The minimum mass of a spherically symmetric object in DD-dimensions, and its implications for the mass hierarchy problem

The existence of both a minimum mass and a minimum density in nature, in the presence of a positive cosmological constant, is one of the most intriguing results in classical general relativity. These results follow rigorously from the Buchdahl inequalities in four dimensional de Sitter space. In this work, we obtain the generalized Buchdahl inequalities in arbitrary space-time dimensions with $\Lambda \neq 0$ and consider both the de Sitter and anti-de Sitter cases. The dependence on $D$, the number of space-time dimensions, of the minimum and maximum masses for stable spherical objects is explicitly obtained. The analysis is then extended to the case of dark energy satisfying an arbitrary linear barotropic equation of state. The Jeans instability of barotropic dark energy is also investigated, for arbitrary $D$, in the framework of a simple Newtonian model with and without viscous dissipation, and we determine the dispersion relation describing the dark energy$-$matter condensation process, along with estimates of the corresponding Jeans mass (and radius). Finally, the quantum mechanical implications of mass limits are investigated, and we show that the existence of a minimum mass scale naturally leads to a model in which dark energy is composed of a `sea' of quantum particles, each with an effective mass proportional to $\Lambda^{1/4}$.Comment: 16 pages, one figure; Section IV extended; references added; accepted for publication in EPJ

A Surprising Similarity Between Holographic CFTs and a Free Fermion in (2+1)(2+1) Dimensions

We compare the behavior of the vacuum free energy (i.e. the Casimir energy) of various $(2+1)$-dimensional CFTs on an ultrastatic spacetime as a function of the spatial geometry. The CFTs we consider are a free Dirac fermion, the conformally-coupled scalar, and a holographic CFT, and we take the spatial geometry to be an axisymmetric deformation of the round sphere. The free energies of the fermion and of the scalar are computed numerically using heat kernel methods; the free energy of the holographic CFT is computed numerically from a static, asymptotically AdS dual geometry using a novel approach we introduce here. We find that the free energy of the two free theories is qualitatively similar as a function of the sphere deformation, but we also find that the holographic CFT has a remarkable and mysterious quantitative similarity to the free fermion; this agreement is especially surprising given that the holographic CFT is strongly-coupled. Over the wide ranges of deformations for which we are able to perform the computations accurately, the scalar and fermion differ by up to 50% whereas the holographic CFT differs from the fermion by less than one percent.Comment: 16+8 pages, 13 figures. v2: References added, minor edit

Physical constraints from holographic duality

The material presented in this thesis mainly consists of two parts under the umbrella topic of Holographic Duality or the AdS/CFT correspondence. In Part II we are mainly interested in the properties of energetic quantities, namely, the energy and free energy of Conformal Field Theory (CFT) under de- formations of spacetime geometry in (2+1) dimensions. By using holography together with analytic and numerical techniques, we find many results on monotonic decreasing of the energy/free energy for static solutions of gravitational theory in asymptotically locally Anti-de Sitter (AlAdS) spacetime and correspondingly for a CFT dual in many different scenarios. These results put nontrivial physical bounds on the energy/free energy of holographic CFT in curved spaces. In Part III, in chapter 6 we study the Gregory-Laflamme (GL) instability of charged black strings in five dimensions. The physical properties of GL unstable mode perturbations and the consequences of the instability are studied in detail. We also solve for numerical solutions of nonuniform phase of charged black strings and obtain a thermodynamic phase structure of charged black strings. In chapter 7, we apply the holographic duality to a black string solution with an extra string charge in the type-IIA supergravity. We utilize the similarity between the properties of charged black strings in five dimensions and our system in type-IIA supergravity to obtain the result on thermodynamics of its holographic dual which is a two- dimensional supersymmetric Yang-Mills theory on a circle in a boosted frame.Open Acces

Political risk, self-protection and market insurance: optimal responses to the threat of expropriation

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