Energy and Angular Momentum in Generic F(Riemann) Theories

We construct the conserved charge of generic gravity theories built on arbitrary contractions of the Riemann tensor (but not on its derivatives) for asymptotically (anti)-de Sitter spacetimes. Our construction is a generalization of the ADT charges of linear and quadratic gravity theories in cosmological backgrounds. As an explicit example we find the energy and angular momentum of the BTZ black hole in the 2+1 dimensional Born-Infeld gravity.Comment: 7 page

Spectra, vacua and the unitarity of Lovelock gravity in D-dimensional AdS spacetimes

We explicitly confirm the expectation that generic Lovelock gravity in D dimensions has a unitary massless spin-2 excitation around any one of its constant curvature vacua just like the cosmological Einstein gravity. The propagator of the theory reduces to that of Einstein's gravity, but scattering amplitudes must be computed with an effective Newton's constant which we provide. Tree-level unitarity imposes a single constraint on the parameters of the theory yielding a wide range of unitary region. As an example, we explicitly work out the details of the cubic Lovelock theory.Comment: 9 pages, 2 references adde

Unitarity analysis of general Born-Infeld gravity theories

We develop techniques of analyzing the unitarity of general Born-Infeld (BI) gravity actions in D-dimensional spacetimes. Determinantal form of the action allows us to find a compact expression quadratic in the metric fluctuations around constant curvature backgrounds. This is highly nontrivial since for the BI actions, in principle, infinitely many terms in the curvature expansion should contribute to the quadratic action in the metric fluctuations around constant curvature backgrounds, which would render the unitarity analysis intractable. Moreover in even dimensions, unitarity of the theory depends only on finite number of terms built from the powers of the curvature tensor. We apply our techniques to some four-dimensional examples.Comment: 26 pages, typos corrected, version to appear in Phys. Rev.

Critical Points of D-Dimensional Extended Gravities

We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D>4 there are in general two distinct (anti)-de Sitter vacua. We show that for appropriate choice of the parameters there exists a critical point for one of the vacua, for which there are only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have vanishing energy (as do black hole solutions). A further restriction of the parameters gives a one-parameter cosmological Einstein plus Weyl^2 model with a unique vacuum, whose \Lambda is determined.Comment: 6 pages, typos correcte

Green's Matrix for a Second Order Self-Adjoint Matrix Differential Operator

A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the general approach of extracting the Green's matrix from the Green's matrix of the corresponding first order system. This construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques.Comment: 19 page

All unitary cubic curvature gravities in D dimensions

We construct all the unitary cubic curvature gravity theories built on the contractions of the Riemann tensor in D -dimensional (anti)-de Sitter spacetimes. Our construction is based on finding the equivalent quadratic action for the general cubic curvature theory and imposing ghost and tachyon freedom, which greatly simplifies the highly complicated problem of finding the propagator of cubic curvature theories in constant curvature backgrounds. To carry out the procedure we have also classified all the unitary quadratic models. We use our general results to study the recently found cubic curvature theories using different techniques and the string generated cubic curvature gravity model. We also study the scattering in critical gravity and give its cubic curvature extensions.Comment: 24 pages, 1 figure, v2: A subsection on cubic curvature extensions of critical gravity is added, v3: The part regarding critical gravity is revised. Version to appear in Class. Quant. Gra

Üç boyutlu sıkıştırılabilir akışlar için navier-stokes denklemlerinin paralel hale getirilmesi.

The aim of this study is to develop a code that is capable of solving three-dimensional compressible flows which are viscous and turbulent, and parallelization of this code. Purpose of parallelization is to obtain a computational efficiency in time respect which enables the solution of complex flow problems in reasonable computational times. In the first part of the study, which is the development of a three-dimensional Navier-Stokes solver for turbulent flows, first step is to develop a two-dimensional Euler code using Roe flux difference splitting method. This is followed by addition of sub programs involving calculation of viscous fluxes. Third step involves implementation of Baldwin-Lomax turbulence model to the code. Finally, the Euler code is generalized to three-dimensions. At every step, code validation is done by comparing numerical results with theoretical, experimental or other numerical results, and adequate consistency between these results is obtained. In the second part, which is the parallelization of the developed code, two-dimensional code is parallelized by using Message Passing Interface (MPI), and important improvements in computational times are obtained.M.S. - Master of Scienc

D-boyutta Born-infeld kütleçekim teorileri

Born-Infeld gravity proposed by Deser and Gibbons takes its origin from two ideas: Born-Infeld electrodynamics and Eddington's gravitational action. The theory is defined with a determinantal action involving the Ricci tensor as in the Eddington's theory; however, in contrast, the independent variable is the metric as in Einstein's gravity and the action is constructed in analogy with the action of the Born-Infeld electrodynamics. Main challenge in defining a Born-Infeld type gravity is obtaining a unitary theory around--at least--flat and maximally symmetric constant curvature backgrounds. In this thesis, a framework for analyzing the tree-level unitarity of a generic D-dimensional Born-Infeld type gravity is developed. Besides, in three dimensions, a Born-Infeld gravity theory which is unitary to all orders in the curvature is studied in detail. This theory was introduced as an extension of a specific quadratic curvature gravity theory dubbed as ``new massive gravity'' which is unitary with a massive spin-2 excitation in its spectrum. Besides having a unitary massive spin-2 excitation, the Born-Infeld gravity in three dimensions has a holographic $c$-function which is the same as Einstein's gravity. In addition, the theory has constant curvature Type-N and Type-D solutions which are the same as the cosmological topologically massive gravity.Ph.D. - Doctoral Progra