On The Role of the Eshelby Energy-Momentum Tensor in Materials with Multiple Natural Configurations

2005 ◽  
Vol 10 (1) ◽  
pp. 3-24 ◽  
Author(s):  
K. R. Rajagopal ◽  
A. R. Srinivasa
Keyword(s):  
Continuum Mechanics ◽  
Energy Momentum Tensor ◽  
Driving Forces ◽  
Momentum Tensor ◽  
Balance Laws ◽  
Inelastic Response ◽  
Seminal Work ◽  
Multiple Natural Configurations ◽  
Intense Activity

We discuss the connection between two important parallel developments in continuum mechanics that has gone unnoticed despite intense activity in both these seemingly disparate areas: the first stems from the pioneering work of Eckart on the role of the evolution of “natural configurations” in the inelastic response of solids; the second stems from the seminal work of Eshelby concerning the energy-momentum tensor associated with the driving forces that arise as a consequence of inhomogeneities and defects during the deformations of solids. We show that a variety of driving forces manifest themselves as a consequence of the evolution of natural configurations, depending on the particular process under consideration. Our study makes it clear that no new balance laws need be invoked in order to accommodate such driving forces, the usual balances laws of mechanics being sufficient.

N=2 SUPERCONFORMAL INTERACTING BOSONIC MODELS

1992 ◽  
Vol 07 (04) ◽  
pp. 345-356 ◽  
Author(s):  
RON COHEN
Keyword(s):  
Free Energy ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Oriented Graph ◽  
Momentum Tensor ◽  
Superconformal Algebra ◽  
Chiral Algebra ◽  
Bosonic Model ◽  
Coset Models

Bosonic representations of N=2 superconformal algebra are studied. We show that the free energy momentum tensor decomposes into an orthogonal sum of the interacting bosonic model (IBM) and a coset-like tensors. We define the notion of flags of models and show that the central charge does not decrease along the flags. We examine the conditions for an arbitrary un-oriented graph to form an IBM. We discuss several properties of the chiral algebra of these models and examine the role of the continuous parameters by studying an example. Finally we discuss the relations between these models and the N=2 superconformal coset models.

scholarly journals CANONICAL APPROACH TO 2D SUPERSYMMETRIC WZNW MODEL COUPLED TO SUPERGRAVITY

2002 ◽  
Vol 17 (29) ◽  
pp. 1923-1936 ◽  
Author(s):  
OLIVERA MIŠKOVIĆ ◽  
BRANISLAV SAZDOVIĆ
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Moody Algebra ◽  
Gauge Transformations ◽  
Local Gauge ◽  
Gauge Symmetries ◽  
Wznw Model ◽  
Canonical Approach ◽  
Explicit Expressions

Starting from the known representation of the Kac–Moody algebra in terms of the coordinates and momenta, we extend it to the representation of the super Kac–Moody and super Virasoro algebras. Then we use general canonical method to construct an action invariant under local gauge symmetries, where components of the super energy–momentum tensor L± and G± play the role of the diffeomorphisms and supersymmetry generators respectively. We obtain covariant extension of WZNW theory with respect to local supersymmetry as well as explicit expressions for gauge transformations.

scholarly journals Spinor field in Bianchi type-IX space–time

2018 ◽  
Vol 96 (10) ◽  
pp. 1074-1084
Author(s):  
Bijan Saha
Keyword(s):  
Spinor Field ◽  
Bianchi Type ◽  
Energy Momentum Tensor ◽  
Early Stage ◽  
Momentum Tensor ◽  
Space Time ◽  
Rapid Expansion ◽  
Coupling Constant ◽  
The One

Within the scope of Bianchi type-IX cosmological model we have studied the role of spinor field in the evolution of the Universe. It is found that unlike the diagonal Bianchi models in this case the components of energy–momentum tensor of spinor field along the principal axis are not the same (i.e., [Formula: see text]), even in the absence of spinor field nonlinearity. The presence of nontrivial non-diagonal components of energy–momentum tensor of the spinor field imposes severe restrictions both on geometry of space–time and on the spinor field itself. As a result the space–time turns out to be either locally rotationally symmetric or isotropic. In this paper we considered the Bianchi type-IX space–time both for a trivial b, that corresponds to standard Bianchi type-IX and the one with a non-trivial b. It was found that a positive self-coupling constant λ1 gives rise to an oscillatory mode of expansion, while a trivial λ1 leads to rapid expansion at the early stage of evolution.

LTB geometry with tilted and nontilted congruences in f(R,T) gravity

2017 ◽  
Vol 26 (09) ◽  
pp. 1750099 ◽  
Author(s):  
Z. Yousaf ◽  
M. Zaeem-ul-Haq Bhatti ◽  
Aamna Rafaqat
Keyword(s):  
Transport Equation ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Imperfect Fluid ◽  
Dynamical Features ◽  
Dust Fluid

We investigate the role of tilted and nontilted congruence in the dynamics of dissipative Lemaître–Tolman–Bondi spacetime in [Formula: see text] gravity. We consider imperfect fluid with its congruences observed by tilted observer and dust fluid filled with LTB geometry observed by the nontilted observer. In order to elaborate the dynamical features of two congruences, we consider well-known [Formula: see text] models and develop relationships between tilted and nontilted dynamical variables. We evaluate the nonzero divergence of energy–momentum tensor for tilted congruence and transport equation for the system in [Formula: see text] gravity. We have also checked the instability regimes for nontilted congruence.

scholarly journals COVARIANT ANOMALIES, HORIZONS AND HAWKING RADIATION

2008 ◽  
Vol 17 (13n14) ◽  
pp. 2539-2542 ◽  
Author(s):  
RABIN BANERJEE
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Hawking Radiation ◽  
Crucial Role ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Diffeomorphism Symmetry

Hawking radiation is obtained from anomalies resulting from a breaking of diffeomorphism symmetry near the event horizon of a black hole. Such anomalies, manifested as a nonconservation of the energy–momentum tensor, occur in two different forms — covariant and consistent. The crucial role of covariant anomalies near the horizon is revealed, since this is the only input required to obtain the Hawking flux, thereby highlighting the universality of this effect. A brief description of the application of this method to obtain thermodynamic entities like entropy or temperature is provided.

Role of structure scalars on viscous and heat conducting spherical systems in f(R,T) gravity

2017 ◽  
Vol 26 (14) ◽  
pp. 1750155 ◽  
Author(s):  
T. Hussain ◽  
M. Khurshudyan ◽  
S. Ahmed ◽  
As. Khurshudyan
Keyword(s):  
Evolution Equations ◽  
Energy Momentum Tensor ◽  
Gravitational Theory ◽  
Riemann Tensor ◽  
Momentum Tensor ◽  
Compact Objects ◽  
Heat Conducting ◽  
Structure Scalars ◽  
Dynamical Features

In this paper, we analyze some dynamical features of spherical celestial objects through structure scalars in [Formula: see text] gravitational theory, where [Formula: see text] and [Formula: see text] are the Ricci scalar and the trace of energy–momentum tensor, respectively. In this framework, we consider our relativistic geometry to be spherical in shape filled with radiating viscous and shearing fluid content. We formulate extended version of structure scalars by orthogonal decomposition of the Riemann tensor with and without constant [Formula: see text] and [Formula: see text] backgrounds. We discuss the effects of dark source corrections on the construction of expansion and shear evolution equations via scalar variables. It is inferred that like general relativity, one can investigate the evolutionary stages of stellar compact objects with the help of extended scalar parameters.

scholarly journals The Energy-Momentum Tensor in Relativistic Kinetic Theory: The Role of the Center of Mass Velocity in the Transport Equations for Multicomponent Mixtures

2019 ◽  
Vol 44 (2) ◽  
pp. 169-179 ◽  
Author(s):  
A. R. Sagaceta-Mejía ◽  
A. Sandoval-Villalbazo ◽  
J. H. Mondragón-Suárez
Keyword(s):  
Kinetic Theory ◽  
Mass Velocity ◽  
Energy Momentum Tensor ◽  
Center Of Mass ◽  
Momentum Tensor ◽  
Multicomponent Mixtures ◽  
Balance Equations ◽  
Relativistic Kinetic Theory ◽  
Physical Features

Abstract Relativistic kinetic theory is applied to the study of the balance equations for relativistic multicomponent mixtures, comparing the approaches corresponding to Eckart’s and Landau–Lifshitz’s frames. It is shown that the concept of particle velocity relative to the center of mass of the fluid is essential to establish the structure of the energy-momentum tensor in both cases. Different operational definitions of the center of mass velocity lead either to the inclusion of heat in the energy-momentum tensor (particle/Eckart frame) or to strictly relativistic contributions to the diffusion fluxes (energy/Landau–Lifshitz frame). The results here obtained are discussed emphasizing the physical features regarding each approach.

scholarly journals Collapse in f(R) gravity and the method of R matching

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Sandip Chowdhury ◽  
Kunal Pal ◽  
Kuntal Pal ◽  
Tapobrata Sarkar
Keyword(s):  
Energy Momentum Tensor ◽  
Normal Derivative ◽  
Analytic Solutions ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Interior Solution ◽  
Zero Shear Viscosity ◽  
Naked Singularities ◽  
Separable Case

AbstractCollapsing solutions in f(R) gravity are restricted due to junction conditions that demand continuity of the Ricci scalar and its normal derivative across the time-like collapsing hypersurface. These are obtained via the method of R-matching, which is ubiquitous in f(R) collapse scenarios. In this paper, we study spherically symmetric collapse with the modification term $$\alpha R^2$$ α R 2 , and use R-matching to exemplify a class of new solutions. After discussing some mathematical preliminaries by which we obtain an algebraic relation between the shear and the anisotropy in these theories, we consider two metric ansatzes. In the first, the collapsing metric is considered to be a separable function of the co-moving radius and time, and the collapse is shear-free, and in the second, a non-separable interior solution is considered, that represents gravitational collapse with non-zero shear viscosity. We arrive at novel solutions that indicate the formation of black holes or locally naked singularities, while obeying all the necessary energy conditions. The separable case allows for a simple analytic expression of the energy-momentum tensor, that indicates the positivity of the pressures throughout collapse, and is further used to study the heat flux evolution of the collapsing matter, whose analytic solutions are presented under certain approximations. These clearly highlight the role of modified gravity in the examples that we consider.

MASS AND ENERGY-MOMENTUM TENSOR OF QUANTUM STRINGS IN GRAVITATIONAL SHOCK-WAVES

1992 ◽  
Vol 07 (13) ◽  
pp. 3043-3064 ◽  
Author(s):  
H. J. DE VEGA ◽  
N. SANCHEZ
Keyword(s):  
Shock Waves ◽  
Energy Momentum Tensor ◽  
Fock Space ◽  
Momentum Tensor ◽  
Space Time ◽  
Integral Representations ◽  
Tree Level ◽  
Expectation Values ◽  
Localized Source

We investigate at the quantum level the nonlinear transformation relating the string operators (zero modes and oscillators) and Fock space states before and after the collision with gravitational shock waves. This throws light on the rôle of the space–time geometry in this problem. We do all the treatment for a general shock wave space–time of any localized source. We compute the exact expectation values of the total number (N) and mass ( M 2) operators and show that they are finite, which generalize our previous results in the Aichelburg–Sexl geometry. We study the energy-momentum tensor of the string and compute the exact expectation values of all its components. We analyze vacuum polarization and quadratic fluctuations. All these physical magnitudes are finite. We express all of them in terms of exact integral representations in which the role of the real pole singularities characteristic of the tree level string spectrum (real mass resonances) are clearly exhibited. The presence of such poles is not at all related to the structure of the space–time geometry (which may or may not be singular).

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