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Ladder Symmetries and Love Numbers of Reissner--Nordstr\"om Black Holes
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It is well known that asymptotically flat black holes in general relativity have vanishing tidal Love numbers. In the case of Schwarzschild and Kerr black holes, this property has been shown to be a consequence of a hidden structure of ladder symmetries for the perturbations. In this work, we extend the ladder symmetries to non-rotating charged black holes in general relativity. As opposed to previous works in this context, we adopt a more general definition of Love numbers, including quadratic operators that mix gravitational and electromagnetic perturbations in the point-particle effective field theory. We show that the calculation of a subset of those couplings in full general relativity is affected by an ambiguity in the split between source and response, which we resolve through an analytic continuation. As a result, we derive a novel master equation that unifies scalar, electromagnetic and gravitational perturbations around Reissner--Nordstr\"om black holes. The equation is hypergeometric and can be obtained from previous formulations via nontrivial field redefinitions, which allow to systematically remove some of the singularities and make the presence of the ladder symmetries more manifest.
Forward citations
Cited by 7 Pith papers
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Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory
A shell-based EFT computes scalar Love numbers for Schwarzschild black holes through O(G^9) and conjectures an all-orders Riemann-zeta structure.
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Dynamical Tidal Response of Schwarzschild Black Holes
The dynamical Love numbers of a Schwarzschild black hole are nonzero at quadratic order in frequency, run logarithmically with a coefficient set by dissipation, and are now matched including their finite, scheme-depen...
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Running Love Numbers and the Effective Field Theory of Gravity
Higher-derivative gravity corrections induce non-zero, classically running tidal Love numbers for black holes, computed here with a new tidal Green function method.
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Higher-Dimensional Black Holes and Effective Field Theory
Higher-dimensional spinning black holes generally have nonzero scalar tidal Love numbers, with patterns of zeroes in special limits, computed via point-particle EFT matching.
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On the logarithmic Love number of black holes beyond general relativity
Logarithmic black hole Love numbers are fixed directly by the Taylor coefficients of the perturbation equation, and perturbative deviations from Schwarzschild/Reissner-Nordström force non-zero running.
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The Vanishing of the Non-linear Static Love Number of Kerr Black Holes and the Role of Symmetries
Using the Ernst formalism, the paper argues that the static quadrupole tidal Love number of a Kerr black hole vanishes at full nonlinear order, because a decaying tidal mode would create a naked curvature singularity ...
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Charged Binaries in Gravitational Tides
Tidal corrections to the ISCO and light ring of a Reissner-Nordström black hole are derived analytically and shown to be suppressed but non-vanishing at extremality.
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