We obtain the full set of tidal Love numbers of non-rotating black holes in an effective field theory extension of general relativity. We achieve our results using a recently introduced modified Teukolsky equation that describes the perturbations of black holes in this theory. We show how to identify the Love numbers and their beta functions in a systematic and gauge invariant way, applying analytic continuation on the angular number $\textit{ℓ}$ when necessary. We observe that there are three types of Love numbers: electric, magnetic, and a “mixing” type, associated to parity-breaking theories, that we identify here for the first time. The modified Teukolsky equation proves to be very useful as it allows us to obtain all the different Love numbers in a unified framework. We compare our results with previous literature that utilized the Regge-Wheeler-Zerilli equations to compute Love numbers, finding perfect agreement. The method introduced here paves the way towards the computation of Love numbers of rotating black holes beyond general relativity.

Spain

Pablo Cano

Love numbers beyond GR from the modified Teukolsky equation

The Cano-Ruipérez 4-dimensional string effective action is the simplest consistent truncation of the first-order in $\textit{α}$ heterotic string effective action compactified on T . This theory contains, on top of the metric, a dilaton and an axion that couple to the Gauss-Bonnet term and to the Pontrjagin density which suggests a very strong relation between the physical and geometrical properties of its solutions. In this paper we study the thermodynamics of the string black-hole solutions of this theory using Wald’s formalism. We construct the on-shell closed generalized Komar, dilaton and axion 2-form charges, and we used them to find the Smarr formula (that we test on the Schwarzschild and Kerr solutions) and to prove no-(primary)-hair theorems for the scalar. We find that $\textit{α}$ plays the role of a thermodynamical variable with an associated chemical potential. We also notice the occurrence of non-standard gravitational charges in the Wald entropy and scalar charges.

Tomás Ortín

Germany

Matteo Zatti

On the thermodynamics of the black holes of the Cano-Ruipérez 4-dimensional string effective action

Higher-derivative corrections in the AdS/CFT correspondence allow us to capture finer details of the dual CFT and to explore the holographic dictionary beyond the infinite N and strong coupling limits. Following an effective field theory approach, we investigate extremal AdS black hole solutions in five-dimensional supergravity with higher-derivative corrections. We provide a general analysis of near-horizon geometries of rotating extremal black holes and show how to obtain their corresponding charges and chemical potentials. We discuss the near-horizon solutions of the two-derivative theory, which we write using a novel parametrization that eases our computation of the higher-derivative corrections. The charges and thermodynamic properties of the black hole are computed while clarifying the ambiguities in their definitions. The charges and potentials turn out to satisfy a near-horizon version of the first law of thermodynamics whose interpretation we make clear. In the supersymmetric case, the results are shown to match the field theory prediction as well as previous results obtained from the on-shell action.

Belgium

Marina David

Near-horizon geometries and black hole thermodynamics in higher-derivative AdS5 supergravity

We investigate higher derivative corrections to the extremal Kerr black hole in the context of heterotic string theory with α′ corrections and of a cubic-curvature extension of general relativity. By analyzing the near-horizon extremal geometry of these black holes, we are able to compute the Iyer-Wald entropy as well as the angular momentum via generalized Komar integrals. In the case of the stringy corrections, we obtain the physically relevant relation S(J) at order α′2. On the other hand, the cubic theories, which are chosen as Einsteinian cubic gravity plus a new odd-parity density with analogous features, possess special integrability properties that enable us to obtain exact results in the higher-derivative couplings. This allows us to find the relation S(J) at arbitrary orders in the couplings and even to study it in a non-perturbative way. We also extend our analysis to the case of the extremal Kerr-(A)dS black hole.

The extremal Kerr entropy in higher-derivative gravities

We compute the first-order α′ corrections of the non-extremal Strominger-Vafa black hole and its non-supersymmetric counterparts in the framework of the Bergshoeff-de Roo formulation of the heterotic superstring effective action. The solution passes several tests: its extremal limit is the one found in an earlier publication and the effect of a T duality transformation on it is another solution of the same form with T dual charges. We compute the Hawking temperature and Wald entropy showing that they are related by the first law and Smarr formula. On the other hand, these two contain additional terms in which the dimensionful parameter α′ plays the role of thermodynamical variable.

Italy

Alejandro Ruipérez

Non-extremal, α′-corrected black holes in 5-dimensional heterotic superstring theory

We consider a broad family of higher-derivative extensions of four-dimensional Einstein gravity and study the multipole moments of rotating black holes therein. We carefully show that the various definitions of multipoles carry over from general relativity, and compute these multipoles for higher-derivative Kerr using the ACMC expansion formalism. We obtain the mass M  n  and current S  n  multipoles as a series expansions in the dimensionless spin; in some cases we are able to resum these series into closed-form expressions. Moreover, we observe the existence of intriguing relations between the corrections to the parity-odd multipoles S 2n  ≠ 0 and M 2n+1 ≠ 0 that break equatorial symmetry, and the parity-preserving corrections that only modify S 2n+1 and M 2n . Further, we comment on the higher-derivative corrections to multipole ratios for Kerr, and we discuss the phenomenological implications of the corrections to the multipole moments for current and future gravitational wave experiments.

France

Bogdan Ganchev

Daniel Mayerson

Black hole multipoles in higher-derivative gravity

We carry out an extensive study of the holographic aspects of any-dimensional higher-derivative Einstein-Maxwell theories in a fully analytic and non-perturbative fashion. We achieve this by introducing the d-dimensional version of Electromagnetic Quasitopological gravities: higher-derivative theories of gravity and electromagnetism that propagate no additional degrees of freedom and that allow one to study charged black hole solutions analytically. These theories contain non-minimal couplings, that in the holographic context give rise to a modified 〈JJ〉 correlator as well as to a general 〈TJJ〉 structure whose coefficients we compute. We constrain the couplings of the theory by imposing CFT unitarity and positivity of energy (which we show to be equivalent to causality in the bulk) as well as positive-entropy bounds from the weak gravity conjecture. The thermodynamic properties of the dual plasma at finite chemical potential are studied in detail, and we find that exotic zeroth-order phase transitions may appear, but that many of them are ruled out by the physical constraints. We further compute the shear viscosity to entropy density ratio, and we show that it can be taken to zero while respecting all the constraints, providing that the chemical potential is large enough. We also obtain the charged Rényi entropies and we observe that the chemical potential always increases the amount of entanglement and that the usual properties of Rényi entropies are preserved if the physical constraints are met. Finally, we compute the scaling dimension and magnetic response of twist operators and we provide a holographic derivation of the universal relations between the expansion of these quantities and the coefficients of 〈JJ〉 and 〈TJJ〉.

Ángel Murcia

Alberto Sánchez

Xuao Zhang

Higher-derivative holography with a chemical potential

We study extremal 5- and 4-dimensional black hole solutions of the Heterotic Superstring effective action at first order in α′ with, respectively, 3 and 4 charges of arbitrary signs. For a particular choice of the relative signs of these charges the solutions are supersymmetric, but other signs give rise to non-supersymmetric extremal black holes. Although at zeroth order all these solutions are formally identical, we show that the α′ corrections are drastically different depending on how we break supersymmetry. We provide fully analytic   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (α′) solutions and we compute their charges, masses and entropies and check that they are invariant under α′-corrected T-duality transformations. The masses of some of these black holes are corrected in a complicated way, but we show that the shift is always negative, in agreement with the Weak Gravity Conjecture. Our formula for the corrected entropy of the four-dimensional black holes generalizes previous results obtained from the entropy function method, as we consider a more general way in which supersymmetry can be broken.

Non-supersymmetric black holes with α′ corrections

We investigate higher-derivative extensions of Einstein-Maxwell theory that are invariant under electromagnetic duality rotations, allowing for non-minimal couplings between gravity and the gauge field. Working in a derivative expansion of the action, we characterize the Lagrangians giving rise to duality-invariant theories up to the eight-derivative level, providing the complete list of operators that one needs to include in the action. We also characterize the set of duality-invariant theories whose action is quadratic in the Maxwell field strength but which are non-minimally coupled to the curvature. Then we explore the effect of field redefinitions and we show that, to six derivatives, the most general duality-preserving theory can be mapped to Maxwell theory minimally coupled to a higher-derivative gravity containing only four non-topological higher-order operators. We conjecture that this is a general phenomenon at all orders, i.e., that any duality-invariant extension of Einstein-Maxwell theory is perturbatively equivalent to a higher-derivative gravity minimally coupled to Maxwell theory. Finally, we study charged black hole solutions in the six-derivative theory and we investigate additional constraints on the couplings motivated by the weak gravity conjecture.

Duality-invariant extensions of Einstein-Maxwell theory

We review and extend results on higher-curvature corrections to different configurations describing a superposition of heterotic strings, KK monopoles, solitonic 5-branes and momentum waves. Depending on which sources are present, the low-energy fields describe a black hole, a soliton or a naked singularity. We show that this property is unaltered when perturbative higher-curvature corrections are included, provided the sources are fixed. On the other hand, this character may be changed by appropriate introduction (or removal) of sources regardless of the presence of curvature corrections, which constitutes a non-perturbative modification of the departing system. The general system of multicenter KK monopoles and their 5-brane charge induced by higher-curvature corrections is discussed in some detail, with special attention paid to the possibility of merging monopoles. Our results are particularly relevant for small black holes (Dabholkar-Harvey states, DH), which remain singular after quadratic curvature corrections are taken into account. When there are four non-compact dimensions, we notice the existence of a black hole with regular horizon whose entropy coincides with that of the DH states, but the charges and supersymmetry preserved by both configurations are different. A similar construction with five non-compact dimensions is possible, in this case with the same charges as DH, although it fails to reproduce the DH entropy and supersymmetry. No such configuration exists if d &gt; 5, which we interpret as reflecting the necessity of having a 5-brane wrapping the compact space.