Rodrigo Panosso Macedo

Phase diagram of 4D field theories with chiral anomaly from holography

A bstractWithin gauge/gravity duality, we study the class of four dimensional CFTs with chiral anomaly described by Einstein-Maxwell-Chern-Simons theory in five dimensions. In particular we determine the phase diagram at finite temperature, chemical potential and magnetic field. At high temperatures the solution is given by an electrically and magnetically charged AdS Reissner-Nordstroem black brane. For sufficiently large Chern-Simons coupling and at sufficiently low temperatures and small magnetic fields, we find a new phase with helical order, breaking translational invariance spontaneously. For the Chern-Simons couplings studied, the phase transition is second order with mean field exponents. Since the entropy density vanishes in the limit of zero temperature we are confident that this is the true ground state which is the holographic version of a chiral magnetic spiral.

Axisymmetric fully spectral code for hyperbolic equations

Abstract We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for the time direction) collocation points. The method solves two issues of previous algorithms which were restricted to one spatial dimension, namely, (i) the inversion of a dense matrix and (ii) the acquisition of a sufficiently good initial-guess for non-linear systems of equations. For the first issue, we use the iterative bi-conjugate gradient stabilized method, which we equip with a pre-conditioner based on a singly diagonally implicit Runge–Kutta (“SDIRK”-) method. In this paper, the SDIRK-method is also used to solve issue (ii). The numerical solutions are correct up to machine precision and we do not observe any restriction concerning the time step in comparison with the spatial resolution. As an application, we solve general-relativistic wave equations on a black-hole space–time in so-called hyperboloidal slices and reproduce some recent results available in the literature.

Holographic quenches and anomalous transport

A bstractWe study the response of the chiral magnetic effect due to continuous quenches induced by time dependent electric fields within holography. Concretely, we consider a holographic model with dual chiral anomaly and compute the electric current parallel to a constant, homogeneous magnetic field and a time dependent electric field in the probe approximation. We explicitly solve the PDEs by means of pseudospectral methods in spatial and time directions and study the transition to an universal “fast” quench response. Moreover, we compute the amplitudes, i.e., residues of the quasi normal modes, by solving the (ODE) Laplace transformed equations. We investigate the possibility of considering the asymptotic growth rate of the amplitudes as a well defined notion of initial time scale for linearized systems. Finally, we highlight the existence of Landau level resonances in the electrical conductivity parallel to a magnetic field at finite frequency and show explicitly that these only appear in presence of the anomaly. We show that the existence of these resonances induces, among others, a long-lived AC electric current once the electric field is switched off.

Axisymmetric constant mean curvature slices in the Kerr spacetime

Recently, there have been efforts to solve Einsteins equation in the context of a conformal compactification of spacetime. Of particular importance in this regard are the so-called constant mean curvature (CMC) foliations, characterized by spatial hyperboloidal hypersurfaces with a constant extrinsic mean curvature K. However, although of interest for general spacetimes, CMC slices are known explicitly only for the spherically symmetric Schwarzschild metric. This work is devoted to numerically determining axisymmetric CMC slices within the Kerr solution. We construct such slices outside the black hole horizon through an appropriate coordinate transformation in which an unknown auxiliary function A is involved. The condition K = const throughout the slice leads to a nonlinear partial differential equation for the function A, which is solved with a pseudo-spectral method. The results exhibit exponential convergence, as is to be expected in a pseudo-spectral scheme for analytic solutions. As a by-product, we identify CMC slices of the Schwarzschild solution which are not spherically symmetric.

Initial data for perturbed Kerr black holes on hyperboloidal slices

We construct initial data corresponding to a single perturbed Kerr black hole in vacuum. These data are defined on specific hyperboloidal (ACMC) slices, on which the mean extrinsic curvature K asymptotically approaches a constant at future null infinity . More precisely, we require that K obeys the Taylor expansion , where is a constant and σ describes a compactified spatial coordinate such that is represented by . We excise the singular interior of the black hole and assume a marginally outer trapped surface as the inner boundary of the computational domain. The momentum and Hamiltonian constraints are solved by means of pseudo-spectral methods and we find exponential rates of convergence of our numerical solutions. Some of the physical properties of the initial data are studied with the calculation of the Bondi mass, together with a multipole decomposition of the horizon. We probe the standard picture of gravitational collapse by assessing a family of Penrose-like inequalities and discuss in particular their rigidity aspects. Dynamical evolutions are planned in a future project.

Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to nonreflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the nonlinear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the nonaxisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.

Spectral methods for the spin-2 equation near the cylinder at spatial infinity

We solve, numerically, the massless spin-2 equations, written in terms of a gauge based on the properties of conformal geodesics, in a neighbourhood of spatial infinity using spectral methods in both space and time. This strategy allows us to compute the solutions to these equations up to the critical sets where null infinity intersects with spatial infinity. Moreover, we use the convergence rates of the numerical solutions to read-off their regularity properties.

Gravitational recoil and time evolution in nonsymmetric Robinson-Trautman spacetimes

We present some preliminary results on the time evolution and gravitational recoil in nonsymmetric Robinson-Trautman spacetimes. These results have been obtained by using an efficient full numerical approach based in the Galerkin spectral method to analyze the non-linear regime of the nonsymmetric Robinson-Trautman equations. We have attained a good accuracy with modest computational resources.