scholarly journals General definition of “conserved quantities” in general relativity and other theories of gravity

2000 ◽  
Vol 61 (8) ◽  
Author(s):  
Robert M. Wald ◽  
Andreas Zoupas
Keyword(s):  
General Relativity ◽  
General Definition ◽  
Conserved Quantities ◽  
Theories Of Gravity ◽  
Definition Of

scholarly journals COLLECTIVE AND RELATIVE VARIABLES FOR A CLASSICAL KLEIN–GORDON FIELD

1999 ◽  
Vol 14 (21) ◽  
pp. 3387-3420 ◽  
Author(s):  
G. LONGHI ◽  
M. MATERASSI
Keyword(s):  
General Relativity ◽  
Asymptotic Behavior ◽  
Harmonic Analysis ◽  
Momentum Space ◽  
Conserved Quantities ◽  
Canonical Transformations ◽  
Collective Variables ◽  
Klein Gordon ◽  
Definition Of

In this paper a set of canonical collective variables is defined for a classical Klein–Gordon field and the problem of the definition of a set of canonical relative variables is discussed. This last point is approached by means of a harmonic analysis in momentum space. This analysis shows that the relative variables can be defined if certain conditions are fulfilled by the field configurations. These conditions are expressed by the vanishing of a set of conserved quantities, referred to as supertranslations since as canonical observables they generate a set of canonical transformations whose algebra is the same as that which arises in the study of the asymptotic behavior of the metric of an isolated system in General Relativity.9

scholarly journals FOURTH-ORDER GRAVITY AND EXPERIMENTAL CONSTRAINTS ON EDDINGTON PARAMETERS

2006 ◽  
Vol 21 (30) ◽  
pp. 2291-2301 ◽  
Author(s):  
S. CAPOZZIELLO ◽  
A. STABILE ◽  
A. TROISI
Keyword(s):  
Experimental Data ◽  
General Relativity ◽  
Alternative Theories Of Gravity ◽  
Third Order ◽  
Definitive Answer ◽  
Order Polynomial ◽  
Theories Of Gravity ◽  
Definition Of ◽  
Ppn Parameters ◽  
Alternative Theories

PPN-limit of alternative theories of gravity represents a still controversial matter of debate and no definitive answer has been provided, up to now, about this issue. By using the definition of the PPN-parameters γ and β in terms of f(R) theories of gravity, we show that a family of third-order polynomial theories, in the Ricci scalar R, turns out to be compatible with the PPN-limit and the deviation from General Relativity, theoretically predicted, can agree with experimental data.

scholarly journals A remark on local fractional calculus and ordinary derivatives

2016 ◽  
Vol 14 (1) ◽  
pp. 1122-1124 ◽  
Author(s):  
Ricardo Almeida ◽  
Małgorzata Guzowska ◽  
Tatiana Odzijewicz
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Short Note ◽  
General Definition ◽  
Local Fractional Derivative ◽  
Fundamental Properties ◽  
Local Fractional Calculus ◽  
Definition Of

AbstractIn this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.

scholarly journals AB0677 REVISING THE DEFINITION OF REACTIVE ARTHRITIS AND DIFFERENTIATION FROM UNDIFFERENTIATED SPONDYLOARTHRITIS

2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 1633.2-1634
Author(s):  
F. Cosan ◽  
O. M. Gedar
Keyword(s):  
Causative Agent ◽  
Reactive Arthritis ◽  
Case Reports ◽  
Experimental Studies ◽  
Classification Criteria ◽  
General Definition ◽  
Parasitic Infections ◽  
Undifferentiated Spondyloarthritis ◽  
Classical Definition ◽  
Definition Of

Background:Reactive arthritis (ReA) is defined by 1999 ACR criteria as arthritis preceding a bacterial genitourinary (GUS) or gastrointestinal (GIS) infection in 3 days-6 weeks and evidence of triggering infection. Recently, ReA is classified as SpA and patients who do not fulfill SpA criteria are classified as undifferentiated spondyloarthritis (USpA) according to ASAS/EULAR SpA classification criteria.Objectives:In several case reports which are associated with other infective agents are reported and the definition is extended for some clinicians so that SpA which is occurred after any infection is called as ReA. On the other hand, some researchers still accept the classical definition of ReA. The problem with the heterogeneity of opinions and unstandardized definition of ReA hinders studies about pathogenesis and standardization of treatments. In this study, we aimed to determine the spectrum of the use of the definition of reactive arthritis in publications in PubMed between 2009-2019.Methods:The ReA keyword is searched in PubMed for the years between 2009-2019. 248 different publications have been identified and included in this research. 89 articles, 47 reviews, 108 case reports, 2 guidelines, and 2 editorials reviewed for the definition of ReA.Results:Only 42.7% (106 patients) of these publications meet the classical definition which suggests ReA after only GIS and GUS infections. In 4 (1.6%) of the publications ReA was defined after GIS, GUS and oropharyngeal infections; in 3 (1,2%) of the publications after any bacterial infection; in 9 (3.6%) of the publications after any infection. In 8 (3.2%) of the publications, ReA and USPA was used correspondingly. In 39 (15,7%) of the publications the term agent related, ReA was used without making a general definition for ReA. 79 publications (31,9%) have not defined ReA.According to causative agent and ReA relationship, in 64 (24,6%) general infective agents, in 75 (30,2%) classical agents, in 22 (8,9%) other bacterial agents, in 23 (9,3%) streptococcus, in 10(4%) intravesical BCG, in 6 (2.4%) HIV, in 6 (2.4%) tuberculosis, in 12 (4,8%) clostrudium difficle, in 2 (0.8%) parasites were reported. In 31 (12,5%) of the publications the causative agent for the ReA was unknown, the diagnosis was made clinically.Conclusion:In this study, it is aimed to draw attention terminology intricacy and the need for the standardization of the definition of ReA and USpA. It is clear that to standardize the definition of Rea and USpA is necessary. Between 2009-2019 there are reported cases diagnosed as ReA associated with bacterial infections (especially with Clostridium difficile, streptococcus and tuberculosis infections), and viral infections (by a majority with HIV), and parasitic infections. It is not clear if we need to define them classically or define them as USPA. Another important consideration is the necessity of extended laboratory investigations to find out the real causative agent even if the patient is clinically diagnosed with ReA. The requirement of the differentiation between ReA and USpA must be revealed for therapeutic researches.References:[1]A proposal for the classification of patients for clinical and experimental studies on reactive arthritis. Pacheco-Tena C, Burgos-Vargas R, Vázquez-Mellado J, Cazarín J, Pérez-Díaz JA. J Rheumatol. 1999 Jun;26(6):1338-46.[2]The Assessment of SpondyloArthritis International Society classification criteria for peripheral spondyloarthritis and for spondyloarthritis in general. Rudwaleit M, van der Heijde D, Landewé R, Akkoc N, Brandt J, Chou CT, Dougados M, Huang F, Gu J, Kirazli Y, et al. Ann Rheum Dis. 2011;70:25–31.Disclosure of Interests:None declared

scholarly journals A lattice-theoretic characterization of pure subgroups of Abelian groups

2021 ◽  
Author(s):  
M. Ferrara ◽  
M. Trombetti
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Subgroup Lattice ◽  
General Definition ◽  
Short Paper ◽  
Theoretic Characterization ◽  
Definition Of

AbstractLet G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice $$\mathcal {L}(H)$$ L ( H ) embeds in $$\mathcal {L}(G)$$ L ( G ) . It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity.

scholarly journals Off-Shell Noether Currents and Potentials for First-Order General Relativity

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 348
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez ◽  
Rodrigo Romero ◽  
Mariano Celada
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Arbitrary Vector ◽  
Four Dimensions ◽  
First Order ◽  
Direct Form ◽  
Definition Of

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

scholarly journals Proportional lumpability and proportional bisimilarity

2021 ◽  
Author(s):  
Andrea Marin ◽  
Carla Piazza ◽  
Sabina Rossi
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Upper And Lower Bounds ◽  
General Definition ◽  
Performance Indices ◽  
State Aggregation ◽  
Structural Regularity ◽  
Original Definition ◽  
Aggregation Technique ◽  
Definition Of

AbstractIn this paper, we deal with the lumpability approach to cope with the state space explosion problem inherent to the computation of the stationary performance indices of large stochastic models. The lumpability method is based on a state aggregation technique and applies to Markov chains exhibiting some structural regularity. Moreover, it allows one to efficiently compute the exact values of the stationary performance indices when the model is actually lumpable. The notion of quasi-lumpability is based on the idea that a Markov chain can be altered by relatively small perturbations of the transition rates in such a way that the new resulting Markov chain is lumpable. In this case, only upper and lower bounds on the performance indices can be derived. Here, we introduce a novel notion of quasi-lumpability, named proportional lumpability, which extends the original definition of lumpability but, differently from the general definition of quasi-lumpability, it allows one to derive exact stationary performance indices for the original process. We then introduce the notion of proportional bisimilarity for the terms of the performance process algebra PEPA. Proportional bisimilarity induces a proportional lumpability on the underlying continuous-time Markov chains. Finally, we prove some compositionality results and show the applicability of our theory through examples.

scholarly journals Conformal mapping of the Misner–Sharp mass from gravitational collapse

2016 ◽  
Vol 25 (07) ◽  
pp. 1650081 ◽  
Author(s):  
Fayçal Hammad
Keyword(s):  
Conformal Mapping ◽  
Gravitational Collapse ◽  
Conformal Transformation ◽  
Conformal Mappings ◽  
Conformal Transformations ◽  
Theories Of Gravity ◽  
Definition Of ◽  
Geometric Definition

The conformal transformation of the Misner–Sharp mass is reexamined. It has recently been found that this mass does not transform like usual masses do under conformal mappings of spacetime. We show that when it comes to conformal transformations, the widely used geometric definition of the Misner–Sharp mass is fundamentally different from the original conception of the latter. Indeed, when working within the full hydrodynamic setup that gave rise to that mass, i.e. the physics of gravitational collapse, the familiar conformal transformation of a usual mass is recovered. The case of scalar–tensor theories of gravity is also examined.

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