Graviton Mass and Memory

Gravitational memory, a residual change, arises after a finite gravitational wave pulse interacts with free masses. We calculate the memory effect in massive gravity as a function of the graviton mass $(m_g)$ and show that it is discretely different from the result of general relativity: the memory is reduced not just via the usual expected Yukawa decay but by a numerical factor which survives even in the massless limit. For the strongest existing bounds on the graviton mass, the memory is essentially wiped out for the sources located at distances above 10 Mpc. On the other hand, for the weaker bounds found in the LIGO observations, the memory is reduced to zero for distances above 0.1 Pc. Hence, we suggest that careful observations of the gravitational wave memory effect can rule out the graviton mass or significantly bound it. We also show that adding higher curvature terms reduces the memory effect.Comment: 6 pages, matches the published versio

More on Cotton Flow

Cotton flow tends to evolve a given initial metric on a three manifold to a conformally flat one. Here we expound upon the earlier work on Cotton flow and study the linearized version of it around a generic initial metric by employing a modified form of the DeTurck trick. We show that the flow around the flat space, as a critical point, reduces to an anisotropic generalization of linearized KdV equation with complex dispersion relations one of which is an unstable mode, rendering the flat space unstable under small perturbations. We also show that Einstein spaces and some conformally flat non-Einstein spaces are linearly unstable. We refine the gradient flow formalism and compute the second variation of the entropy and show that generic critical points are extended Cotton solitons. We study some properties of these solutions and find a Topologically Massive soliton that is built from Cotton and Ricci solitons. In the Lorentzian signature, we also show that the pp-wave metrics are both Cotton and Ricci solitons.Comment: 22 pages, typos corrected, version to appear in JHE

Weyl-gauging of Topologically Massive Gravity

We construct a Weyl-invariant extension of topologically massive gravity which, remarkably, turns out to include topologically massive electrodynamics, with a Proca mass term, conformally coupled to a scalar field. The action has no dimensionful parameters, therefore, the masses are generated via symmetry breaking either radiatively in flat backgrounds or spontaneously in constant curvature backgrounds. The broken phase of the theory, generically, has a single massive spin-2 and a massive spin-1 excitation. Chiral gravity in asymptotically anti-de Sitter spacetimes does not arise as a low energy theory, while chiral gravity in de Sitter spacetime is not ruled out.Comment: 10 pages, minor changes made, version to appear in Phys. Rev.

Exotic Massive Gravity: Causality and a Birkhoff-like Theorem

We study the local causality issue via the Shapiro time-delay computations in the on-shell consistent exotic massive gravity in three dimensions. The theory shows time-delay as opposed to time-advance despite having a ghost at the linearized level both for asymptotically flat and anti-de Sitter spacetimes. We also prove a Birkhoff-like theorem: any solution with a hypersurface orthogonal non-null Killing vector field is conformally flat; and find some exact solutions.Comment: 14 pages, 1 figure, typos corrected, matches the published versio

Causality in 3D Massive Gravity Theories

We study the constraints coming from local causality requirement in various $2+1$ dimensional dynamical theories of gravity. In topologically massive gravity, with a single parity non-invariant massive degree of freedom, and in new massive gravity, with two massive spin-$2$ degrees of freedom, causality and unitarity are compatible with each other and both require the Newton's constant to be negative. In their extensions, such as the Born-Infeld gravity and the minimal massive gravity the situation is similar and quite different from their higher dimensional counterparts, such as quadratic (e.g., Einstein-Gauss-Bonnet) or cubic theories, where causality and unitarity are in conflict. We study the problem both in asymptotically flat and asymptotically anti-de Sitter spaces.Comment: This version has significant improvements: causality discussion of all the well-known gravity theories in flat space is extended to the AdS space, references added, 29 pages, latest version matches the published on

Unitarity problems in 3D gravity theories

We revisit the problem of the bulk-boundary unitarity clash in 2 + 1 dimensional gravity theories, which has been an obstacle in providing a viable dual two-dimensional conformal field theory for bulk gravity in anti-de Sitter (AdS) spacetime. Chiral gravity, which is a particular limit of cosmological topologically massive gravity (TMG), suffers from pertur- bative log-modes with negative energies inducing a non-unitary logarithmic boundary field theory. We show here that any f(R) extension of TMG does not improve the situation. We also study the perturbative modes in the metric formulation of minimal massive gravity- originally constructed in a first-order formulation-and find that the massive mode has again negative energy except in the chiral limit. We comment on this issue and also discuss a possible solution to the problem of negative energy modes. In any of these theories, the infinitesimal dangerous deformations might not be integrable to full solutions; this suggests a linearization instability of AdS spacetime in the direction of the perturbative log-modes.Comment: 15 pages, matches the Physics. Rev. D versio

THE IMPACT OF CONTRUCTIVISM BASED GENERAL CHEMISTRY LABORATORY PRACTICES ON STUDENTS' THE ACHIEVEMENT, SCIENTIFIC PROCESS SKILLS AND LABORATORY PERFORMANCE

Bu araştırmanın amacı, geleneksel ve yapılandırmacı yaklaşıma göre tasarlanmış genel kimya laboratuar öğretim uygulamalarının öğrencilerin akademik başarısı, bilimsel süreç becerileri ve laboratuar performanslarına olan etkisini belirleyebilmektir. Bu araştırmada, "Öntest-Sontest Kontrol Gruplu Deneme Modeli" kullanılmıştır. Araştırma, Marmara Üniversitesi, Atatürk Eğitim Fakültesi, Fen Bilgisi Öğretmenliği Ana Bilim Dalı'nda öğrenim gören 120 birinci sınıf öğrencisi ile Genel Kimya Laboratuarı-II dersi bünyesinde bir öğrenim dönemi boyunca yürütülmüştür. Deney grubunda bir dönem boyunca uygulanacak olan Genel Kimya Laboratuarı-II dersinde yer alan toplam 10 deney yapılandırmacı öğretim metoduna göre uygulanmıştır. Kontrol grubu da aynı 10 deneyi geleneksel (doğrulama) metoda göre gerçekleştirmiştir. Araştırma sonucunda elde edilen bulgular ışığında; akademik başarı, bilimsel süreç becerileri testi ve laboratuar performanslarına göre deney grubu lehine anlamlı bir fark oluşmuştur. The aim of this study, designed according to traditional and constructivist approaches to teaching applications of scientific achievements, skills development and the scientific process of laboratory performance is to determine the effect. In this study, "Pre-Trial Model finaltest Control Group" is used. Research, Marmara University, Faculty of Education, Science Education Department of freshmen who are studying at the General Chemistry Lab within the course during the study period was conducted. In the experimental group, which will be implemented over a period of general chemistry laboratory courses in total, 10 tests were administered according to the constructivist teaching methods. Control group the same 10 esttraditional (authentication) performed according to the method. Research findings in light of the results obtained from the experimental and control groups did not create a meaningful difference in academic achievement pretest and post test in the experimental group was a significant difference

Analysis of Obesity And Axillary Lymph Nodes on Mammography

Fat-infiltrated lymph nodes mostly seen on mammograms (MG) of the elderly and obese women. We analyzed the fat infiltration of lymph nodes for its potential use in estimating body mass index (BMI). 2D digital MG of 157 women assessed by one breast radiologist and one radiology resident. For each patient, the largest lymph node chosen as the index by analyzing the medial, lateral oblique (MLO) views. The width and length of the node and the hilum, the cortex, and the Hilo-cortical ratio (HCR) were measured. Breast density was categorized according to the ACR BI-RADS 4th edition and divided into two groups as dense and non-dense. Obesity was defined as BMI ≥ 30 kg/m2, overweight as BM