arXiv subjects

Ignacio J. Araya

Publications and source records attributed to Ignacio J. Araya.

At least 19 recordsLinked to original sources

arXiv2026

Conformal Renormalisation of 8D Einstein Gravity

We show that Holographic Renormalisation (HR) in eight dimensions is encoded in the unique conformal gravity theory that admits an Einstein sector with constant negative curvature. We explicitly relate HR to Topological Regularisation (TR), where the latter prescribes to add the Euler term to the Einstein-Hilbert Lagrangian density, with a precise coefficient so as to ensure that the resulting density is polynomial in the anti de Sitter (AdS) curvature. The polynomial is still asymptotically divergent. We find that the aforementioned, unique conformal gravity action in 8D, reproduces the polynomial, together with extra boundary terms that cancel the divergent terms in the action. We conjecture that, in arbitrary even dimension, HR is equivalent to conformally completing the Einstein-Hilbert action with negative cosmological constant, plus the Euler term with fixed coupling prescribed by TR.

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arXiv2026

Universality of pseudoentropy for deformed spheres in dS/CFT

We determine the universal part of pseudoentropy for small shape deformations of spherical entangling surfaces in the context of de Sitter/conformal field theory (dS/CFT) correspondence. The leading correction at quadratic order in the deformation parameter is controlled by the analytic continuation of the coefficient of the two-point stress-energy tensor correlator in AdS/CFT (i.e., $\left. L_{*} \right|_{\text{AdS}}\rightarrow -i \left. L_{*} \right|_{\text{dS}}$), thereby establishing the sphere as a local extremum. The same structure holds in higher-curvature theories, as we check explicitly for quadratic curvature gravity, suggesting a universal behavior across non-unitary holographic CFTs. Our findings extend the Mezei formula to the dS/CFT setting and indicate that the shape dependence of pseudoentropy in dS holography resembles that of entanglement entropy in AdS space. Thus, we conjecture this coefficient to be the $C_T$ for the non-unitary CFT dual.

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arXiv2026

Renormalized pseudoentropy in dS/CFT

We study holographic pseudoentropy for subregions in non-unitary Euclidean conformal field theories (CFTs) within the framework of the de Sitter/conformal field theory (dS/CFT) correspondence. Pseudoentropy, defined as the von Neumann entropy of a transition matrix, is computed holographically from codimension-two extremal surfaces in dS space and is divergent due to the asymptotic bulk volume at future infinity. We show that a finite and regulator-independent definition follows from the on-shell action of conformal gravity in four and six dimensions, implemented through the replica construction. We illustrate the formalism for spherical entangling surfaces and small shape deformations thereof. The renormalized pseudoentropy isolates the universal contribution, which for a spherical entangling surface is proportional to the complex-valued central charge $a^\star$ of the non-unitary CFT. On an equal footing, for infinitesimal deformations away from the sphere, we recover, at quadratic order in the deformation parameter, an analytic continuation of the Mezei-like formula in its anti-de Sitter counterpart.

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arXiv2026

Bulkcone Singularities and Complex Geodesics

Thermal correlators in holographic CFTs on a sphere exhibit bulk-cone singularities at points connected by null geodesics in the bulk. The operator product expansion analysis of the stress-tensor sector of the correlator shows that there are analogous singularities at spacelike separation for thermal CFTs on a plane. We show that these are associated with complex null geodesics. There is a phase transition between the real and complex spacelike geodesics underpinning this picture. We also provide a phase-shift calculation of the position of these generalised bulk-cone singularities.

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arXiv2026

Renormalization of Einstein-Gauss-Bonnet AdS gravity

The asymptotic analysis for the metric of a generic solution of Einstein-Gauss-Bonnet AdS theory is provided by solving the field equations in the Fefferman-Graham frame. Using standard holographic renormalization, the counterterms that render the action finite are found up to seven spacetime dimensions. In the case of 6D, an equivalent formulation that permits a fully covariant determination of the counterterms is introduced, based on the finiteness of conformal invariants. It is shown that both schemes end up in the same holographic stress-energy tensor. Physical properties of six-dimensional topological Boulware-Deser black holes in Einstein-Gauss-Bonnet-AdS$_6$ gravity, whose boundary has nontrivial conformal features, are worked out in detail. Employing both renormalization prescriptions, finite asymptotic charges are found, and the correct black hole thermodynamics is recovered.

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arXiv2024

Gravitational to Coulomb force ratio and the origin of the Cosmic magnetic field

The origin of the seeds of galactic magnetic fields is a subject that remains under debate. Here we will explore a simple source based on tiny charge asymmetries in slowly rotating protogalaxies. We use current knowledge of galaxy formation and evolution to estimate that a charge imbalance of $1$ every $\sim 10^{38\pm 5}$ charge carriers in slowly rotating protogalaxies can provide adequate seeds for the galactic dynamos. Interestingly, this is of the same order than the ratio of gravitational to Coulomb forces between the elementary plasma constituents. Motivated by this fact, we study different mechanisms for generating such charge imbalances from a direct interplay of gravitational and Coulomb forces, namely the possibility that these are of primordial origin, that stellar or primordial black holes redistribute charge in protogalaxies, or that the imbalance is sourced by gravity as the galaxy forms in quasi-hydrostatic equilibrium. Our results show that primordial asymmetries drop to small values by the onset of galaxy formation, with an amplitude that is similar to the possible charge asymmetries that could be produced by black holes. Although these charge asymmetries can have values within the range of interest, they are much smaller than the gravitationally induced one in hydrostatic equilibrium conditions. The latter lies in the upper range of the required charge imbalance.

astro-ph.CO↗

arXiv2024

Higher-dimensional Willmore energy as holographic entanglement entropy

The vacuum entanglement entropy of a general conformal field theory (CFT) in $d=5$ spacetime dimensions contains a universal term, $F(A)$, which has a complicated and non-local dependence on the geometric details of the region $A$ and the theory. Analogously to the previously known $d=3$ case, we prove that for CFTs in $d=5$ which are holographically dual to Einstein gravity, $F(A)$ is equal to a four-dimensional version of the ``Willmore energy'' associated to a doubled and closed version of the Ryu-Takayanagi (RT) surface of $A$ embedded in $\mathbb{R}^5$. This generalized Willmore energy is shown to arise from a conformal-invariant codimension-two functional obtained by evaluating six-dimensional Conformal Gravity on the conically-singular orbifold of the replica trick. The new functional involves an integral over the doubled RT surface of a linear combination of three quartic terms in extrinsic curvatures and is free from ultraviolet divergences by construction. We verify explicitly the validity of our new formula for various entangling regions and argue that, as opposed to the $d=3$ case, $F(A)$ is not globally minimized by a round ball $A=\mathbb{B}^4$. Rather, $F(A)$ can take arbitrarily positive and negative values as a function of $A$. Hence, we conclude that the round ball is not a global minimizer of $F(A)$ for general five-dimensional CFTs.

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arXiv2024

Extrinsic Holographic Renormalization for a Scalar Field

In the context of the holographic correspondence, we introduce a purely extrinsic renormalization prescription, exemplified with the case of a minimally-coupled scalar field in AdS space. The counterterms depend only on the field and its radial derivatives. This would seem to conflict with the Dirichlet variational principle, but we show that consistency follows from the fact that the asymptotic structure of asymptotically locally AdS spacetimes requires not only the leading, but also all of the subleading non-normalizable modes to be fixed as a boundary condition. Crucially, as seen from a path integral definition of the bulk partition function involved in the standard GKPW formula, this condition is valid away from the saddle. We find that the extrinsic renormalization prescription is maximally efficient when the scalar field is massless, which is suggestive of a connection with the Kounterterm method for renormalization of pure gravity.

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arXiv2024

The electric charge of black holes within galaxies

We present improved estimates of the electric charge that black holes could hold when these are embedded in the ionised plasma within galaxies. We have implemented the spontaneous emission of charges of opposite sign to that of the black hole via athermal Hawking evaporation, including its dependence on black hole spin, and we have estimated the equilibrium charge that arises as this charge loss is balanced by the continuous accretion of charges from the surrounding plasma. The resulting charge can be several orders of magnitude lower than previously estimated upper limits, but it can surpass the pair production limit noted by Gibbons (1974) by a margin that increases with the amplitude of the black hole spin and the density of the plasma. We also implement a calculation for the net charge of galaxies due to their stellar black holes and to primordial black holes in the case these make up a fraction of the dark matter. We find that these charges lie within the range that would produce adequate magnetic field seeds at the onset of galaxy formation.

astro-ph.CO↗

arXiv2023

Weyl-invariant scalar-tensor gravities from purely metric theories

We describe a method to generate scalar-tensor theories with Weyl symmetry, starting from arbitrary purely metric higher derivative gravity theories. The method consists in the definition of a conformally-invariant metric $\hat{g}_{μν}$, that is a rank (0,2)-tensor constructed out of the metric tensor and the scalar field. This new object has zero conformal weight and is given by $ϕ^{2/Δ}g_{μν}$, where ($-Δ$) is the conformal dimension of the scalar. As $g_{μν}$ has conformal dimension of 2, the resulting tensor is trivially a conformal invariant. Then, the generated scalar-tensor theory, which we call the Weyl uplift of the original purely metric theory, is obtained by replacing the metric by $\hat{g}_{μν}$ in the action that defines the original theory. This prescription allowed us to define the Weyl uplift of theories with terms of higher order in the Riemannian curvature. Furthermore, the prescription for scalar-tensor theories coming from terms that have explicit covariant derivatives in the Lagrangian is discussed. The same mechanism can also be used for the derivation of the equations of motion of the scalar-tensor theory from the original field equations in the Einstein frame. Applying this method of Weyl uplift allowed us to reproduce the known result for the conformal scalar coupling to Lovelock gravity and to derive that of Einsteinian cubic gravity. Finally, we show that the renormalization of the theory given by the conformal scalar coupling to Einstein-Anti-de Sitter gravity originates from the Weyl uplift of the original renormalized theory, which is relevant in the framework of conformal renormalization.

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arXiv2023

Conformal Renormalization of topological black holes in AdS$_6$

We present a streamlined proof that any Einstein-AdS space is a solution of the Lu, Pang and Pope conformal gravity theory in six dimensions. The reduction of conformal gravity into Einstein theory manifestly shows that the action of the latter can be written as the Einstein-Hilbert term plus the Euler topological density and an additional contribution that depends on the Laplacian of the bulk Weyl tensor squared. The prescription for obtaining this form of the action by embedding the Einstein theory into a Weyl-invariant purely metric theory, was dubbed Conformal Renormalization and its resulting action was shown to be equivalent to the one obtained by holographic renormalization. As a non-trivial application of the method, we compute the Noether-Wald charges and thermodynamic quantities for topological black hole solutions with generic transverse section in Einstein-AdS$_6$ theory.

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arXiv2023

Conformal renormalization of scalar-tensor theories

We study a conformally coupled scalar-tensor theory with a quartic potential possessing local conformal symmetry up to a boundary term. We show that requiring the restoration of the full local conformal symmetry fixes the counterterms that render the on-shell action finite. The building block of the resulting action is a conformally covariant tensor which is constructed out of the metric and the scalar field and it has the same conformal weight as the Weyl tensor. This allows us to obtain the counterterms for the scalar-tensor sector in a closed form. The finiteness of the conformally complete version of the action is suggestive on the validity of the Conformal Renormalization prescription. We extend this theory by adding the Conformal Gravity action and also the Einstein-AdS action written in McDowell-Mansouri form. Even though the latter breaks the conformal symmetry, we find that the action is still renormalized provided a suitable falloff of the scalar field when considering asymptotically locally anti-de Sitter solutions. Black hole solutions in these theories are studied, for which the Hawking temperature and the partition function to first order in the saddle-point approximation are calculated, providing a concrete example of this renormalization scheme.

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arXiv2023

Dark matter from primordial black holes would hold charge

We explore the possibility that primordial black holes (PBHs) contain electric charge down to the present day. We find that PBHs should hold a non-zero net charge at their formation, due to either Poisson fluctuations at horizon crossing or high-energy particle collisions. Although initial charge configurations are subject to fast discharge processes through particle accretion or quantum particle emission, we show that maximally rotating PBHs could produce magnetic fields able to shield them from discharge. Moreover, given that electrons are the lightest and fastest charge carriers, we show that the plasma within virialised dark matter haloes can endow PBHs with net negative charge. We report charge-to-mass ratios between $10^{-31}\,C/\mbox{kg}$ and $10^{-15}\,C/\mbox{kg}$ for PBHs within the mass windows that allow them to constitute the entirety of the dark matter in the Universe.

astro-ph.CO↗

arXiv2023

Extended primordial black hole mass functions with a spike

We introduce a modification of the Press-Schechter formalism aimed to derive general mass functions for primordial black holes (PBHs). In this case, we start from primordial power spectra (PPS) which include a monochromatic spike, typical of ultra slow-roll inflation models. We consider the PBH formation as being associated to the amplitude of the spike on top of the linear energy density fluctuations, coming from a PPS with a blue index. By modelling the spike with a log-normal function, we study the properties of the resulting mass function spikes, and compare these to the underlying extended mass distributions. When the spike is at PBH masses which are much lower than the exponential cutoff of the extended distribution, very little mass density is held by the PBHs within the spike, and it is not ideal to apply the Press-Schechter formalism in this case as the resulting characteristic overdensity is too different from the threshold for collapse. It is more appropriate to do so when the spike mass is similar to, or larger than the cutoff mass. Additionally, it can hold a similar mass density as the extended part. Such particular mass functions also contain large numbers of small PBHs, especially if stable PBH relics are considered, and they can provide $\sim 1000M_\odot$ seeds for the supermassive black holes at the centres of present-day galaxies. The constraints on the fraction of dark matter in PBHs for monochromatic mass functions are somewhat relaxed when there is an additional underlying extended distribution of masses.

astro-ph.CO↗

arXiv2022

CFT correlators from shape deformations in Cubic Curvature Gravity

We find a covariant expression for the universal part of the holographic entanglement entropy which is valid for CFTs dual to generic higher curvature gravities in up to five bulk dimensions. We use this functional to compute universal coefficients of stress-tensor correlators in three-dimensional CFTs dual to Cubic Curvature Gravity. Using gauge/gravity duality, we work out an expression for the entanglement entropy of deformed entangling regions and read the coefficients from the power expansion of the entropy in the deformation parameter. In particular, we obtain the $t_4$ coefficient of the 3-point function and exhibit a difference between the results obtained using the entanglement entropy functional for minimal and non-minimal splittings. We compare the obtained expressions for $t_{4}$ derived considering both splittings with results obtained through other holographic methods which are splitting-independent. We find agreement with the result obtained from the non-minimal splitting, whereas the result derived from the minimal splitting is inconsistent and it is therefore ruled out.

hep-th↗

arXiv2022

Energy functionals from Conformal Gravity

We provide a new derivation of the Hawking mass and Willmore energy functionals for asymptotically AdS spacetimes, by embedding Einstein-AdS gravity in Conformal Gravity. By construction, the evaluation of the four-dimensional Conformal Gravity action in a manifold with a conical defect produces a codimension-2 conformal invariant functional $L_Σ$. The energy functionals are then particular cases of $L_Σ$ for Einstein-AdS and pure AdS ambient spaces, respectively. The bulk action is finite for AdS asymptotics and both Hawking mass and Willmore energy are finite as well. The result suggests a generic relation between conformal invariance and renormalization, where the codimension-2 properties are inherited from the bulk gravity action.

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arXiv2021

Renormalized holographic entanglement entropy for Quadratic Curvature Gravity

We derive a covariant expression for the renormalized holographic entanglement entropy for Conformal Field Theories (CFTs) dual to Quadratic Curvature Gravity in arbitrary dimensions. This expression is written as the sum of the bare entanglement entropy functional obtained using standard conical defect techniques, and a counterterm defined at the boundary of the extremal surface of the functional. The latter corresponds to the cod-2 self-replicating part of the extrinsic counterterms when evaluated on the replica orbifold. This renormalization method isolates the universal terms of the holographic entanglement entropy functional. We use it to compute the standard C-function candidate for CFTs of arbitrary dimension, and the type-B anomaly coefficient c for 4-dimensional CFTs.

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arXiv2021

Press-Schechter primordial black hole mass functions and their observational constraints

We present a modification of the Press-Schechter (PS) formalism to derive general mass functions for primordial black holes (PBHs), considering their formation as being associated to the amplitude of linear energy density fluctuations. To accommodate a wide range of physical relations between the linear and non-linear conditions for collapse, we introduce an additional parameter to the PS mechanism, and that the collapse occurs at either a given cosmic time, or as fluctuations enter the horizon. We study the case where fluctuations obey Gaussian statistics and follow a primordial power spectrum of broken power-law form with a blue spectral index for small scales. We use the observed abundance of super-massive black holes (SMBH) to constrain the extended mass functions taking into account dynamical friction. We further constrain the modified PS by developing a method for converting existing constraints on the PBH mass fraction, derived assuming monochromatic mass distributions for PBHs, into constraints applicable for extended PBH mass functions. We find that when considering well established monochromatic constraints there are regions in parameter space where all the dark matter can be made of PBHs. Of special interest is the region for the characteristic mass of the distribution ~10^2 M_Sun, for a wide range of blue spectral indices in the scenario where PBHs form as they enter the horizon, where the linear threshold for collapse is of the order of the typical overdensities, as this is close to the black hole masses detected by LIGO which are difficult to explain by stellar collapse.

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