scholarly journals Charge conservation, entropy current and gravitation

2021 ◽  
Author(s):  
Sinya Aoki ◽  
Tetsuya Onogi ◽  
Shuichi Yokoyama
Keyword(s):  
Field Theory ◽  
Vector Field ◽  
Vector Fields ◽  
Plane Waves ◽  
Momentum Tensor ◽  
Entropy Density ◽  
Global Symmetry ◽  
Timelike Vector ◽  
First Law Of Thermodynamics ◽  
Entropy Current

We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy–momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even without global symmetry. We also argue that the conserved current constructed from the (asymptotically) timelike vector field can be identified with the entropy current of the system. As a piece of evidence we show that the conserved charge defined therefrom satisfies the first law of thermodynamics for an isotropic system with a suitable definition of temperature. We apply our formulation to several gravitational systems such as the expanding universe, Schwarzschild and Banãdos, Teitelboim and Zanelli (BTZ) black holes, and gravitational plane waves. We confirm the conservation of the proposed entropy density under any homogeneous and isotropic expansion of the universe, the precise reproduction of the Bekenstein–Hawking entropy incorporating the first law of thermodynamics, and the existence of gravitational plane wave carrying no charge, respectively. We also comment on the energy conservation during gravitational collapse in simple models.

scholarly journals Field theory in normal conical coordinates

2021 ◽  
Vol 244 ◽  
pp. 09004
Author(s):  
Dmitry Nesnov
Keyword(s):  
Field Theory ◽  
Vector Field ◽  
Computer Graphics ◽  
Vector Fields ◽  
Complex Structure ◽  
Curvilinear Coordinates ◽  
Mathematical Apparatus ◽  
Spherical Coordinate ◽  
Geometrical Modeling ◽  
Scalar And Vector Fields

In the scientific literature, the field theory is most fully covered in the cylindrical and spherical coordinate systems. This is explained by the fact that the mathematical apparatus of these systems is most well studied. When the source of field has a more complex structure than a point or a straight line, there is a need for new approaches to their study. The goal of this research is to adapt the field theory related to curvilinear coordinates in order to represent it in the normal conical coordinates. In addition, an important part of the research is the development of a geometrical modeling apparatus for scalar and vector field level surfaces using computer graphics. The paper shows the dependences of normal conical coordinates on rectangular Cartesian coordinates, Lame coefficients. The differential characteristics of the scalar and vector fields in normal conical coordinates are obtained: Laplacian of scalar and vector fields, divergence, rotation of the vector field. The example case shows the features of the application of the mathematical apparatus of geometrical field modeling in normal conical coordinates. For the first time, expressions for the characteristics of the scalar and vector fields in normal conical coordinates are obtained. Methods for geometrical modeling of fields using computer graphics have been developed to provide illustration in their study.

scholarly journals Field theory in normal toroidal coordinates

2018 ◽  
Vol 193 ◽  
pp. 03022
Author(s):  
Dmitry V. Nesnov
Keyword(s):  
Field Theory ◽  
Vector Field ◽  
Computer Graphics ◽  
Geometric Modeling ◽  
Vector Fields ◽  
Scientific Paper ◽  
Curvilinear Coordinates ◽  
Coordinate Systems ◽  
Scalar And Vector Fields ◽  
Toroidal Coordinates

Field theory is widely represented in spherical and cylindrical coordinate systems, since the mathematical apparatus of these coordinate systems has been thoroughly studied. Sources of field with more complex structures require new approaches to their study. The purpose of this research is to adapt the field theory referred to curvilinear coordinates and represent it in normal toroidal coordinates. Another purpose is to develop the foundations of geometric modeling with the use of computer graphics for visualizing the level surfaces. The dependence of normal toroidal coordinates on rectangular Cartesian coordinates and Lame coefficients is shown in this scientific paper. Differential characteristics of scalar and vector fields in normal toroidal coordinates are obtained: scalar and vector field laplacians, divergence, and rotation of vector field. The example shows the technique of modeling the field and its further computer visualization. The technique of reading the internal equation of the surface is presented and the influence of the values of the parameters on the shape of the surface is shown. For the first time, expressions of scalar and vector field characteristics in normal toroidal coordinates are obtained, the fundamentals of geometric modeling of fields with the use of computer graphics tools are developed for the purpose of providing visibility for their study.

scholarly journals Kähler metrics via Lorentzian Geometry in dimension four

2019 ◽  
Vol 7 (1) ◽  
pp. 36-61 ◽  
Author(s):  
Amir Babak Aazami ◽  
Gideon Maschler
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Plane Waves ◽  
Killing Vector ◽  
Lorentzian Geometry ◽  
De Sitter ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Open Set ◽  
Sitter Spacetime

AbstractGiven a semi-Riemannian 4-manifold (M, g) with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of Kähler metrics gK is constructed, defined on an open set in M, which coincides with M in many typical examples. Under certain conditions g and gK share various properties, such as a Killing vector field or a vector field with a geodesic flow. In some cases the Kähler metrics are complete. The Ricci and scalar curvatures of gK are computed under certain assumptions in terms of data associated to g. Many examples are described, including classical spacetimes in warped products, for instance de Sitter spacetime, as well as gravitational plane waves, metrics of Petrov type D such as Kerr and NUT metrics, and metrics for which gK is an SKR metric. For the latter an inverse ansatz is described, constructing g from the SKR metric.

scholarly journals Power-law Genesis: Strong coupling and Galileon-like vector fields

2020 ◽  
Vol 35 (37) ◽  
pp. 2050305
Author(s):  
P. K. Petrov
Keyword(s):  
Field Theory ◽  
Vector Field ◽  
Power Law ◽  
Vector Fields ◽  
Energy Condition ◽  
Classical Field Theory ◽  
Flat Space ◽  
Space Time ◽  
Classical Field ◽  
Negative Power

A simple way to construct models with early cosmological Genesis epoch is to employ bosonic fields whose Lagrangians transform homogeneously under scaling transformation. We show that in these theories, for a range of parameters defining the Lagrangian, there exists a homogeneous power-law solution in flat space-time, whose energy density vanishes, while pressure is negative (power-law Genesis). We find the condition for the legitimacy of the classical field theory description of such a situation. We note that this condition does not hold for our earlier Genesis model with vector field. We construct another model with vector field and power-law background solution in flat space-time, which is legitimately treated within classical field theory, violates the Null Energy Condition (NEC) and is stable. Upon turning on gravity, this model describes the early Genesis stage.

scholarly journals WEYL GEOMETRIES AND TIMELIKE GEODESICS

2012 ◽  
Vol 09 (05) ◽  
pp. 1220006 ◽  
Author(s):  
L. FATIBENE ◽  
M. FRANCAVIGLIA
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Timelike Vector ◽  
Weyl Geometry ◽  
Gravitational Fields ◽  
Complete Framework

In view of Ehlers–Pirani–Schild formalism, since 1972 Weyl geometries should be considered to be the most appropriate and complete framework to represent (relativistic) gravitational fields. We shall here show that in any given Lorentzian spacetime (M, g) that admits global timelike vector fields any such vector field u determines an essentially unique Weyl geometry ([g], Γ) such that u is Γ-geodesic (i.e. parallel with respect to Γ).

scholarly journals Canonical transformation path to gauge theories of gravity-II: Space-time coupling of spin-0 and spin-1 particle fields

2019 ◽  
Vol 28 (01n02) ◽  
pp. 1950007 ◽  
Author(s):  
J. Struckmeier ◽  
J. Muench ◽  
P. Liebrich ◽  
M. Hanauske ◽  
J. Kirsch ◽  
...  
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Vector Field ◽  
Vector Fields ◽  
Energy Momentum Tensor ◽  
Scalar Fields ◽  
Momentum Tensor ◽  
Space Time ◽  
Complex Scalar ◽  
Time Dynamics

The generic form of space-time dynamics as a classical gauge field theory has recently been derived, based on only the action principle and on the principle of general relativity. It was thus shown that Einstein’s general relativity is the special case where (i) the Hilbert Lagrangian (essentially the Ricci scalar) is supposed to describe the dynamics of the “free” (uncoupled) gravitational field, and (ii) the energy–momentum tensor is that of scalar fields representing real or complex structureless (spin-[Formula: see text]) particles. It followed that all other source fields — such as vector fields representing massive and nonmassive spin-[Formula: see text] particles — need careful scrutiny of the appropriate source tensor. This is the subject of our actual paper: we discuss in detail the coupling of the gravitational field with (i) a massive complex scalar field, (ii) a massive real vector field, and (iii) a massless vector field. We show that different couplings emerge for massive and nonmassive vector fields. The massive vector field has the canonical energy–momentum tensor as the appropriate source term — which embraces also the energy density furnished by the internal spin. In this case, the vector fields are shown to generate a torsion of space-time. In contrast, the system of a massless and charged vector field is associated with the metric (Hilbert) energy–momentum tensor due to its additional [Formula: see text] symmetry. Moreover, such vector fields do not generate a torsion of space-time. The respective sources of gravitation apply for all models of the dynamics of the “free” (uncoupled) gravitational field — which do not follow from the gauge formalism but must be specified based on separate physical reasoning.

scholarly journals Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yi Li ◽  
Yang Zhou
Keyword(s):  
Field Theory ◽  
Euclidean Plane ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
Conformal Field ◽  
Operator Identity ◽  
Pure Gravity ◽  
Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

scholarly journals Precision Higgs couplings in neutral naturalness models: an effective field theory approach

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Lucien Heurtier ◽  
Hao-Lin Li ◽  
Huayang Song ◽  
Shufang Su ◽  
Wei Su ◽  
...  
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Goldstone Boson ◽  
Higgs Sector ◽  
New Physics ◽  
Effective Field ◽  
Precision Measurements ◽  
Global Symmetry ◽  
Theory Approach ◽  
Decay Channels

AbstractThe Higgs sector in neutral naturalness models provides a portal to the hidden sectors, and thus measurements of Higgs couplings at current and future colliders play a central role in constraining the parameter space of the model. We investigate a class of neutral naturalness models, in which the Higgs boson is a pseudo-Goldstone boson from the universal SO(N)/SO(N −1) coset structure. Integrating out the radial mode from the spontaneous global symmetry breaking, we obtain various dimension-six operators in the Standard Model effective field theory, and calculate the low energy Higgs effective potential with radiative corrections included. We perform aχ2fit to the Higgs coupling precision measurements at current and future colliders and show that the new physics scale could be explored up to 2.3 (2.4) TeV without (with) the Higgs invisible decay channels at future Higgs factories. The limits are comparable to the indirect constraints obtained via electroweak precision measurements.

scholarly journals Pairings between bounded divergence-measure vector fields and BV functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Graziano Crasta ◽  
Virginia De Cicco ◽  
Annalisa Malusa
Keyword(s):  
Vector Field ◽  
Conservation Laws ◽  
Bounded Variation ◽  
Vector Fields ◽  
Hyperbolic Conservation Laws ◽  
Divergence Measure ◽  
Compensated Compactness ◽  
Hyperbolic Conservation ◽  
Bv Functions ◽  
Bounded Functions

AbstractWe introduce a family of pairings between a bounded divergence-measure vector field and a function u of bounded variation, depending on the choice of the pointwise representative of u. We prove that these pairings inherit from the standard one, introduced in [G. Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. (4) 135 1983, 293–318], [G.-Q. Chen and H. Frid, Divergence-measure fields and hyperbolic conservation laws, Arch. Ration. Mech. Anal. 147 1999, 2, 89–118], all the main properties and features (e.g. coarea, Leibniz, and Gauss–Green formulas). We also characterize the pairings making the corresponding functionals semicontinuous with respect to the strict convergence in \mathrm{BV}. We remark that the standard pairing in general does not share this property.

scholarly journals The geometry of null-like disformal transformations

2019 ◽  
Vol 16 (11) ◽  
pp. 1950180 ◽  
Author(s):  
I. P. Lobo ◽  
G. G. Carvalho
Keyword(s):  
Vector Field ◽  
Conformal Transformation ◽  
Vector Fields ◽  
Killing Vector ◽  
Killing Vector Fields ◽  
Spinor Structure ◽  
Schwarzschild Metric ◽  
Killing Vectors ◽  
Symmetry Properties ◽  
Geometric Objects

Motivated by the hindrance of defining metric tensors compatible with the underlying spinor structure, other than the ones obtained via a conformal transformation, we study how some geometric objects are affected by the action of a disformal transformation in the closest scenario possible: the disformal transformation in the direction of a null-like vector field. Subsequently, we analyze symmetry properties such as mutual geodesics and mutual Killing vectors, generalized Weyl transformations that leave the disformal relation invariant, and introduce the concept of disformal Killing vector fields. In most cases, we use the Schwarzschild metric, in the Kerr–Schild formulation, to verify our calculations and results. We also revisit the disformal operator using a Newman–Penrose basis to show that, in the null-like case, this operator is not diagonalizable.

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