning BHs.

Venus internal structure and global deformation

<p>Tidal forces acting on a planet cause a deformation and mass redistribution in its interior, involving surface motions and variation in the gravity field, which may be observed in geodetic experiments. The change in the gravitational field of the planet, due to the influence of an external gravity field, described primarily by its tidal Love number k of degree 2 (denoted by k<sub>2</sub>) can be observed from analysis of a spacecraft radio tracking. The planet’s deformation is linked to its internal structure, most effectively to its density and rigidity. Hence the tidal Love number k<sub>2</sub> can be theoretically approximated for different planetary models, which means comparing the observed and theoretical calculation of k<sub>2</sub> of a planet is a window to its internal structure.</p> <p>The terrestrial planet Venus is reminiscent of the Earth twin planet in size and density, which leads to the assumption that the Earth and Venus have similar internal structures. In this work, with a Venus we investigate the structure and elastic parameters of the planet’s major layers to calculate its frequency dependent tidal Love number k<sub>2</sub>. The calculation of k<sub>2</sub> is done with ALMA, a Fortran 90 program by <em>Spada [2008]</em> for computing the tidal and load Love numbers using the Post-Widder Laplace inversion formula. We test the effect of different parameters in the Venus model (as a layer’s density, rigidity, viscosity and thickness) on the tidal Love numbers k<sub>2 </sub>and different linear and non-linear combinations of k<sub>2</sub> and<sub> </sub>h<sub>2</sub> (as the tidal Love number h<sub>2</sub> describes the radial displacement due to tidal effects).</p>

Gravitational wave signatures of highly magnetized neutron stars

Motivated by the recent gravitational wave detection by the LIGO–VIRGO observatories, we study the Love number and dimensionless tidal polarizability of highly magnetized stars. We also investigate the fundamental quasi-normal mode of neutron stars subject to high magnetic fields. To perform our calculations we use the chaotic field approximation and consider both nucleonic and hyperonic stars. As far as the fundamental mode is concerned, we conclude that the role played by the constitution of the stars is far more relevant than the intensity of the magnetic field, and if massive stars are considered, the ones constituted by nucleons only present frequencies somewhat lower than the ones with hyperonic cores. This feature that can be used to point out the real internal structure of neutron stars. Moreover, our studies clearly indicate that strong magnetic fields play a crucial role in the deformability of low mass neutron stars, with possible consequences on the interpretation of the detected gravitational waves signatures.