scholarly journals ADM MASS, BONDI MASS, AND ENERGY CONSERVATION IN TWO-DIMENSIONAL DILATON GRAVITIES

1996 ◽  
Vol 11 (03) ◽  
pp. 553-561 ◽  
Author(s):  
WON T. KIM ◽  
JULIAN LEE
Keyword(s):  
Boundary Condition ◽  
Energy Conservation ◽  
Radiation Energy ◽  
Two Dimensional ◽  
Dilaton Gravity ◽  
Null Infinity ◽  
Adm Mass ◽  
Stress Energy ◽  
Bondi Mass ◽  
Definition Of

We show how a stress-energy pseudotensor can be constructed in two-dimensional dilaton gravity theories (classical, CGHS and RST) and derive from it the expression for the ADM mass in these theories. We compare this expression with the ones in the literature obtained by other methods. We define the Bondi mass for these theories by using the pseudotensor formalism. The resulting expression is the generalization of the expression for the ADM mass. The boundary condition needed for the energy conservation is also investigated. It is shown that under appropriate boundary conditions, our definition of the Bondi mass is exactly the ADM mass minus the matter radiation energy at null infinity.

scholarly journals Classifying boundary conditions in JT gravity: from energy-branes to α-branes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Akash Goel ◽  
Luca V. Iliesiu ◽  
Jorrit Kruthoff ◽  
Zhenbin Yang
Keyword(s):  
Boundary Condition ◽  
Black Holes ◽  
Boundary Conditions ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Ensemble Averaging ◽  
Matrix Integral ◽  
Two Dimensional Model ◽  
Definition Of ◽  
Extremal Black Holes

Abstract We classify the possible boundary conditions in JT gravity and discuss their exact quantization. Each boundary condition that we study will reveal new features in JT gravity related to its matrix integral interpretation, its factorization properties and ensemble averaging interpretation, the definition of the theory at finite cutoff, its relation to the physics of near-extremal black holes and, finally, its role as a two-dimensional model of cosmology.

scholarly journals A new look at the Bondi-Sachs energy-momentum

2021 ◽  
Author(s):  
Jörg Frauendiener ◽  
Chris Stevens
Keyword(s):  
Unit Sphere ◽  
Gauss Curvature ◽  
Null Infinity ◽  
Conformally Invariant ◽  
Lorentzian Metric ◽  
Correct Definition ◽  
Ghp Formalism ◽  
Bondi Mass ◽  
Definition Of ◽  
Bondi Energy

Abstract How does one compute the Bondi mass on an arbitrary cut of null infinity I when it is not presented in a Bondi system? What then is the correct definition of the mass aspect? How does one normalise an asymptotic translation computed on a cut which is not equipped with the unit-sphere metric? These are questions which need to be answered if one wants to calculate the Bondi-Sachs energy-momentum for a space-time which has been determined numerically. Under such conditions there is not much control over the presentation of I so that most of the available formulations of the Bondi energy-momentum simply do not apply. The purpose of this article is to provide the necessary background for a manifestly conformally invariant and gauge independent formulation of the Bondi energy-momentum. To this end we introduce a conformally invariant version of the GHP formalism to rephrase all the well-known formulae. This leads us to natural definitions for the space of asymptotic translations with its Lorentzian metric, for the Bondi news and the mass-aspect. A major role in these developments is played by the “co-curvature”, a naturally appearing quantity closely related to the Gauß curvature on a cut of I.

scholarly journals Two-dimensional dilaton gravity theory and lattice Schwarzian theory

2019 ◽  
Vol 34 (29) ◽  
pp. 1950176
Author(s):  
Su-Kuan Chu ◽  
Chen-Te Ma ◽  
Chih-Hung Wu
Keyword(s):  
Boundary Condition ◽  
Cosmological Constant ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Gravity Theory ◽  
Boundary Theory ◽  
Two Dimensional ◽  
Dilaton Field ◽  
Dilaton Gravity ◽  
Cosmological Constants

We report a holographic study of a two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the cases of nonvanishing and vanishing cosmological constants. Our result shows that the boundary theory of the two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the case of nonvanishing cosmological constants is the Schwarzian term coupled to a dilaton field, while for the case of vanishing cosmological constant, a theory does not have a kinetic term. We also include the higher derivative term [Formula: see text], where [Formula: see text] is the scalar curvature that is coupled to a dilaton field. We find that the form of the boundary theory is not modified perturbatively. Finally, we show that a lattice holographic picture is realized up to the second-order perturbation of boundary cutoff [Formula: see text] under a constant boundary dilaton field and the nonvanishing cosmological constant by identifying the lattice spacing [Formula: see text] of a lattice Schwarzian theory with the boundary cutoff [Formula: see text] of the two-dimensional dilaton gravity theory.

Gravitational radiation near spatial and null infinity

1987 ◽  
Vol 410 (1838) ◽  
pp. 201-208 ◽  
Keyword(s):  
Radiation Field ◽  
Gravitational Radiation ◽  
Null Infinity ◽  
Adm Mass ◽  
Formal Expansion ◽  
Bondi Mass ◽  
Expansion Coefficients ◽  
Analytic Behaviour

Taking Bondi’s approach to an extreme by adding a 1/ u -expansion to the usual 1/ r -expansion, one can study the effects of the presence of mass at space-like infinity. Assuming convergence of the formal expansion one finds: (1) the limit of the Bondi mass agrees with the ADM-mass of certain space-like hypersurfaces; (2) relations between expansion coefficients on space-like hypersurfaces and the radiation field on J + can be given; (3) analytic properties in J + lead to non-analytic behaviour on space-like hypersurfaces.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

scholarly journals Multi-objective parametrization of interatomic potentials for large deformation pathways and fracture of two-dimensional materials

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Xu Zhang ◽  
Hoang Nguyen ◽  
Jeffrey T. Paci ◽  
Subramanian K. R. S. Sankaranarayanan ◽  
Jose L. Mendoza-Cortes ◽  
...  
Keyword(s):  
Large Deformation ◽  
Functional Form ◽  
Principal Component ◽  
Interatomic Potentials ◽  
Two Dimensional ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Two Dimensional Materials ◽  
Definition Of

AbstractThis investigation presents a generally applicable framework for parameterizing interatomic potentials to accurately capture large deformation pathways. It incorporates a multi-objective genetic algorithm, training and screening property sets, and correlation and principal component analyses. The framework enables iterative definition of properties in the training and screening sets, guided by correlation relationships between properties, aiming to achieve optimal parametrizations for properties of interest. Specifically, the performance of increasingly complex potentials, Buckingham, Stillinger-Weber, Tersoff, and modified reactive empirical bond-order potentials are compared. Using MoSe2 as a case study, we demonstrate good reproducibility of training/screening properties and superior transferability. For MoSe2, the best performance is achieved using the Tersoff potential, which is ascribed to its apparent higher flexibility embedded in its functional form. These results should facilitate the selection and parametrization of interatomic potentials for exploring mechanical and phononic properties of a large library of two-dimensional and bulk materials.

scholarly journals Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clifford V. Johnson ◽  
Felipe Rosso
Keyword(s):  
Phase Structure ◽  
Scalar Potential ◽  
String Equation ◽  
Two Dimensional ◽  
Leading Order ◽  
Classical Analysis ◽  
First Order ◽  
First Order Phase Transition ◽  
Definition Of ◽  
First Order Phase

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation

2018 ◽  
Vol 61 (4) ◽  
pp. 768-786 ◽  
Author(s):  
Liangliang Li ◽  
Jing Tian ◽  
Goong Chen
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Method Of Characteristics ◽  
Nonlinear Boundary ◽  
Chaotic Oscillation ◽  
Nonlinear Boundary Conditions ◽  
Rigorous Proof ◽  
Two Dimensional ◽  
Chaotic Vibration

AbstractThe study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.

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