Non-equilibrium thermodynamics near the horizon and holography

A bstract We explore asymptotically locally anti-de Sitter spacetimes exhibiting gravitational radiative behavior, employing null gauges that allow for a well-defined flat limit. The radiative content in the bulk is captured by the boundary Cotton and stress tensor, which we collect into a radiative vector. We reinterpret this vector holographically in terms of fluid variables in the dual boundary theory. For algebraically special solutions, we uncover a close connection between bulk radiation and dissipative corrections in the boundary stress tensor, demonstrating a direct link between radiation and entropy production in the boundary fluid. This reveals a rich interplay between radiative dynamics in the bulk and out-of-equilibrium conformal physics at the boundary. We then investigate the flat limit of this correspondence in the context of flat-space holography. In this setting, we construct a Carrollian analogue of the radiative vector and introduce Celestial observables, such as energy detectors, which emerge naturally from the bulk’s radiative structure. Our analysis shows that bulk radiation sources the Carrollian viscous stress tensor and heat current, which encodes the Bondi news in this framework. We illustrate our results with explicit examples, including Robinson-Trautman spacetimes and accelerating black holes.

The electromagnetic and gravitational quasinormal spectra of (3+1)-dimensional plane-symmetric anti-de Sitter black holes are analyzed in the context of the AdS/CFT correspondence. According to such a correspondence, the electromagnetic and gravitational quasinormal frequencies of these black holes are associated respectively to the poles of retarded correlation functions of R-symmetry currents and stress-energy tensor in the holographically dual conformal field theory: the (2+1)-dimensional = 8 super-Yang-Mills theory. The connection between AdS black holes and the corresponding field theory is used to unambiguously fix the boundary conditions that enter the proper definition of quasinormal modes. Such a procedure also helps one to decide, among the various different possibilities, what are the appropriate gauge-invariant quantities one should use in order to correctly describe the electromagnetic and gravitational blackhole perturbations. These choices imply in different dispersion relations for the quasinormal modes when compared to some of the results in the literature. In particular, the long-distance, low-frequency limit of dispersion relations presents the characteristic hydrodynamic behavior of a conformal field theory with the presence of diffusion, shear, and sound wave modes. There is also a family of purely damped electromagnetic modes which tend to the bosonic Matsubara frequencies in the long-wavelength regime.

We derive an optical theorem for perturbative CFTs which computes the double discontinuity of conformal correlators from the single discontinuities of lower order correlators, in analogy with the optical theorem for flat space scattering amplitudes. The theorem takes a purely multiplicative form in the CFT impact parameter representation used to describe high-energy scattering in the dual AdS theory. We use this result to study four-point correlation functions that are dominated in the Regge limit by the exchange of the graviton Regge trajectory (Pomeron) in the dual theory. At one-loop the scattering is dominated by double Pomeron exchange and receives contributions from tidal excitations of the scattering states which are efficiently described by an AdS vertex function, in close analogy with the known Regge limit result for one-loop string scattering in flat space at finite string tension. We compare the flat space limit of the conformal correlator to the flat space results and thus derive constraints on the one-loop vertex function for type IIB strings in AdS and also on general spinning tree level type IIB amplitudes in AdS.

We study meson thermalization in a strongly coupled plasma of quarks and gluons using AdS/CFT duality technique. Four dimensional large-Nc QCD is considered as a theory governing this quark–gluon plasma (QGP) and D4/D6-brane model is chosen to be its holographic dual theory. In order to investigate meson thermalization, we consider a time-dependent change of baryon number chemical potential. Thermalization in gauge theory side corresponds to horizon formation on the probe flavor brane in the gravity side. The gravitational dual theory is compactified on a circle that the inverse of its radius is proportional to energy scale of dual gauge theory. It is seen that increase of this energy scale results in thermalization time dilation. In addition we study the effect of magnetic field on meson thermalization. It will be seen that magnetic field also prolongs thermalization process by making mesons more stable.

Using the counterterm subtraction technique we calculatehe stress-energy tensor, action, and other physical quantities for Kerr-AdS black holes in various dimensions. For Kerr-AdS_5 with both rotation parameters non-zero, we demonstrate that stress-energy tensor, in the zero mass parameter limit, is equal to the stress tensor of the weakly coupled four dimensional dual field theory. As a result, the total energy of the generalKerr-AdS_5 black hole at zero mass parameter, exactly matches the Casimir energy of the dual field theory. We show that at high temperature, the general Kerr-AdS_5 and perturbative field theory stress-energy tensors are equal, up to the usual factor of 3/4. We also use the counterterm technique to calculate the stress tensors and actions for Kerr-AdS_6, and Kerr-AdS_7 black holes, with one rotation parameter, and we display the results. We discuss the conformal anomalies of the field theories dual to the Kerr-AdS_5 and Kerr-AdS_7 spacetimes. In these two field theories, we show that the rotation parameters break conformal invariance but not scale invariance, a novel result for a non-trivial field theory. For Kerr-AdS_7 the conformal anomalies calculated on the gravity side and the dual (0,2) tensor multiplet theory are equal up to 4/7 factor. We expect that the Casimir energy of the free field theory is the same as the energy of the Kerr-AdS_7 black hole (with zero mass parameter), up to that factor.

Following the membrane paradigm, we explore the effect of the gravitational $\Theta$-term on the behavior of the stretched horizon of a black hole in (3+1)-dimensions. We reformulate the membrane paradigm from a quantum path-integral point of view where we interpret the macroscopic properties of the horizon as effects of integrating out the region inside the horizon. The gravitational $\Theta$-term is a total derivative, however, using our framework we show that this term affects the transport properties of the horizon. In particular, the horizon acquires a third order parity violating, dimensionless transport coefficient which affects the way localized perturbations scramble on the horizon. Then we consider a large-N gauge theory in (2+1)-dimensions which is dual to an asymptotically AdS background in (3+1)-dimensional spacetime to show that the $\Theta$-term induces a non-trivial contact term in the energy-momentum tensor of the dual theory. As a consequence, the dual gauge theory in the presence of the $\Theta$-term acquires the same third order parity violating transport coefficient.

It has recently been demonstrated that black hole dynamics in a large number of dimensions D reduces to the dynamics of a codimension one membrane propagating in flat space. In this paper we define a stress tensor and charge current on this membrane and explicitly determine these currents at low orders in the expansion in frac{1}{D} . We demonstrate that dynamical membrane equations of motion derived in earlier work are simply conservation equations for our stress tensor and charge current. Through the paper we focus on solutions of the membrane equations which vary on a time scale of order unity. Even though the charge current and stress tensor are not parametrically small in such solutions, we show that the radiation sourced by the corresponding membrane currents is generically of order frac{1}{D^D} . In this regime it follows that the ‘near horizon’ membrane degrees of freedom are decoupled from asymptotic flat space at every perturbative order in the frac{1}{D} expansion. We also define an entropy current on the membrane and use the Hawking area theorem to demonstrate that the divergence of the entropy current is point wise non negative. We view this result as a local form of the second law of thermodynamics for membrane motion.

The horizon of a static black hole in Anti-deSitter space can be spherical, planar, or hyperbolic. The microscopic dynamics of the first two classes of black holes have been extensively discussed recently within the context of the AdS/CFT correspondence. We argue that hyperbolic black holes introduce new and fruitful features in this respect, allowing for more detailed comparisons between the weak and strong coupling regimes. In particular, by focussing on the stress tensor and entropy of some particular states, we identify unexpected increases in the entropy of Super-Yang-Mills theory at strong coupling that are not accompanied by increases in the energy. We describe a highly degenerate state at zero temperature and zero energy density. We also find that the entanglement entropy across a Rindler horizon in exact AdS_5 is larger than might have been expected from the dual SYM theory. Besides, we show that hyperbolic black holes can be described as thermal Rindler states of the dual conformal field theory in flat space.

We study the hydrodynamic excitations of backreacted holographic superfluids by computing the full set of quasinormal modes (QNMs) at finite momentum and matching them to the existing hydrodynamic theory of superfluids. Additionally, we analyze the behavior of the low-energy excitations in real frequency and complex momentum, going beyond the standard QNM picture. Finally, we carry out a novel type of study of the model by computing the support of the hydrodynamic modes across the phase diagram. We achieve this by determining the support of the corresponding QNMs on the different operators in the dual theory, both in complex frequency and complex momentum space. From the support, we are able to reconstruct the hydrodynamic dispersion relations using the hydrodynamic constitutive relations. Our analysis rules out a role-reversal phenomenon between first and second sound in this model, contrary to results obtained in a weakly coupled field theory framework.

One of the main predictions of general relativity is the existence of black holes featuring a horizon beyond which nothing can escape. Gravitational waves from the remnants of compact binary coalescences have the potential to probe new physics close to the black hole horizons. This prospect is of particular interest given several quantum-gravity models that predict the presence of horizonless and singularity-free compact objects. The membrane paradigm is a generic framework that allows one to parametrize the interior of compact objects in terms of the properties of a fictitious fluid located at the object’s radius. It has been used to derive the quasinormal mode spectrum of static horizonless compact objects. Extending the membrane paradigm to rotating objects is crucial to constrain the properties of the spinning merger remnants. In this work, we extend the membrane paradigm to linear order in spin and use it to analyze the relationships between the quasinormal modes, the object’s reflectivity, and the membrane parameters. We find a breaking of isospectrality between axial and polar modes when the object is partially reflecting or the compactness differs from the black hole case. We also find that in reflective ultracompact objects some of the modes tend toward instability as the spin increases. Finally, we show that the spin enhances the deviations from the black-hole quasinormal mode spectrum as the compactness decreases. This implies that spinning horizonless compact objects may be more easily differentiated than nonspinning ones in the prompt ringdown. Published by the American Physical Society 2024

Teukolsky equations for $|s|=2$ provide efficient ways to solve for curvature perturbations around Kerr black holes. Imposing regularity conditions on these perturbations on the future (past) horizon corresponds to imposing an ingoing (outgoing) wave boundary condition. For exotic compact objects (ECOs) with external Kerr spacetime, however, it is not yet clear how to physically impose boundary conditions for curvature perturbations on their boundaries. We address this problem using the membrane paradigm, by considering a family of zero-angular-momentum fiducial observers (FIDOs) that float right above the horizon of a linearly perturbed Kerr black hole. From the reference frame of these observers, the ECO will experience tidal perturbations due to ingoing gravitational waves, respond to these waves, and generate outgoing waves. As it also turns out, if both ingoing and outgoing waves exist near the horizon, the Newman-Penrose (NP) quantity ${\ensuremath{\psi}}_{0}$ will be numerically dominated by the ingoing wave, while the NP quantity ${\ensuremath{\psi}}_{4}$ will be dominated by the outgoing wave---even though both quantities contain full information regarding the wave field. In this way, we obtain the ECO boundary condition in the form of a relation between ${\ensuremath{\psi}}_{0}$ and the complex conjugate of ${\ensuremath{\psi}}_{4}$, in a way that is determined by the ECO's tidal response in the FIDO frame. We explore several ways to modify gravitational-wave dispersion in the FIDO frame and deduce the corresponding ECO boundary condition for Teukolsky functions. Using the Starobinsky-Teukolsky identity, we subsequently obtain the boundary condition for ${\ensuremath{\psi}}_{4}$ alone, as well as for the Sasaki-Nakamura and Detweiler functions. As it also turns out, the reflection of spinning ECOs will generically mix between different $\ensuremath{\ell}$ components of the perturbation fields, and it will be different for perturbations with different parities. It is straightforward to apply our boundary condition to computing gravitational-wave echoes from spinning ECOs, and to solve for the spinning ECOs' quasinormal modes.

Comparing dualities and gauge symmetries

Quasinormal frequencies of electromagnetic and gravitational perturbations in asymptotically anti-de Sitter spacetime can be identified with poles of the corresponding real-time Green's functions in a holographically dual finite temperature field theory. The quasinormal modes are defined for gauge-invariant quantities which obey an incoming-wave boundary condition at the horizon and a Dirichlet condition at the boundary. As an application, we explicitly find poles of retarded correlation functions of $R$-symmetry currents and the energy-momentum tensor in strongly coupled finite temperature $\mathcal{N}=4$ supersymmetric $SU({N}_{c})$ Yang-Mills theory in the limit of large ${N}_{c}$.

Conservation laws in de Sitter space from action principles in five-space

We consider a simple class of holographic massive gravity models for which the dual field theories break translational invariance spontaneously. We study, in detail, the longitudinal sector of the quasi-normal modes at zero charge density. We identify three hydrodynamic modes in this sector: a pair of sound modes and one diffusion mode. We numerically compute the dispersion relations of the hydrodynamic modes. The obtained speed and the attenuation of the sound modes are in agreement with the hydrodynamic predictions. On the contrary, we surprisingly find disagreement in the case of the diffusive mode; its diffusion constant extracted from the quasi-normal mode data does not agree with the expectations from hydrodynamics. We confirm our numerical results using ana- lytic tools in the decoupling limit and we comment on some possible reasons behind the disagreement. Finally, we extend the analysis of the collective longitudinal modes beyond the hydrodynamic limit by displaying the dynamics of the higher quasi-normal modes at large frequencies and momenta.