Testing strong-field gravity with tidal Love numbers (1701.01116v4)

Abstract: The tidal Love numbers (TLNs) encode the deformability of a self-gravitating object immersed in a tidal environment and depend significantly both on the object's internal structure and on the dynamics of the gravitational field. An intriguing result in classical general relativity is the vanishing of the TLNs of black holes. We extend this result in three ways, aiming at testing the nature of compact objects: (i) we compute the TLNs of exotic compact objects, including different families of boson stars, gravastars, wormholes, and other toy models for quantum corrections at the horizon scale. In the black-hole limit, we find a universal logarithmic dependence of the TLNs on the location of the surface; (ii) we compute the TLNs of black holes beyond vacuum general relativity, including Einstein-Maxwell, Brans-Dicke and Chern-Simons gravity; (iii) We assess the ability of present and future gravitational-wave detectors to measure the TLNs of these objects, including the first analysis of TLNs with LISA. Both LIGO, ET and LISA can impose interesting constraints on boson stars, while LISA is able to probe even extremely compact objects. We argue that the TLNs provide a smoking gun of new physics at the horizon scale, and that future gravitational-wave measurements of the TLNs in a binary inspiral provide a novel way to test black holes and general relativity in the strong-field regime.

Overview of Tidal Love Numbers in Strong-Field Gravity

Introduction

The paper, authored by Vitor Cardoso and collaborators, investigates the applicability of tidal Love numbers (TLNs) in the field of gravitational physics, especially under strong-field conditions. TLNs characterize the deformability of compact objects when subjected to external tidal forces and hold significant implications for understanding self-gravitating bodies like neutron stars, black holes (BHs), and exotic compact objects (ECOs) such as boson stars and wormholes. Remarkably, the paper affirms the null TLNs of BHs in classical general relativity (GR) and advances this insight into the paper of such objects in modified gravity theories and proposals concerning the near-horizon quantum corrections.

Methodology

The authors present an analytical and numerical framework to compute TLNs across various models:

1. Exotic Compact Objects: The paper explores TLNs for different families of ECOs, including boson stars, gravastars, and wormholes. The extensions simulate these objects in configurations that range from solutions in standard GR to those incorporating hypothetical quantum corrections.
2. Beyond GR: TLNs are evaluated for BHs in modified gravity settings, such as Brans-Dicke, Einstein-Maxwell, and Chern-Simons gravity frameworks. These extensions offer platforms to examine speculative aspects like scalar fields and electromagnetic effects that might alter or present TLNs.

TLNs of Various Objects

1. Black Holes in Classical General Relativity: Classical GR ascertains TLNs of Schwarzschild BHs as null, owing to their event horizon absorbing all tidal perturbations.
2. Exotic Compact Objects: For configurations approaching the BH limit (compactness $C \to 1/2$), the TLNs exhibit a universal logarithmic dependence with respect to the compactness parameter. This logarithmic nature implies that ECOs maintain finite TLNs, even when their configuration is extremely compact.
3. Boson Stars: Different types of boson stars (minimal, massive, solitonic) display distinct TLN characteristics based on their compactness and internal structure. Notably, solitonic boson stars remain highly compact.
4. Modified Theories of Gravity: The paper indicates that while Einstein-Maxwell BHs have zero TLNs akin to their GR counterparts, solutions in Chern-Simons gravity exhibit non-zero axial TLNs. This poses intriguing prospects for observational tests of deviations from GR through gravitational-wave detectors.

Implications and Future Research

1. Future Detector Observations: GW detectors like LIGO, ET, and LISA possess the capacity to impose considerable constraints on non-BH models like boson stars. LISA has displayed particular prowess in probing high mass and high compactness ranges where ECOs significantly vary from traditional BH predictions.
2. Modified Gravity Theories: Since BHs present null TLNs in most modified gravity frameworks, it is challenging to leverage these metrics as primary tests of GR deviations. The colored non-zero axial component in Chern-Simons gravity might offer a potential observational avenue.
3. Theoretical Developments: The universal logarithmic dependency suggests an interesting pathway for future research into how quantum corrections near BH horizons may further detail TLN properties or introduce observable anomalies.

Conclusion

Cardoso and colleagues have expanded the discourse on tidal interactions to incorporate speculations around ECOs and modified gravity theories. This work does not only reinforce the foundational attributes of BHs in GR but also challenges researchers to consider TLNs as a robust metric in current and future GW studies, thereby enriching theoretical understanding of gravity in regimes yet uncharted. As observational technologies continue to evolve, the insights gleaned from this paper will serve as an instrumental reference for predictive studies and innovative gravitational physics research methodologies.