Christos Charmousis

Effective Holographic Theories for low-temperature condensed matter systems

The IR dynamics of effective holographic theories capturing the interplay between charge density and the leading relevant scalar operator at strong coupling are analyzed. Such theories are parameterized by two real exponents (γ, δ) that control the IR dynamics. By studying the thermodynamics, spectra and conductivities of several classes of charged dilatonic black hole solutions that include the charge density back reaction fully, the landscape of such theories in view of condensed matter applications is characterized. Several regions of the (γ, δ) plane can be excluded as the extremal solutions have unacceptable singularities. The classical solutions have generically zero entropy at zero temperature, except when γ = δ where the entropy at extremality is finite. The general scaling of DC resistivity with temperature at low temperature, and AC conductivity at low frequency and temperature across the whole (γ, δ) plane, is found. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for planar (3d) systems. Regions are identified where the theory at finite density is a Mott-like insulator at T = 0. We also find that at low enough temperatures the entropy due to the charge carriers is generically larger than at zero charge density.

General second-order scalar-tensor theory and self-tuning

Starting from the most general scalar-tensor theory with second order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent selftuning mechanism on FLRW backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincaré invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining non-trivial cosmological solutions.

General brane cosmologies and their global spacetime structure

Starting from a completely general standpoint, we find the most general brane-universe solutions for a 3-brane in a five-dimensional spacetime. The brane can border regions of spacetime with or without a cosmological constant. Making no assumptions other than the usual cosmological symmetries of the metric, we prove that the equations of motion form an integrable system, and find the exact solution. The cosmology is indeed a boundary of a (class II) Schwarzschild-AdS spacetime, or a Minkowski (class I) spacetime. We analyse the various cosmological trajectories focusing particularly on those bordering vacuum spacetimes. We find, not surprisingly, that not all cosmologies are compatible with an asymptotically flat spacetime branch. We comment on the role of the radion in this picture.

General Gauss–Bonnet brane cosmology

We consider five-dimensional spacetimes of constant three-dimensional spatial curvature in the presence of a bulk cosmological constant. We find the general solution of such a configuration in the presence of a Gauss–Bonnet term. Two classes of non-trivial bulk solutions are found. The first class is valid only under a fine-tuning relation between the Gauss–Bonnet coupling constant and the cosmological constant of the bulk spacetime. The second class of solutions are static and are the extensions of the AdS–Schwarzchild black holes. Hence in the absence of a cosmological constant or if the fine-tuning relation is not true, the generalized Birkhoffs staticity theorem holds even in the presence of Gauss–Bonnet curvature terms. We examine the consequences in braneworld cosmology obtaining the generalized Friedmann equations for a perfect fluid 3-brane and discuss how this modifies the usual scenario.

Higher Order Gravity Theories and Their Black Hole Solutions

In this chapter, we will discuss a particular higher order gravity theory, Lovelock theory, that generalises in higher dimensions than 4, general relativity. After briefly motivating modifications of gravity, we will introduce the theory in question and we will argue that it is a unique, mathematically sensible, and physically interesting extension of general relativity. We will see, by using the formalism of differential forms, the relation of Lovelock gravity to differential geometry and topology of even-dimensional manifolds. We will then discuss a generic staticity theorem, quite similar to Birkhoff’s theorem in general relativity, which will give us the charged static black hole solutions. We will examine their asymptotic behaviour, analyse their horizon structure and briefly their thermodynamics. For the thermodynamics we will give a geometric justification of why the usual entropy–area relation is broken. We will then examine the distributional matching conditions for Lovelock theory. We will see how induced four-dimensional Einstein–Hilbert terms result on the brane geometry from the higher order Lovelock terms. With the junction conditions at hand, we will go back to the black hole solutions and give applications for braneworlds: perturbations of codimension 1 braneworlds and the exact solution for braneworld cosmology as well as the determination of maximally symmetric codimension 2 braneworlds. In both cases, the staticity theorem evoked beforehand will give us the general solution for braneworld cosmology in codimension 1 and maximal symmetry warped branes of codimension 2. We will then end with a discussion of the simplest Kaluza–Klein reduction of Lovelock theory to a four-dimensional vector–scalar–tensor theory which has the unique property of retaining second-order field equations. We will comment briefly the non-linear generalisation of Maxwell’s theory and scalar–tensor theory. We will conclude by listing some open problems and common difficulties.

Self-tuning and the derivation of a class of scalar-tensor theories

We have recently proposed a special class of scalar tensor theories known as the Fab Four. These arose from attempts to analyse the cosmological constant problem within the context of Horndeski’s most general scalar tensor theory. The Fab Four together give rise to a model of self-tuning, with the relevant solutions evading Weinberg’s no-go theorem by relaxing the condition of Poincaré invariance in the scalar sector. The Fab Four are made up of four geometric terms in the action with each term containing a free potential function of the scalar field. In this paper we rigorously derive this model from the general model of Horndeski, proving that the Fab Four represents the only classical scalar tensor theory of this type that has any hope of tackling the cosmological constant problem. We present the full equations of motion for this theory, and give an heuristic argument to suggest that one might be able to keep radiative corrections under control. We also give the Fab Four in terms of the potentials presented in Deffayet et al’s version of Horndeski.

Einstein-Maxwell-Dilaton theories with a Liouville potential

We find and analyze solutions of Einsteins equations in arbitrary dimensions and in the presence of a scalar field with a Liouville potential coupled to a Maxwell field. We consider spacetimes of cylindrical symmetry or again subspaces of dimension

Avoidance of naked singularities in dilatonic brane world scenarios with a Gauss-Bonnet term

d\ensuremath{-}2

Matching conditions for a brane of arbitrary codimension

with constant curvature and analyze in detail the field equations and manifest their symmetries. The field equations of the full system are shown to reduce to a single or couple of ordinary differential equations, which can be used to solve analytically or numerically the theory for the symmetry at hand. Further solutions can also be generated by a solution-generating technique akin to the electromagnetic duality in the absence of a cosmological constant. We then find and analyze explicit solutions including black holes and gravitating solitons for the case of four-dimensional relativity and the higher-dimensional oxidized five-dimensional spacetime. The general solution is obtained for a certain relation between couplings in the case of cylindrical symmetry.

Einstein gravity on an even-codimension brane

Abstract We consider, in 5 dimensions, the low energy effective action induced by heterotic string theory including the leading stringy correction of order α′. In the presence of a single positive tension flat brane, and an infinite extra dimension, we present a particular class of solutions with finite 4-dimensional Planck scale and no naked singularity. A “self-tuning” mechanism for relaxing the cosmological constant on the brane, without a drastic fine tuning of parameters, is discussed in this context. Our solutions are distinct from the standard self-tuning solutions discussed in the context of vanishing quantum corrections in α′, and become singular in this limit.