arXiv subjects

Christiana Pantelidou

Publications and source records attributed to Christiana Pantelidou.

At least 19 recordsLinked to original sources

arXiv2026

Turbulent gravitational wakes

We construct turbulent gravitational wakes in asymptotically AdS$_4$ spacetimes by solving the full non-linear Einstein equations in the characteristic formulation. Specifically, we show that a localized boundary deformation acting on a boosted black brane generates a wake whose boundary dynamics exhibit the formation of coherent vortical structures that are advected downstream by the background flow. Analysing a wake propagating along the x direction, we show that it displays the characteristic self-similar scaling of classical turbulent wakes. We then identify the geometric imprint of the wake on the horizon area density, the traceless horizon extrinsic curvature, and bulk metric perturbations, finding coherent structures that extend from the asymptotic boundary to the horizon. These results provide the first study of turbulent gravitational wakes in four-dimensional asymptotically AdS spacetimes.

hep-th↗

arXiv2026

Bilinear products and the orthogonality of quasinormal modes on hyperboloidal foliations

We explore the properties of bilinear products for black-hole quasinormal modes (QNMs) formulated on hyperboloidal foliations. We find that, although QNM solutions are smooth and finite on future-directed hyperboloids, the integrand of the bilinear form with respect to which the modes are orthogonal is still divergent. This is a result of the reflection (equivalently, CPT) transformation required in the definition of the products, which modifies the behaviour of the integrand at the boundaries. We present several regularisation procedures that yield a finite and well-defined bilinear form. In addition, we examine an alternative definition of the bilinear products that incorporates flux contributions, discussing its advantages and limitations. Finally, we define the QNM excitation factors and coefficients within the hyperboloidal framework in terms of the bilinear products, and compute them explicitly for a choice of mode numbers and constant initial data. For concreteness, we work with the QNMs associated to scalar perturbations of the Schwarzschild family of spacetimes.

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arXiv2025

Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism

Extreme mass-ratio inspirals are among the key sources of gravitational waves for the Laser Interferometer Space Antenna space-based gravitational-wave detector. Achieving sufficient accuracy in the gravitational-wave template for these binaries requires modeling the effects of the spin of the comparably light secondary compact object. In this work, we employ the solution of the Hamilton-Jacobi equations for the motion of spinning bodies in Kerr space-time for the first time to obtain general bound orbits. Specifically, we implement a new solver for the Mathisson-Papapetrou-Dixon equations of motion reduced to first-order form. Our approach provide novel semianalytical expressions for the spin corrections to the orbital motion and frequencies, valid for any choice of referential geodesics, and new analytic expressions for the constants of motion shifts. Then, using the Teukolsky formalism, we compute gravitational-wave energy and angular-momentum fluxes sourced by these orbits valid to linear order in secondary spin and provide waveform snapshots corresponding to the motion. The solver and the novel method we have developed substantially improve on previous studies in terms of speed and accuracy. Additionally, we include the full effect of a general precessing secondary spin in the waveform for the first time. As such, it provides a breakthrough building block for the modeling of waveforms of precessing compact binaries at large mass ratios.

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arXiv2025

Non-modal effects in black hole perturbation theory: Transient Superradiance

We study the non-modal stability of black hole spacetimes under linear perturbations. We show that large-amplitude growth can occur at finite time, despite asymptotic decay of linear perturbations. In the example presented, the physical mechanism is a transient form of superradiance, and is qualitatively similar to the transition to turbulence in Navier-Stokes shear flows. As part of the construction we provide a theorem for the positivity of QNM energies, and introduce a truncated-Hamiltonian approach to black hole pseudospectra which does not suffer from convergence issues.

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arXiv2025

Transients in black hole perturbation theory

Black hole quasinormal modes arise as eigenmodes of a non-normal Hamiltonian and consequently they do not obey orthogonality relations with respect to commonly used inner products, for example, the energy inner product. A direct consequence of this is the appearance of transient phenomena. This review summarises current developments on the topic, both in frequency- and time-domain. In particular, we discuss the appearance of i) transient plateaus: arbitrarily long-lived sums of quasinormal modes, corresponding to localised energy packets near the future horizon; ii) transient growth, with the latter either appearing in the vicinity of black hole phase transitions or in the context of higher-derivative Sobolev norms.

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arXiv2024

The pseudospectra of black holes in AdS

We study the stability of quasinormal modes (QNMs) in electrically charged black brane spacetimes that asymptote to AdS by means of the pseudospectrum. Methodologically, we adopt ingoing Eddington-Finkelstein coordinates to cast QNMs in terms of a generalised eigenvalue problem involving a non-selfadjoint operator; this simplifies the computation significantly in comparison with previous results in the literature. Our analysis reveals spectral instability for (neutral) scalar as well as gravitoelectric perturbations. This indicates that the equilibration process of perturbed black branes is sensitive to external perturbations. Particular attention is given on the hydrodynamic modes, which are found to be the least unstable. In contrast with computations in hyperboloidal coordinates, we find that the pseudospectral contour lines cross to the upper half plane. This indicates the existence of pseudo-resonances as well as the possibility of transient instabilities. We also investigate the asymptotic structure of pseudospectral contour levels and we find remarkable universality across all sectors, persistent in the extremal limit.

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arXiv2023

Black hole excited states from broken translations in Euclidean time

We prepare an excited finite temperature state in ${\cal N}=4$ SYM by means of a Euclidean path integral with a relevant deformation. The deformation explicitly breaks imaginary-time translations along the thermal circle whilst preserving its periodicity. We then study how the state relaxes to thermal equilibrium in real time. Computations are performed using real-time AdS/CFT, by constructing novel mixed-signature black holes in numerical relativity corresponding to Schwinger-Keldysh boundary conditions. These correspond to deformed cigar geometries in the Euclidean, glued to a pair of dynamical spacetimes in the Lorentzian. The maximal extension of the Lorentzian black hole exhibits a `causal shadow', a bulk region which is spacelike separated from both boundaries. We show that causal shadows are generic in path-integral prepared states where imaginary-time translations along the thermal circle are broken.

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arXiv2022

Thermal three-point functions from holographic Schwinger-Keldysh contours

We compute fully retarded scalar three-point functions of holographic CFTs at finite temperature using real-time holography. They describe the nonlinear response of a holographic medium under scalar forcing, and display single and higher-order poles associated to resonant QNM excitations. This involves computing the bulk-to-bulk propagator on a piecewise mixed-signature spacetime, the dual of the Schwinger-Keldysh contour. We show this construction is equivalent to imposing ingoing boundary conditions on a single copy of a black hole spacetime, similar to the case of the two-point function. We also compute retarded scalar correlators with stress-tensor insertions in general CFTs by solving Ward identities on the Schwinger-Keldysh contour.

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arXiv2022

Holographic Dissipation from the Symplectic Current

We develop analytic techniques to construct the leading dissipative terms in a derivative expansion of holographic fluids. Our basic ingredient is the Crnkovic-Witten symplectic current of classical gravity which we use to extract the dissipative transport coefficients of holographic fluids, assuming knowledge of the thermodynamics and the near horizon geometries of the bulk black hole geometries. We apply our techniques to non-conformal neutral fluids to reproduce previous results on the shear viscosity and generalise a known expression for the bulk viscosity.

hep-th↗

arXiv2022

Higgs/Amplitude Mode Dynamics From Holography

Second order phase transitions are universally driven by an order parameter which becomes trivial at the critical point. At the same time, collective excitations which involve the amplitude of the order parameter develop a gap which smoothly closes to zero at criticality. We develop analytical techniques to study this "Higgs" mode in holographic systems which undergo a continuous phase transition at finite temperature and chemical potential. This allows us to study the linear response of the system at energy scales of the order of the gap. We express the Green's functions of scalar operators in terms of thermodynamic quantities and a single transport coefficient which we fix in terms of black hole horizon data.

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arXiv2022

Gravitational quasinormal modes for Lifshitz black branes

We study the scalar and vector channels of gravitational quasinormal modes for Lifshitz black branes emerging in Einstein-Maxwell-Dilaton and Einstein-Proca theories in four and five dimensions, finding significant differences between the two models. In particular, rather surprisingly, in the Einstein-Maxwell-Dilaton model the dispersion relations for the shear and sound modes are given by $ω_{shear} \sim -i\,k^4$ and $ω_{sound}\sim-i \,k^2$, while in the Einstein-Proca model they take the more conventional form $ω_{shear} \sim -i\,k^2$ and $ω_{sound}\sim k$, the proportionality constants depend on the dynamical exponent and the appropriate factors of temperature. Through the holographic duality, this calculation provides information about the relaxation of the momentum and energy flux operators in a putative dual Lifshitz field theory. Comparing with the dispersion relations obtained directly by considering Lifshitz hydrodynamics suggest that the mass density of the equilibrium state in the Einstein-Maxwell-Dilaton model is infinite.

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arXiv2021

Dissipation in Holographic Superfluids

We study dissipation in holographic superfluids at finite temperature and zero chemical potential. The zero overlap with the heat current allows us to isolate the physics of the conserved current corresponding to the broken global $U(1)$. By using analytic techniques we write constitutive relations including the first non-trivial dissipative terms. The corresponding transport coefficients are determined in terms of thermodynamic quantities and the black hole horizon data. By analysing their behaviour close to the phase transition we show explicitly the breakdown of the hydrodynamic expansion. Finally, we study the pseudo-Goldstone mode that emerges upon introducing a perturbative symmetry breaking source and we determine its resonant frequency and decay rate.

hep-th↗

arXiv2021

Incoherent hydrodynamics of density waves in magnetic fields

We use holography to derive effective theories of fluctuations in spontaneously broken phases of systems with finite temperature, chemical potential, magnetic field and momentum relaxation in which the order parameters break translations. We analytically construct the hydrodynamic modes corresponding to the coupled thermoelectric and density wave fluctuations and all of them turn out to be purely diffusive for our system. Upon introducing pinning for the density waves, some of these modes acquire not only a gap, but also a finite resonance due to the magnetic field. Finally, we study the optical properties and perform numerical checks of our analytical results. A crucial byproduct of our analysis is the identification of the correct current which describes the transport of heat in our system.

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arXiv2021

Incoherent hydrodynamics and density waves

We consider thermal phases of holographic lattices at finite chemical potential in which a continuous internal bulk symmetry can be spontaneously broken. In the normal phase, translational symmetry is explicitly broken by the lattice and the only conserved quantities are related to time translations and the electric charge. The long wavelength excitations of the corresponding charge densities are described by incoherent hydrodynamics yielding two perturbative modes which are diffusive. In the broken phase an additional hydrodynamic degree of freedom couples to the local chemical potential and temperature and we write an effective theory describing the coupled system at leading order in a derivative expansion.

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arXiv2020

Quasinormal modes in charged fluids at complex momentum

We investigate the convergence of relativistic hydrodynamics in charged fluids, within the framework of holography. On the one hand, we consider the analyticity properties of the dispersion relations of the hydrodynamic modes on the complex frequency and momentum plane and on the other hand, we perform a perturbative expansion of the dispersion relations in small momenta to a very high order. We see that the locations of the branch points extracted using the first approach are in good quantitative agreement with the radius of convergence extracted perturbatively. We see that for different values of the charge, different types of pole collisions set the radius of convergence. The latter turns out to be finite in the neutral case for all hydrodynamic modes, while it goes to zero at extremality for the shear and sound modes. Furthermore, we also establish the phenomenon of pole-skipping for the Reissner-Nordstrom black hole, and we find that the value of the momentum for which this phenomenon occurs need not be within the radius of convergence of hydrodynamics.

hep-th↗

arXiv2020

Holographic Abrikosov Lattices

We study black hole solutions of $D=4$ Einstein-Maxwell theory coupled to a charged scalar field that are holographically dual to a $d=3$ conformal field theory with a non-vanishing chemical potential and constant magnetic field. We numerically construct black hole solutions that are dual to a superfluid phase with a periodic lattice of vortices. For the specific model we investigate, we find that the thermodynamically preferred configuration is given by a triangular lattice and moreover the vortices are associated with the lowest Landau level. We also construct black holes describing a lattice of vortices associated with the next to lowest Landau level and while theses are not thermodynamically preferred they exhibit some interesting features that could be realised for other holographic models.

hep-th↗

arXiv2019

Driven black holes: from Kolmogorov scaling to turbulent wakes

General relativity governs the nonlinear dynamics of spacetime, including black holes and their event horizons. We demonstrate that forced black hole horizons exhibit statistically steady turbulent spacetime dynamics consistent with Kolmogorov's theory of 1941. As a proof of principle we focus on black holes in asymptotically anti-de Sitter spacetimes in a large number of dimensions, where greater analytic control is gained. We also demonstrate that tidal deformations of the horizon induce turbulent dynamics. When set in motion relative to the horizon a deformation develops a turbulent spacetime wake, indicating that turbulent spacetime dynamics may play a role in binary mergers and other strong-field phenomena.

hep-th↗

arXiv2019

Hydrodynamics of broken global symmetries in the bulk

We consider holographic theories at finite temperature in which a continuous global symmetry in the bulk is spontaneously broken. We study the linear response of operators in a regime which is dual to time dependent, long wavelength deformations of solutions generated by the symmetry. By computing the boundary theory retarded Green's function we show the existence of a gapless mode with a diffusive dispersion relation. The diffusive character of the mode is compatible with the absence of a conserved charge from the field theory point of view. We give an analytic expression for the corresponding diffusion constant in terms of thermodynamic data and a new transport coefficient $σ_{b}$ which is fixed by the black hole horizon data. After adding a perturbative source on the boundary, we compute the resulting gap $δω_{g}$ as a simple function of $σ_{b}$ and of data of the thermal state.

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