arXiv subjects

Luca Santoni

Publications and source records attributed to Luca Santoni.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical Tidal Response of Neutron Stars: from Effective Field Theory to Gravitational Waveforms

We investigate the fully relativistic dynamical tidal response of neutron stars up to second order in the frequency. Combining the worldline effective field theory for extended gravitating bodies with perturbation theory of relativistic stellar models, we derive the tidal deformation induced by an external time-dependent field, including a universal logarithmic running term. In the effective theory, we work in dimensional regularization and, through a consistent matching procedure, obtain for the first time the complete leading-order dynamical tidal corrections to both the conservative dynamics and the gravitational-wave signal of compact binaries, including the scheme-dependent finite terms in addition to the running. We show that, in the relativistic regime, dynamical effects cannot be fully captured by mode excitations alone. The magnitude of the additional contribution depends on the stellar compactness, the equation of state, and the running term. Dynamical Love numbers are significantly enhanced with respect to their static counterparts for relatively small compactness. As a result, although they formally enter the gravitational-wave phase at 8th post-Newtonian order, dynamical tidal effects yield a non-negligible contribution during the late inspiral. Using a Fisher-matrix analysis, we show that third-generation detectors such as the Einstein Telescope could measure dynamical Love numbers for a range of neutron-star masses and equations of state. Conversely, neglecting these effects can lead to significant biases in the inference of static Love numbers, and hence on the nuclear equation of state. Our results highlight the importance of dynamical tidal effects for high-precision gravitational-wave modeling with future detectors.

gr-qc↗

arXiv2026

Love numbers of black holes and compact objects

The Love numbers of a gravitating body are response coefficients encoding its tidal deformability. In compact binary systems, they appear in the gravitational waveform during the inspiral phase and will be measurable by upcoming gravitational-wave observatories. This review provides a comprehensive and pedagogical account of the theoretical foundations of Love numbers and surveys the most recent advances in the study of tidal effects in compact objects, with particular emphasis on black holes and neutron stars. We begin with a gentle introduction to tidal effects in Newtonian gravity, leading into a discussion of how to robustly define tidal responses in general relativity using the effective field theory and post-Newtonian frameworks. After an overview of the perturbation theory of black holes and neutron stars, we review the computation of Love numbers and dissipative response coefficients in a wide range of settings, including the static, dynamical, and nonlinear tidal responses of Kerr black holes and neutron stars in four-dimensional general relativity. We further discuss the extension of these results to charged black holes and a number of "new physics" scenarios, including higher-dimensional black holes and other black objects, (anti-) de Sitter black holes, supergravity black holes, and theories beyond general relativity. Finally we provide an overview of the tantalizing zoo of hidden symmetries of general relativity that have been uncovered in the attempt to explain the famous vanishing of static black hole Love numbers.

gr-qc↗

arXiv2025

Nonlinear Relativistic Tidal Response of Neutron Stars

We investigate the nonlinear tidal response of relativistic neutron stars by computing the fully relativistic, static, quadratic Love numbers. Using both the worldline effective field theory for extended gravitating bodies and second-order perturbations of relativistic stellar models, we derive the nonlinear tidal deformation induced by an external gravito-electric tidal field to quadratic order. Through a suitable matching procedure, we provide for the first time the leading nonlinear tidal corrections to the conservative dynamics and gravitational-wave signal of binary systems. Quadratic Love numbers are enhanced more than the linear ones in the small-compactness limit. Because of this, despite entering the gravitational-wave phase at 8th post-Newtonian (PN) order, the leading quadratic Love number can be as important as the next-to-next-to-leading order linear tidal correction, which enters at 7th PN order, and is larger than the subleading point-particle contribution entering at 4th PN order. In particular, quadratic Love numbers can be as large as ~10% of the linear Love numbers in the late inspiral phase. Our approach provides a framework to also compute the (subleading) nonlinear effects induced by magnetic tidal fields and higher multipole moments, and sets the foundations for incorporating nonlinear tidal effects in high-precision gravitational-wave modeling.

gr-qc↗

arXiv2025

Dynamical Tidal Response of Schwarzschild Black Holes

Dynamical Love numbers capture the conservative response of an object to a time-dependent external tidal gravitational field. We compute the dynamical Love numbers of Schwarzschild black holes in general relativity within a point-particle effective field theory framework. In addition to the known logarithmic running, we compute the finite scheme-dependent contributions to the Love number couplings. We do this by matching the renormalized one-point function in the effective theory to the classical field profile computed in general relativity. On the general relativity side, we solve the Regge-Wheeler and Zerilli equations perturbatively in a small frequency expansion. In order to match on the effective field theory side we include gravitational interactions using the Born series and employ dimensional regularization to obtain a renormalized field profile.

gr-qc↗

arXiv2024

Higher-Dimensional Black Holes and Effective Field Theory

We study the scalar tidal responses of spinning higher-dimensional black holes, and their effective field theory description. After constructing the effective field theory of a spinning point particle in general dimension, we apply this theory to match the scalar responses of a variety of black hole solutions. In addition to the five-dimensional Myers--Perry black hole, we derive the scalar responses of spinning black holes in the large $D$ limit, and also study the responses of black holes in the ultra-spinning regime. We find that in the most generic case, the static responses of higher-dimensional spinning black holes do not vanish, but for special cases we find a pattern of zeroes in the responses, similar to other known examples. Further, we observe various interesting relations between the responses.

hep-th↗

arXiv2024

Symmetries of Vanishing Nonlinear Love Numbers of Schwarzschild Black Holes

The tidal Love numbers parametrize the conservative induced tidal response of self-gravitating objects. It is well established that asymptotically-flat black holes in four-dimensional general relativity have vanishing Love numbers. In linear perturbation theory, this result was shown to be a consequence of ladder symmetries acting on black hole perturbations. In this work, we show that a black hole's tidal response induced by a static, parity-even tidal field vanishes for all multipoles to all orders in perturbation theory. Our strategy is to focus on static and axisymmetric spacetimes for which the dimensional reduction to the fully nonlinear Weyl solution is well-known. We define the nonlinear Love numbers using the point-particle effective field theory, matching with the Weyl solution to show that an infinite subset of the static, parity-even Love number couplings vanish, to all orders in perturbation theory. This conclusion holds even if the tidal field deviates from axisymmetry. Lastly, we discuss the symmetries underlying the vanishing of the nonlinear Love numbers. An $\mathfrak{sl}(2,\mathbb R)$ algebra acting on a covariantly-defined potential furnishes ladder symmetries analogous to those in linear theory. This is because the dynamics of the potential are isomorphic to those of a static, massless scalar on a Schwarzschild background. We comment on the connection between the ladder symmetries and the Geroch group that is well-known to arise from dimensional reduction.

gr-qc↗

arXiv2024

Vanishing of Quadratic Love Numbers of Schwarzschild Black Holes

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.

gr-qc↗

arXiv2024

Perturbations of the Vaidya metric in the frequency domain: Quasi-normal modes and tidal response

The mass of a black hole can dynamically evolve due to various physical processes, such as for instance accretion, Hawking radiation, absorption of gravitational/electromagnetic waves, superradiance, etc. This evolution can have an impact on astrophysical observables, like the ringdown gravitational signal. An effective description of a spherically symmetric black hole with evolving mass is provided by the Vaidya metric. In our investigation, we explore the dynamics of linear perturbations on this background, assuming a constant rate of change for the mass. Despite the time-dependent background, a judicious change of coordinates allows us to treat the perturbations in the frequency domain, and to compute explicitly the quasi-normal modes and the tidal Love numbers.

gr-qc↗

arXiv2024

Ladder Symmetries and Love Numbers of Reissner--Nordstr\"om Black Holes

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.

gr-qc↗

arXiv2023

Fermions at finite density in the path integral approach

We study relativistic fermionic systems in $3+1$ spacetime dimensions at finite chemical potential and zero temperature, from a path-integral point of view. We show how to properly account for the $i\varepsilon$ term that projects on the finite density ground state, and compute the path integral analytically for free fermions in homogeneous external backgrounds, using complex analysis techniques. As an application, we show that the ${\rm U}(1)$ symmetry is always linearly realized for free fermions at finite charge density, differently from scalars. We study various aspects of finite density QED in a homogeneous magnetic background. We compute the free energy density, non-perturbatively in the electromagnetic coupling and the external magnetic field, obtaining the finite density generalization of classic results of Euler--Heisenberg and Schwinger. We also obtain analytically the magnetic susceptibility of a relativistic Fermi gas at finite density, reproducing the de Haas--van Alphen effect. Finally, we consider a (generalized) Gross--Neveu model for $N$ interacting fermions at finite density. We compute its non-perturbative effective potential in the large-$N$ limit, and discuss the fate of the ${\rm U}(1)$ vector and $\mathbb{Z}_2^A$ axial symmetries.

hep-th↗

arXiv2023

Vanishing of Nonlinear Tidal Love Numbers of Schwarzschild Black Holes

It is well known that asymptotically flat Schwarzschild black holes in general relativity in four spacetime dimensions have vanishing induced linear tidal response. We extend this result beyond linear order for the polar sector, by solving the static nonlinear Einstein equations for the perturbations of the Schwarzschild metric and computing the quadratic corrections to the electric-type tidal Love numbers. After explicitly performing the matching with the point-particle effective theory at leading order in the derivative expansion, we show that the Love number couplings remain zero at higher order in perturbation theory.

gr-qc↗

arXiv2023

Black Hole Ringdown as a Probe for Dark Energy

Under the assumption that a dynamical scalar field is responsible for the current acceleration of the Universe, we explore the possibility of probing its physics in black hole merger processes with gravitational wave interferometers. Remaining agnostic about the microscopic physics, we use an effective field theory approach to describe the scalar dynamics. We investigate the case in which some of the higher derivative operators, that are highly suppressed on cosmological scales, instead become important on typical distances for black holes. If a coupling to the Gauss-Bonnet operator is one of them, a non-trivial background profile for the scalar field can be sourced in the surroundings of the black hole, resulting in a potentially large amount of "hair". In turn, this can induce sizeable modifications to the spacetime geometry or a mixing between the scalar and the gravitational perturbations. Both effects will ultimately translate into a modification of the quasi-normal mode spectrum in a way that is also sensitive to other operators besides the one sourcing the scalar background. The presence of deviations from the predictions of general relativity in the observed spectrum can therefore serve as a window onto dark energy physics.

gr-qc↗

arXiv2023

Black hole superradiance with (dark) matter accretion

Studies of black hole superradiance often focus on the growth of a cloud in isolation, accompanied by the spin-down of the black hole. In this paper, we consider the additional effect of the accretion of matter and angular momentum from the environment. We show that, in many cases, the black hole evolves by drifting along the superradiance threshold, in which case the evolution of its parameters can be described analytically or semi-analytically. We quantify the conditions under which accretion can serve as a mechanism to increase the cloud-to-black hole mass ratio, beyond the standard maximum of about 10%. This occurs by a process we call over-superradiance, whereby accretion effectively feeds the superradiance cloud, by way of the black hole. We give two explicit examples: accretion from a vortex expected in wave dark matter and accretion from a baryonic disk. In the former case, we estimate the accretion rate by using an analytical fit to the asymptotic behavior of the confluent Heun function. Level transition, whereby one cloud level grows while the other shrinks, can be understood in a similar way.

gr-qc↗

arXiv2023

The connection between nonzero density and spontaneous symmetry breaking for interacting scalars

We consider ${\rm U}(1)$-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously broken along with Lorentz boosts and time translations. We show that, in $d>2$ spacetime dimensions, this expectation is always realized at one loop for arbitrary non-derivative interactions, confirming that the physically distinct phenomena of nonzero charge density and spontaneous symmetry breaking occur simultaneously in these systems. We quantify this result by deriving universal scaling relations for the symmetry breaking scale as a function of the charge density, at low and high density. Moreover, we show that the critical value of $\mu$ above which a nonzero density develops coincides with the pole mass in the unbroken, Poincar\'e invariant vacuum of the theory. The same conclusions hold non-perturbatively for an ${\rm O}(N)$ theory with quartic interactions in $d=3$ and $4$, at leading order in the $1/N$ expansion. We derive these results by computing analytically the zero-temperature, finite-$\mu$ one-loop effective potential. We check our results against the one-loop low-energy effective action for the superfluid phonons in $\lambda \phi^4$ theory in $d=4$ previously derived by Joyce and ourselves, which we further generalize to arbitrary potential interactions and arbitrary dimensions. As a byproduct, we find analytically the one-loop scaling dimension of the lightest charge-$n$ operator for the $\lambda \phi^6$ conformal superfluid in $d=3$, at leading order in $1/n$, reproducing a numerical result of Badel et al. For a $\lambda \phi^4$ superfluid in $d=4$, we also reproduce the Lee--Huang--Yang relation and compute relativistic corrections to it. Finally, we discuss possible extensions of our results beyond perturbation theory.

hep-th↗

arXiv2023

Dissipative Inflation via Scalar Production

We describe a new mechanism that gives rise to dissipation during cosmic inflation. In the simplest implementation, the mechanism requires the presence of a massive scalar field with a softly-broken global $U(1)$ symmetry, along with the inflaton field. Particle production in this scenario takes place on parametrically sub-horizon scales, at variance with the case of dissipation into gauge fields. Consequently, the backreaction of the produced particles on the inflationary dynamics can be treated in a \textit{local} manner, allowing us to compute their effects analytically. We determine the parametric dependence of the power spectrum which deviates from the usual slow-roll expression. Non-Gaussianities are always sizeable whenever perturbations are generated by the noise induced by dissipation: $f_{\rm NL}^{\rm eq} \gtrsim {O}(10)$.

hep-th↗

arXiv2023

Black hole hairs in scalar-tensor gravity and the lack thereof

Scalar-tensor theories are a natural alternative to general relativity, as they may provide an effective dark energy phenomenology on cosmological scales while passing local tests, but their black hole solutions are still poorly understood. Here, we generalize existing no-hair theorems for spherical black holes and specific theories in the scalar-tensor class. We show that shift symmetry prevents the appearance of scalar hairs in rotating (asymptotically flat, stationary and axisymmetric) black holes for all theories in the Horndeski/beyond Horndeski/DHOST classes, but for those with a coupling between the scalar and the Gauss--Bonnet invariant. Our proof also applies to higher dimensions. We also compute the values of the scalar hair charges if shift symmetry and asymptotic flatness are violated by a time growth of the scalar field at infinity, under suitable regularity conditions at the event horizon.

gr-qc↗

arXiv2023

Love Numbers for Rotating Black Holes in Higher Dimensions

We compute the tidal Love numbers and static response coefficients associated to several rotating black holes in higher dimensions, including Myers-Perry black holes, black rings, and black strings. These coefficients exhibit a rich and complex structure as a function of the black hole parameters and multipoles. Our results agree in limiting cases with known and new expressions for various lower-dimensional black holes. In particular, we provide an alternative approach to the computation of the static response of Kerr black holes as a limiting case of the boosted black string.

hep-th↗

arXiv2022

Soft theorems for boosts and other time symmetries

We derive soft theorems for theories in which time symmetries -- symmetries that involve the transformation of time, an example of which are Lorentz boosts -- are spontaneously broken. The soft theorems involve unequal-time correlation functions with the insertion of a soft Goldstone in the far past. Explicit checks are provided for several examples, including the effective theory of a relativistic superfluid and the effective field theory of inflation. We discuss how in certain cases these unequal-time identities capture information at the level of observables that cannot be seen purely in terms of equal-time correlators of the field alone. We also discuss when it is possible to phrase these soft theorems as identities involving equal-time correlators.

hep-th↗