arXiv subjects

Alejandro Ruipérez

Publications and source records attributed to Alejandro Ruipérez.

At least 19 recordsLinked to original sources

arXiv2026

Decoupling saddles of the gravitational index and the Farey tail

We first construct general saddles of the five-dimensional gravitational supersymmetric index with $S^1\times\mathbb{R}^4$ asymptotics, carrying an arbitrary number of electric charges and Gibbons-Hawking centers. We then uplift the three-charge configurations to type IIB supergravity, obtaining solutions asymptotic to $S^1\times \mathbb{R}^4\times S^1\times {\rm K}3$, carrying D1-D5-P charges. Upon taking a decoupling limit, these solutions yield asymptotically Euclidean AdS$_3\times S^3\times {\rm K}3$ candidate saddles of the dual CFT$_2$ elliptic genus. We focus on the two-center saddles, which involve three integers specifying an orbifold action. Depending on these integers, the saddles may or may not possess a Euclidean horizon, and may be smooth or exhibit orbifold singularities. We give the on-shell action of these two-center saddles in the appropriate ensemble and establish a precise match with the Farey-tail expansion of the elliptic genus. The horizonless saddles are the Euclidean version of fractional spectral-flow solutions previously discussed in the literature, corresponding to $({\rm AdS}_3\times S^3)/\mathbb{Z}_k$ orbifolds. The black hole saddles are modular images of the horizonless ones. They generalize the well-known ${\rm SL}(2,\mathbb{Z})$ family of BTZ black holes by placing it in the background of the $\mathbb{Z}_k$ orbifold. We also consider the asymptotically AdS$_3\times S^3$ solutions arising as decoupling limit of five-dimensional black ring and black lens saddles, provide their on-shell action and confirm that they do not contribute to the D1-D5 elliptic genus.

hep-th↗

arXiv2026

Gravitational waveforms from binaries in higher-derivative gravity: a Love story

We study the emission of gravitational waves by a test particle orbiting a non-rotating black hole in higher-derivative gravity theories with cubic and quartic contractions of the Riemann tensor. To this aim, we first derive the master equations describing even- and odd-parity perturbations in the presence of an arbitrary source term, and then construct a Post-Minkowskian expansion of the solutions to the homogeneous master equations. Specializing to a circular binary system, we compute the Post-Newtonian expansion of the waveform, as well as the energy and angular-momentum fluxes at infinity. We show that higher-derivative corrections to the waveform and to the fluxes always appear at 5PN order, and are universally proportional to the Love number describing the deformability of the geometry under the $\ell=2$ mode perturbation. These analytical results are validated against numerical computations, which also allow us to extend the analysis to larger velocities.

gr-qc↗

arXiv2026

BMPV black hole at first order in $α'$

We consider the low-energy effective action of the heterotic string and derive an analytic solution describing the first-order $α'$ corrections to the supersymmetric and extremal BMPV black hole with three unequal charges. The solution interpolates between an asymptotically-flat region and the near-horizon geometry. We compute the corrected black hole entropy using a generalization of Wald formula available in the literature, which correctly accounts for the Lorentz Chern-Simons term. The resulting expression agrees with recent results in the literature, which are based on the evaluation of an appropriate supersymmetric index.

hep-th↗

arXiv2025

Bubbling saddles of the gravitational index

We consider the five-dimensional supergravity path integral that computes a supersymmetric index, and uncover a wealth of semiclassical saddles with bubbling topology. These are complex finite-temperature configurations asymptotic to $S^1\times\mathbb{R}^4$, solving the supersymmetry equations. We assume a ${\rm U}(1)^3$ symmetry given by the thermal isometry and two rotations, and present a general construction based on a rod structure specifying the fixed loci of the ${\rm U}(1)$ isometries and their three-dimensional topology. These fixed loci may correspond to multiple horizons or three-dimensional bubbles, and they may have $S^3$, $S^2\times S^1$, or lens space topology. Allowing for conical singularities gives additional topologies involving spindles and branched spheres or branched lens spaces. As a particularly significant example, we analyze in detail the configurations with a horizon and a bubble just outside of it. We determine the possible saddle-point contribution of these configurations to the gravitational index by evaluating their on-shell action and the relevant thermodynamic relations. We also spell out two limits leading to well-defined Lorentzian solutions. The first is the extremal limit, which gives the known BPS black ring and black lens solutions. The on-shell action and chemical potentials remain well-defined in this limit and should thus provide the contribution of the black ring and black lens to the gravitational index. The second is a limit leading to horizonless bubbling solutions, which have purely imaginary action.

hep-th↗

arXiv2025

Rotating Topological Stars

We construct a three-parameter family of smooth and horizonless rotating solutions of Einstein-Maxwell theory with Chern-Simons term in five dimensions and discuss their stringy origin in terms of three-charge brane systems in Type IIB and M-theory. The general solution interpolates smoothly between Kerr and static Topological Star geometries. We show that for specific choices of the parameters and quantized values of the angular momentum the geometry terminates on a smooth five-dimensional cap, and it displays neither ergoregion nor closed timelike curves. We discuss the propagation of particles and waves showing that geodetic motion is integrable and the radial and angular propagation of scalar perturbations can be separated and described in terms of two ordinary differential equations of confluent Heun type.

hep-th↗

arXiv2024

Localization of the 5D supergravity action and Euclidean saddles for the black hole index

We investigate equivariant localization of the gravitational on-shell action in odd dimensions, focusing on five-dimensional ungauged supergravity. We analyze the conditions for cancellation of boundary terms, so that the full action integral is given in terms of the odd-dimensional analog of the nuts and bolts of Gibbons-Hawking. We specialize to supersymmetric configurations with an additional ${\rm U}(1)$ symmetry preserving the supercharge and provide a formula for the localized on-shell action. We construct asymptotically flat Euclidean supersymmetric non-extremal solutions with two independent rotations and an arbitrary number of electric charges, providing black hole saddles of the gravitational path integral that computes a supersymmetric index, and evaluate their action equivariantly. We find that these Euclidean saddles interpolate between supersymmetric extremal black holes and two-center horizonless microstate geometries. The interpolation involves dialing the temperature and implementing different analytic continuations. The corresponding on-shell action does not depend on temperature but is affected by the analytic continuations.

hep-th↗

arXiv2024

Non-spinning tops are stable

We consider coupled gravitational and electromagnetic perturbations of a family of five-dimensional Einstein-Maxwell solutions that describes both magnetized black strings and horizonless topological stars. We find that the odd perturbations of this background lead to a master equation with five Fuchsian singularities and compute its quasinormal mode spectrum using three independent methods: Leaver, WKB and numerical integration. Our analysis confirms that odd perturbations always decay in time, while spherically symmetric even perturbations may exhibit for certain ranges of the magnetic fluxes instabilities of Gregory-Laflamme type for black strings and of Gross-Perry-Yaffe type for topological stars. This constitutes evidence that topological stars and black strings are classically stable in a finite domain of their parameter space.

hep-th↗

arXiv2024

Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography

A Cardy-like regime of the four-dimensional superconformal index has been shown to be governed by 't Hooft anomalies and to single out a large-$N$ saddle carrying the Bekenstein-Hawking entropy of dual supersymmetric black holes in AdS$_5$. For the universal index where no flavour fugacities are turned on, this correspondence has been improved by matching the first subleading corrections to the saddle-point action with the four-derivative corrections to the black hole action in minimal gauged supergravity, as well as the respective corrected entropies. Here, we extend this match by including flavour symmetries. We consider five-dimensional gauged supergravity with vector multiplet and four-derivative couplings, and provide an effective theory reproducing the 't Hooft anomalies of the R- and flavour symmetries of generic holographic superconformal field theories at next-to-leading order in the large-$N$ expansion. Then we focus on a specific model dual to $\mathbb{C}^3/\mathbb{Z}_ν$ quiver gauge theories, where the 't Hooft anomaly coefficients receive simple but sufficiently generic corrections. In this model, we evaluate the four-derivative corrections to the on-shell action of the supersymmetric multi-charge black hole, showing agreement with the flavoured Cardy-like formula from the index. We give a prediction for the corrected entropy of the supersymmetric black hole and discuss the general validity of our results. Taking the limit of infinite AdS$_5$ radius, we also obtain four-derivative corrections to the action and entropy of supersymmetric asymptotically flat black holes.

hep-th↗

arXiv2024

Revisiting $α'$ corrections to heterotic two-charge black holes

We find solutions of the heterotic string effective action describing the first-order $α'$ corrections to two-charge black holes at finite temperature. Making explicit use of these solutions, we compute the corrections to the thermodynamic quantities: temperature, chemical potentials, mass, charges and entropy. We check that the first law of black hole mechanics is satisfied and that the thermodynamics agrees with the one extracted from the Euclidean on-shell action. Finally, we show that our results are in agreement with the corrections for the thermodynamics recently predicted by Chen, Maldacena and Witten.

hep-th↗

arXiv2023

Extremal stringy black holes in equilibrium at first order in $α'$

We compute the first-order $α'$ corrections to well-known families of heterotic multi-center black-hole solutions in five and four dimensions. The solutions can be either supersymmetric or non-supersymmetric, depending on the relative sign between two of the black-hole charges. For both cases, we find that the equilibrium of forces persists after including the $α'$ corrections, as the existence of multi-center solutions free of unphysical singularities shows. We analyze the possibility of black-hole fragmentation.

hep-th↗

arXiv2023

Boundary terms and conserved charges in higher-derivative gauged supergravity

We address some issues in higher-derivative gauged supergravity with Chern-Simons terms, focusing on the five-dimensional case. We discuss the variational problem with Dirichlet boundary conditions as well as holographic renormalization in asymptotically locally AdS spacetimes, and derive the corresponding boundary terms. We then employ Wald's formalism in order to define conserved charges associated to local symmetries (diffeomorphisms and U(1) gauge transformations), taking into account the effect of generic gauge Chern-Simons terms. We prove that the first law of black hole mechanics and the quantum statistical relation hold in this setup. Chern-Simons terms also lead us to distinguish between Noether charges and Page (or Komar) charges which satisfy the Gauss law. We make use of the latter to compute corrections to the angular momentum and electric charge of the supersymmetric black hole in AdS$_5$ from its corrected near-horizon geometry. This also allows us to derive the microcanonical form of the entropy as a function of the conserved charges relying entirely on the near-horizon geometry. Finally, we comment on four-derivative gauged supergravity in four dimensions, showing that field redefinitions permit to simplify the action at linear order in the corrections, so that the equations of motion are those of the two-derivative theory.

hep-th↗

arXiv2023

Black Hole Multipoles in Higher-Derivative Gravity

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 $S_{2n}\neq 0$ and $M_{2n+1}\neq 0$ 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.

gr-qc↗

arXiv2022

Corrections to AdS$_5$ Black Hole Thermodynamics from Higher-Derivative Supergravity

We study four-derivative corrections to five-dimensional minimal gauged supergravity. We evaluate the on-shell action of the AdS$_5$ black hole solution with two independent angular momenta and one electric charge at linear order in the corrections. After imposing supersymmetry, we are able to recast the action in terms of the supersymmetric chemical potentials and match the result obtained from the dual superconformal index on the second sheet. To achieve this, we exploit the freedom to implement field redefinitions to recast the action in a much simpler form, as well as the fact that the two-derivative solution is enough. We use the on-shell action to determine the corrections to the black hole thermodynamics, including those to the entropy and the charges. We then specialize to the supersymmetric and extremal case and find a simple expression for the microcanonical entropy. In particular, for the case with one independent angular momentum the corrections are entirely encoded in the dual superconformal anomaly coefficients. We corroborate this result for the entropy by constructing the corrected near-horizon solution and applying Wald's formula.

hep-th↗

arXiv2022

Non-extremal, $α'$-corrected black holes in 5-dimensional Heterotic Superstring Theory

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.

hep-th↗

arXiv2021

Non-supersymmetric black holes with $α'$ corrections

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 $\mathcal{O}(α')$ 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.

hep-th↗

arXiv2021

String gravity in $D=4$

We revisit the four-dimensional theory of gravity that arises from string theory with higher-derivative corrections. By compactifying and truncating the ten-dimensional effective action of heterotic string theory at first order in $α'$, and carefully dealing with field redefinitions, we show that the four-dimensional theory takes the form of an axidilaton model where the scalars couple to the Gauss-Bonnet and Pontryagin densities. Thus, the actual string gravity is a generalization of the well-studied Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons models. Using this action we compute the stringy corrections to the Kerr geometry and we obtain, for the first time, the corrections to the entropy of the Kerr black hole at order $α'^2$. We check that the first law of black hole mechanics is satisfied and discuss several properties of the solution. Our results suggest that there exist black hole solutions with $J>M^2$ and therefore the extremal ratio $J/M^2$ must be modified positively.

hep-th↗

arXiv2021

On small black holes, KK monopoles and solitonic 5-branes

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 $d>5$, which we interpret as reflecting the necessity of having a 5-brane wrapping the compact space.

hep-th↗

arXiv2021

Higher-derivative corrections to small black rings

We compute the first-order $α'$-corrections to a general family of supersymmetric heterotic backgrounds which describes a rotating superposition of a fundamental string and a momentum wave. We focus on a particular solution within this family that gives raise, upon dimensional reduction to five dimensions, to a black ring with two charges and one dipole that has a singular horizon with vanishing area in the supergravity approximation, better known as small black ring. We show that the singularity at the horizon persists even after the first-order $α'$-corrections have been taken into account. This implies, contrary to what has been argued in the literature, that higher-derivative corrections do not resolve the singular horizon of the 5-dimensional small black ring, at least at first-order in $α'$.

hep-th↗