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.

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

Kütleli yüksek türevli kütleçekim kuramları.

In this thesis massive higher derivative gravity theories are analyzed in some detail. One-particle scattering amplitude between two covariantly conserved sources mediated by a graviton exchange is found at tree-level in D dimensional (Anti)-de Sitter and flat spacetimes for the most general quadratic curvature theory augmented with the Pauli-Fierz mass term. From the amplitude expression, the Newtonian potential energies are calculated for various cases. Also, from this amplitude and the propagator structure, a three dimensional unitary theory is identified. In the second part of the thesis, the found three dimensional unitary theory is studied in more detail from a canonical point of view. The general higher order action is written in terms of gauge-invariant functions both in flat and de Sitter backgrounds. The analysis is extended by adding static sources, spinning masses and the gravitational Chern-Simons term separately to the theory in the case of flat spacetime. For all cases the microscopic spectrum and the masses are found. In the discussion of curved spacetime, the masses are found in the relativistic and non-relativistic limits. In the Appendix, some useful calculations that are frequently used in the bulk of the thesis are given.Ph.D. - Doctoral Progra

Asimptotik (anti)-de sitter uzayzamanında korunan yükler

In this master̕s thesis, the Killing vectors are introduced and the Killing equation is derived. Also, some information is given about the cosmological constant. Then, the Abbott-Deser (AD) energy is reformulated by linearizing the Einstein equation with cosmological constant. From the linearized Einstein equation, Killing charges are derived by using the properties of Killing vectors. Using this formulation, energy is calculated for some specific cases by using the Schwarzschild-de Sitter metric. Last, the Einstein-Gauss-Bonnet model is studied. The equations of motion are calculated by solving the generic action at quadratic order. Following this, all energy calculations are renewed for this model. Some useful relations and calculations are shown in Appendix (A-B) parts. ÖZ ASiMPTOTiK (ANTi)-DE SITTER UZAYZAMANINDA KORUNAN YÜKLER GÜLLÜ, İBRAHİM Yüksek Lisans, Fizik Bölümü Tez Yöneticisi: Assoc. Prof. Dr. Bayram Tekin Ağustos 2005, 77 sayfa. Bu master çalışmasında, Killing vektörler tanımlandı ve Killing denklemi çıkarıldı. Ayrıca evrenbilimsel sabit, de-Sitter ve Anti-de Sitter uzayları hakkında bilgi verildi. Sonra, Abbott-Deser (AD) enerjisi, evrenbilimsel sabitli Einstein denklemi doğrusallaştırılarak yeniden formüle edildi. Doğrusallaştırılmış Einstein denkleminden, Killing vektörlerin özellikleri kullanılarak Killing yükleri (Deser-Tekin denklemi) çıkarıldı. Schwarzschild-de Sitter metriği kullanılarak özel durumlar için enerji hesaplandı. Son olarak Einstein-Gauss-Bonnet (GB) modeli çalışıldı. İkinci dereceden genel eylem çözülerek hareket denklemleri hesaplandı. Bundan sonra, tüm enerji hesaplamaları bu model için tekrarlandı. Bazı faydalı hesaplamalar ek (A-B) kısımlarında gösterilmiştir.M.S. - Master of Scienc

Türkiye’de Bölgesel Jeoid Tespiti için Yüksek Dereceli Jeopotansiyel Modellerin Değerlendirilmesi

High-degree geopotential models of spherical harmonic coefficients are used for modelling the exterior gravity field of the Earth. These coefficients are derived from satellite tracking data, altimeter data, and terrestrial and airborne gravity data. Hundreds of thousands of coefficients and standard deviation values for these coefficients are estimated from millions of measurements. The geopotential model accuracy is affected by the amount, the distribution and the type of measurements. The satellite gravity field missions have provided accurate data forming geopotential models since 1960’s. The geopotential models related to the satellite gravity field missions are experienced by interior validation (estimated error degree variances of fully-normalized coefficients) or outer validation (comparison of model based gravity anomalies and geoid heights with terrestrial measurements). In this paper, recent high-degree geopotential models are primarily explained and evaluated by GNSS/levelling data of a selected study area. The objective of this evaluation is to determine the high-degree geopotential model giving a better fit to the GNSS/levelling data over the study area for the contribution to the regional geoid determination studies in Turkey.Küresel harmonik katsayılardan oluşan yüksek dereceli jeopotansiyel modeller Dünya’nın dış gravite alanının modellenmesi için kullanılır. Bu katsayılar uydu takip verisinden, altimetre verisinden ve yersel graviteden türetilir. Yüzbinlerce katsayı ve bu katsayıların standart sapma değerleri milyonlarca ölçümden hesaplanır. Jeopotansiyel modelin doğruluğu ölçümlerin miktarından, dağılımından ve türünden etkilenir. Uydu gravite görevleri, 1960 lardan beri jeopotansiyel modelleri oluşturan doğru veri sağlamaktadır. Uydu gravite görevleri ile bağlantılı jeopotansiyel modeller iç geçerlilik (tam normalleştirilmiş katsayıların hesaplanan hata derece varyansları) veya dış geçerlilik (model bazlı gravite anomalilerinin ve jeoid yüksekliklerinin yersel ölçüler ile karşılaştırılması) ile değerlendirilir. Bu çalışmada, güncel yüksek dereceli jeopotansiyel modeller öncelikli olarak açıklanmış ve seçilmiş bir çalışma alanında GNSS/nivelman verisi kullanılarak değelendirilmiştir. Bu değerlendirmenin amacı, Türkiye’deki bölgesel jeoid tespiti çalışmalarına katkıda bulunmak için, çalışma alanındaki GNSS/nivelman verisine daha iyi uyan yüksek dereceli jeopotansiyel modelin belirlenmesidir