Preprint

PUBDB-2024-06039

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Vanishing of Quadratic Love Numbers of Schwarzschild Black Holes

Iteanu, S. ; Riva, M. M. (Corresponding author)DESY* ; Santoni, L. ; Savić, N. ; Vernizzi, F.

2024

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Please use a persistent id in citations: doi:10.3204/PUBDB-2024-06039

Report No.: DESY-24-141; arXiv:2410.03542

Abstract: The induced conservative tidal response of self-gravitating objects in general relativity is parametrized in terms of a set of coefficients, which are commonly referred to as Love numbers. For asymptotically-flat black holes in four spacetime dimensions, the Love numbers are notoriously zero in the static regime. In this work, we show that this result continues to hold upon inclusion of nonlinearities in the theory for Schwarzschild black holes. We first solve the quadratic Einstein equations in the static limit to all orders in the multipolar expansion, including both even and odd perturbations. We show that the second-order solutions take simple analytic expressions, generically expressible in the form of finite polynomials. We then define the quadratic Love numbers at the level of the point-particle effective field theory. By performing the matching with the full solution in general relativity, we show that quadratic Love number coefficients are zero to all orders in the derivative expansion, like the linear ones.

Note: 55 pages, 3 figures

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Contributing Institute(s):

1. Theorie-Gruppe (T)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. DFG project G:(GEPRIS)390833306 - EXC 2121: Quantum Universe (390833306) (390833306)
3. LHCtoLISA - Precision Gravity: From the LHC to LISA (817791) (817791)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2024

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