Phuc H. Nguyen

Holographic entanglement entropy and the extended phase structure of STU black holes

A bstractWe study the extended thermodynamics, obtained by considering the cosmological constant as a thermodynamic variable, of STU black holes in 4-dimensions in the fixed charge ensemble. The associated phase structure is conjectured to be dual to an RG-flow on the space of field theories. We find that for some charge configurations the phase structure resembles that of a Van der Waals gas: the system exhibits a family of first order phase transitions ending in a second order phase transition at a critical temperature. We calculate the holographic entanglement entropy for several charge configurations and show that for the cases where the gravity background exhibits Van der Waals behavior, the entanglement entropy presents a transition at the same critical temperature. To further characterize the phase transition we calculate appropriate critical exponents and show that they coincide. Thus, the entanglement entropy successfully captures the information of the extended phase structure. Finally, we discuss the physical interpretation of the extended space in terms of the boundary QFT and construct various holographic heat engines dual to STU black holes.

Noether charge, black hole volume, and complexity

A bstractIn this paper, we study the physical significance of the thermodynamic volumes of AdS black holes using the Noether charge formalism of Iyer and Wald. After applying this formalism to study the extended thermodynamics of a few examples, we discuss how the extended thermodynamics interacts with the recent complexity = action proposal of Brown et al. (CA-duality). We, in particular, discover that their proposal for the late time rate of change of complexity has a nice decomposition in terms of thermodynamic quantities reminiscent of the Smarr relation. This decomposition strongly suggests a geometric, and via CA-duality holographic, interpretation for the thermodynamic volume of an AdS black hole. We go on to discuss the role of thermodynamics in complexity = action for a number of black hole solutions, and then point out the possibility of an alternate proposal, which we dub “complexity = volume 2.0”. In this alternate proposal the complexity would be thought of as the spacetime volume of the Wheeler-DeWitt patch. Finally, we provide evidence that, in certain cases, our proposal for complexity is consistent with the Lloyd bound whereas CA-duality is not.

An equal area law for holographic entanglement entropy of the AdS-RN black hole

A bstractThe Anti-de Sitter-Reissner-Nordström (AdS-RN) black hole in the canonical ensemble undergoes a phase transition similar to the liquid-gas phase transition, i.e. the isocharges on the entropy-temperature plane develop an unstable branch when the charge is smaller than a critical value. It was later discovered that the isocharges on the entanglement entropy -temperature plane also exhibit the same van der Waals-like structure, for spherical entangling regions. In this paper, we present numerical results which sharpen this similarity between entanglement entropy and black hole entropy, by showing that both of these entropies obey Maxwell’s equal area law to an accuracy of around 1%. Moreover, we checked this for a wide range of size of the spherical entangling region, and the equal area law holds independently of the size. We also checked the equal area law for AdS-RN in 4 and 5 dimensions, so the conclusion is not specific to a particular dimension. Finally, we repeated the same procedure for a similar, van der Waals-like transition of the dyonic black hole in AdS in a mixed ensemble (fixed electric potential and fixed magnetic charge), and showed that the equal area law is not valid in this case. Thus the equal area law for entanglement entropy seems to be specific to the AdS-RN background.

Analytical families of two-component anisotropic polytropes and their relativistic extensions

In this paper, we study a family of two-component anisotropic polytropes which model a wide range of spherically symmetric astrophysical systems such as early-type baryonic galaxies. This family is found to contain a large class of models such as the hypervirial family (which satisfy the virial theorem locally), the Plummer and Hernquist models and Navarro-Frenk-White (NFW)-like models. The potential--density pair for these models are derived, as well as their velocity dispersions and anisotropy parameters. The projected quantities are computed and found to reduce to analytical expressions in some cases. The first section of this paper presents an extension of the two-term anisotropic polytropes to encompass a very wide range of potential-density pairs. In the next section, we present the general relativistic extension of the potential-density pair, and calculate the stress-energy tensor, the relativistic anisotropy parameter, the velocity of circular orbits and the angular momentum. Remarkably, for the case of the hypervirial family, the relativistic pressure in the Newtonian limit and the relativistic anisotropy parameter are found to coincide with the corresponding Newtonian expressions. The weak, dominant and strong energy conditions are found to be satisfied only for a certain range of the free parameters. We show that the relativistic hypervirial family also has a finite total mass like its Newtonian counterpart. In the first appendix, a relativistic extension of a different hypervirial family of models is studied, and the relativistic anisotropy parameter is found to coincide with the Newtonian one. Finally, we present a family of models obtained from our distribution function that are similar to the Ossipkov-Merritt models; by computing their anisotropy parameters, we show that they model systems with isotropic cores and radially anisotropic exteriors.

Fluctuation and dissipation in de Sitter space

A bstractIn this paper we study some thermal properties of quantum field theories in de Sitter space by means of holographic techniques. We focus on the static patch of de Sitter and assume that the quantum fields are in the standard Bunch-Davies vacuum. More specifically, we follow the stochastic motion of a massive charged particle due to its interaction with Hawking radiation. The process is described in terms of the theory of Brownian motion in inhomogeneous media and its associated Langevin dynamics. At late times, we find that the particle undergoes a regime of slow diffusion and never reaches the horizon, in stark contrast to the usual random walk behavior at finite temperature. Nevertheless, the fluctuation-dissipation theorem is found to hold at all times.

On holographic entanglement entropy of Horndeski black holes

A bstractWe study entanglement entropy in a particular tensor-scalar theory: Horndeski gravity. Our goal is two-fold: investigate the Lewkowycz-Maldacena proposal for entanglement entropy in the presence of a tensor-scalar coupling and address a puzzle existing in the literature regarding the thermal entropy of asymptotically AdS Horndeski black holes. Using the squashed cone method, i.e. turning on a conical singularity in the bulk, we derive the functional for entanglement entropy in Horndeski gravity. We analyze the divergence structure of the bulk equation of motion. Demanding that the leading divergence of the transverse component of the equation of motion vanishes we identify the surface where to evaluate the entanglement functional. We show that the surface obtained is precisely the one that minimizes said functional. By evaluating the entanglement entropy functional on the horizon we obtain the thermal entropy for Horndeski black holes; this result clarifies discrepancies in the literature. As an application of the functional derived we find the minimal surfaces numerically and study the entanglement plateaux.

Modelling LARES temperature distribution and thermal drag

The LARES satellite, a laser-ranged space experiment to contribute to geophysics observation, and to measure the general relativistic Lense-Thirring effect, has been observed to undergo an anomalous along-track orbital acceleration of −0.4 pm/s2 (pm : = picometer). This thermal “drag” is not surprising; along-track thermal drag has previously been observed with the related LAGEOS satellites (−3.4 pm/s2). It is hypothesized that the thermal drag is principally due to anisotropic thermal radiation from the satellite’s exterior. We report the results of numerical computations of the along-track orbital decay of the LARES satellite during the first 126 days after launch. The results depend to a significant degree on the visual and IR absorbance α and emissivity ε of the fused silica Cube Corner Reflectors. We present results for two values of αIR = εIR : 0.82, a standard number for “clean” fused silica; and 0.60, a possible value for silica with slight surface contamination subjected to the space environment. The heating and the resultant along-track acceleration depend on the plane of the orbit, the sun position, and, in particular, on the occurrence of eclipses, all of which are functions of time. Thus we compute the thermal drag for specific days. We compare our model to observational data, available for a 120 day period starting with the 7th day after launch, which shows the average acceleration of −0.4 pm/s2. With our model the average along-track thermal drag over this 120 day period for CCR αIR = εIR = 0.82 was computed to be −0.59 pm/s2. For CCR αIR = εIR = 0.60 we compute −0.36 pm/s2. LARES consists of a solid spherical tungsten sphere, into which the CCRs are set in colatitude circles. Our calculation models the satellite as 93 isothermal elements: the tungsten part, and each of the 92 Cube Corner Reflectors. The satellite is heated from two sources: sunlight and Earth’s infrared (IR) radiation. We work in the fast-spin regime, where CCRs with the same colatitude can be taken to have the same temperature. Since all temperature variations (temporal or spatial) are expected to be small, we linearize the Stefan-Boltzmann law and, taking advantage of the linearity, we perform a Fourier series analysis. The variations are indeed small, validating our Fourier analysis.

A defect in holographic interpretations of tensor networks

A bstractWe initiate the study of how tensor networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and boundary CFTs and compare them to the structure of the requisite MERA networks predicted by the theory of minimal updates. When the CFT is deformed, certain tensors require updating. On the other hand, even identical tensors can contribute differently to estimates of entanglement entropies. We interpret these facts holographically by associating tensor updates to turning on non-normalizable modes in the bulk. In passing, we also clarify and complement existing arguments in support of the theory of minimal updates, propose a novel ansatz called rayed MERA that applies to a class of generalized interface CFTs, and analyze the kinematic spaces of the thin wall and AdS3-Janus geometries.

LARES satellite thermal forces and a test of general relativity

We summarize a laser-ranged satellite test of frame dragging, a prediction of General Relativity, and then concentrate on the estimate of thermal thrust, an important perturbation affecting the accuracy of the test. The frame dragging study analysed 3.5 years of data from the LARES satellite and a longer period of time for the two LAGEOS satellites. Using the gravity field GGM05S obtained via the Grace mission, which measures the Earths gravitational field, the prediction of General Relativity is confirmed with a 1-σ formal error of 0.002, and a systematic error of 0.05. The result for the value of the frame dragging around the Earth is μ = 0.994, compared to μ = 1 predicted by General Relativity. The thermal force model assumes heat flow from the sun (visual) and from Earth (IR) to the satellite core and to the fused silica reflectors on the satellite, and reradiation into space. For a roughly current epoch (days 1460 - 1580 after launch) we calculate an average along track drag of -0.50pm/sec2.

Greenhouse effect: temperature of a metal sphere surrounded by a glass shell and heated by sunlight

We study the greenhouse effect on a model satellite consisting of a tungsten sphere surrounded by a thin spherical, concentric glass shell, with a small gap between the sphere and the shell. The system sits in vacuum and is heated by sunlight incident along the z-axis. This development is a generalization of the simple treatment of the greenhouse effect given by Kittel and Kroemer (1980 Thermal Physics (San Francisco: Freeman)) and can serve as a very simple model demonstrating the much more complex Earth greenhouse effect. Solution of the model problem provides an excellent pedagogical tool at the Junior/Senior undergraduate level.