scholarly journals Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Ion V. Vancea
Keyword(s):  
Evolution Equations ◽  
Equations Of Motion ◽  
Target Space ◽  
Nonequilibrium Dynamics ◽  
De Sitter ◽  
Field Representation ◽  
The North ◽  
Penrose Diagram ◽  
Heisenberg Type ◽  
Model Equations

The two-dimensional σ-model with the de Sitter target space is locally canonic in the north pole diamond of the Penrose diagram in the cosmological gauge. The left and right moving modes on the cylindrical base space are entangled among themselves and interact with the de Sitter metric. Firstly, we show that the untangled oscillators can be obtained from the entangled operators by applying a set of Bogoliubov transformations constrained by the requirement that the partial evolution generator be diagonal. Secondly, we determine the nonequilibrium dynamics of the untangled modes in the nonequilibrium thermofield dynamics formalism. The thermal modes are represented as thermal doublet oscillators that satisfy partial evolution equations of Heisenberg-type. From these we compute the local free one-body propagator of an arbitrary mode between two times. Thirdly, we discuss the field representation of the thermal modes. We show that there is a set of thermal doublet fields that satisfy the equal time canonical commutation relations, are solutions to the σ-model equations of motion, and can be decomposed in terms of thermal doublet oscillators. Finally, we construct a local partial evolution functional of Hamilton-like form for the thermal doublet fields.

A STRING MODEL FOR D-DIMENSIONAL DE SITTER SPACE–TIME AND EQUATIONS OF MOTION

2005 ◽  
Vol 20 (26) ◽  
pp. 6065-6081
Author(s):  
PAUL BRACKEN
Keyword(s):  
Evolution Equations ◽  
Gordon Equation ◽  
Equations Of Motion ◽  
String Model ◽  
De Sitter Space ◽  
Space Time ◽  
System Of Equations ◽  
De Sitter ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

De Sitter space–time is considered to be represented by a D-dimensional hyperboloid embedded in (D+1)-dimensional Minkowski space–time. The string equation is derived from a string action which contains a Lagrange multiplier to restrict coordinates to de Sitter space–time. The string system of equations is equivalent to a type of generalized sinh–Gordon equation. The evolution equations for all the variables including the coordinates and their derivatives are obtained for D=2,3 and 4.

scholarly journals The third way to 3D gravity

2015 ◽  
Vol 24 (12) ◽  
pp. 1544015 ◽  
Author(s):  
Eric Bergshoeff ◽  
Wout Merbis ◽  
Alasdair J. Routh ◽  
Paul K. Townsend
Keyword(s):  
Equations Of Motion ◽  
Massive Gravity ◽  
De Sitter ◽  
Gravitational Field Equation ◽  
Third Way ◽  
Metric Tensor ◽  
The Third ◽  
Higher Dimensional ◽  
Conservation Condition ◽  
3D Gravity

Consistency of Einstein’s gravitational field equation [Formula: see text] imposes a “conservation condition” on the [Formula: see text]-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a “nongeometrical” action: one not constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D “minimal massive gravity” model, which resolves the “bulk versus boundary” unitarity problem of topologically massive gravity with Anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher dimensional theories.

scholarly journals DUALITY AND SELF-DUAL TRIPLET SOLUTIONS IN EUCLIDEAN GRAVITY

1996 ◽  
Vol 11 (34) ◽  
pp. 2669-2679
Author(s):  
SWAPNA MAHAPATRA
Keyword(s):  
String Theory ◽  
The Self ◽  
Target Space ◽  
De Sitter ◽  
Gravitational Instanton ◽  
Duality Symmetry ◽  
Sitter Solution

Starting from the self-dual “triplet” of gravitational instanton solutions in Euclidean gravity, we obtain the corresponding instanton solutions in string theory by making use of the target space duality symmetry. We show that these dual triplet solutions can be obtained from the general dual Taub-NUT de Sitter solution through some limiting procedure as in the Euclidean gravity case. The dual gravitational instanton solutions obtained here are self-dual for some cases, with respect to certain isometries, but not always.

scholarly journals LOOP VARIABLES AND THE INTERACTING OPEN STRING IN A CURVED BACKGROUND

2005 ◽  
Vol 20 (14) ◽  
pp. 1037-1045
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Invariance ◽  
Equations Of Motion ◽  
Interaction Strength ◽  
Flat Space ◽  
Open String ◽  
Target Space ◽  
Gauge Invariant ◽  
Free Case ◽  
New Feature ◽  
Generally Covariant

Applying the loop variable proposal to a sigma model (with boundary) in a curved target space, we give a systematic method for writing the gauge and generally covariant interacting equations of motion for the modes of the open string in a curved background. As in the free case described in an earlier paper, the equations are obtained by covariantizing the flat space (gauge invariant) interacting equations and then demanding gauge invariance in the curved background. The resulting equation has the form of a sum of terms that would individually be gauge invariant in flat space or at zero interaction strength, but mix amongst themselves in curved space when interactions are turned on. The new feature is that the loop variables are deformed so that there is a mixing of modes. Unlike the free case, the equations are coupled, and all the modes of the open string are required for gauge invariance.

scholarly journals Charged anti-de Sitter BTZ black holes in Maxwell-f(T) gravity

2018 ◽  
Vol 33 (13) ◽  
pp. 1850076 ◽  
Author(s):  
G. G. L. Nashed ◽  
S. Capozziello
Keyword(s):  
Black Holes ◽  
Special Form ◽  
Energy Content ◽  
Equations Of Motion ◽  
Main Task ◽  
Cauchy Horizon ◽  
De Sitter ◽  
Vector Form ◽  
Charged Case ◽  
General Vector

Inspired by the Bañados, Teitelboim and Zanelli (BTZ) formalism, we discuss the Maxwell-[Formula: see text] gravity in [Formula: see text] dimensions. The main task is to derive exact solutions for a special form of [Formula: see text], with [Formula: see text] being the torsion scalar of Weitzenböck geometry. To this end, a triad field is applied to the equations of motion of charged [Formula: see text] and sets of circularly symmetric noncharged and charged solutions have been derived. We show that, in the charged case, the monopole-like and the [Formula: see text] terms are linked by a correlative constant despite the known results in teleparallel geometry and its extensions.[Formula: see text] Furthermore, it is possible to show that the event horizon is not identical with the Cauchy horizon due to such a constant. The singularities and the horizons of these black holes are examined: they are new and have no analogue in the literature due to the fact that their curvature singularities are soft. We calculate the energy content of these solutions by using the general vector form of the energy–momentum within the framework of [Formula: see text] gravity. Finally, some thermodynamical quantities, like entropy and Hawking temperature, are derived.

Dynamics of extended bodies in general relativity. I. Momentum and angular momentum

1970 ◽  
Vol 314 (1519) ◽  
pp. 499-527 ◽  
Keyword(s):  
Equations Of Motion ◽  
Potential Energy Function ◽  
Test Body ◽  
The Body ◽  
External Fields ◽  
De Sitter ◽  
Extended Body ◽  
Rest Energy ◽  
Momentum Vector ◽  
De Sitter Universe

Definitions are proposed for the total momentum vector p α and spin tensor S αβ of an extended body in arbitrary gravitational and electromagnetic fields. These are based on the requirement that a symmetry of the external fields should imply conservation of a corresponding component of momentum and spin. The particular case of a test body in a de Sitter universe is considered in detail, and used to support the definition p β S αβ = 0 for the centre of mass. The total rest energy M is defined as the length of the momentum vector. Using equations of motion to be derived in subsequent papers on the basis of these definitions, the time dependence of M is studied, and shown to be expressible as the sum of two contributions, the change in a potential energy function ϕ and a term representing energy inductively absorbed, as in Bondi’s illustration of Tweedledum and Tweedledee. For a body satisfying certain conditions described as ‘dynamical rigidity’, there exists, for motion in arbitrary external fields, a mass constant m such that M = m + ½ S κ Ω κ + ϕ , where Ω k is the angular velocity of the body and S κ its spin vector.

CRITICAL BEHAVIOR IN TWO-DIMENSIONAL QUANTUM GRAVITY AND EQUATIONS OF MOTION OF THE STRING

1990 ◽  
Vol 05 (11) ◽  
pp. 799-813 ◽  
Author(s):  
SUMIT R. DAS ◽  
AVINASH DHAR ◽  
SPENTA R. WADIA
Keyword(s):  
Equations Of Motion ◽  
Two Dimensions ◽  
Target Space ◽  
Two Dimensional ◽  
Minimal Models ◽  
Conformally Invariant ◽  
Motion Time ◽  
Dynamical Degree ◽  
Renormalization Group Equations

We show how consistent quantization determines the renormalization of couplings in a quantum field theory coupled to gravity in two dimensions. The special status of couplings corresponding to conformally invariant matter is discussed. In string theory, where the dynamical degree of freedom of the two-dimensional metric plays the role of time in target space, these renormalization group equations are themselves the classical equations of motion. Time independent solutions, like classical vacuua, correspond to the situation in which matter is conformally invariant. Time dependent solutions, like tunnelling configurations between vacuua, correspond to special trajectories in theory space. We discuss an example of such a trajectory in the space containing the c < 1 minimal models. We also discuss the connection between this work and the recent attempts to construct non-perturbative string theories based on matrix models.

Exact solutions for scalar field cosmology in f(R) gravity

2017 ◽  
Vol 32 (30) ◽  
pp. 1750164 ◽  
Author(s):  
S. D. Maharaj ◽  
R. Goswami ◽  
S. V. Chervon ◽  
A. V. Nikolaev
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Scalar Curvature ◽  
Evolution Equations ◽  
Initial Conditions ◽  
De Sitter ◽  
Airy Functions ◽  
Special Cases ◽  
The Universe ◽  
Current Stage

We study scalar field FLRW cosmology in the content of f(R) gravity. Our consideration is restricted to the spatially flat Friedmann universe. We derived the general evolution equations of the model, and showed that the scalar field equation is automatically satisfied for any form of the f(R) function. We also derived representations for kinetic and potential energies, as well as for the acceleration in terms of the Hubble parameter and the form of the f(R) function. Next we found the exact cosmological solutions in modified gravity without specifying the f(R) function. With negligible acceleration of the scalar curvature, we found that the de Sitter inflationary solution is always attained. Also we obtained new solutions with special restrictions on the integration constants. These solutions contain oscillating, accelerating, decelerating and even contracting universes. For further investigation, we selected special cases which can be applied with early or late inflation. We also found exact solutions for the general case for the model with negligible acceleration of the scalar curvature in terms of special Airy functions. Using initial conditions which represent the universe at the present epoch, we determined the constants of integration. This allows for the comparison of the scale factor in the new solutions with that for current stage of the universe evolution in the [Formula: see text]CDM model.

scholarly journals INFLATIONARY DILATONIC de SITTER UNIVERSE FROM ${\mathcal N} = 4$ SUPER-YANG–MILLS THEORY PERTURBED BY SCALARS

2003 ◽  
Vol 18 (18) ◽  
pp. 1257-1264
Author(s):  
JOHN QUIROGA HURTADO
Keyword(s):  
Effective Action ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Scale Factor ◽  
Conformal Anomaly ◽  
Inflationary Universe ◽  
De Sitter ◽  
Yang Mills ◽  
The Stability ◽  
Super Yang Mills Theory

In this paper a quantum [Formula: see text] super-Yang–Mills theory perturbed by dilaton-coupled scalars, is considered. The induced effective action for such a theory is calculated on a dilaton-gravitational background using the conformal anomaly found via AdS/CFT correspondence. Considering such an effective action (using the large N method) as a quantum correction to the classical gravity action with cosmological constant we study the effect from dilaton to the scale factor (which corresponds to the inflationary universe without dilaton). It is shown that, depending on the initial conditions for the dilaton, the dilaton may slow down, or accelerate, the inflation process. At late times, the dilaton is decaying exponentially. At the end of this work, we consider the question how the perturbation of the solution for the scale factor affects the stability of the solution for the equations of motion and therefore the stability of the Inflationary Universe, which could be eternal.

scholarly journals STRING QUANTIZATION IN CURVED SPACETIMES: NULL STRING APPROACH

1995 ◽  
Vol 10 (32) ◽  
pp. 2479-2484 ◽  
Author(s):  
H.J. DE VEGA ◽  
I. GIANNAKIS ◽  
A. NICOLAIDIS
Keyword(s):  
Equations Of Motion ◽  
Critical Dimension ◽  
String Tension ◽  
Conformal Anomaly ◽  
De Sitter ◽  
Gravitational Fields ◽  
First Order ◽  
Sitter Spacetime ◽  
The Right ◽  
Null String

We study quantum strings in strong gravitational fields. The relevant small parameter is [Formula: see text] where Rc is the curvature of the spacetime and T0 is the string tension. Within our systematic expansion we obtain to zeroth-order the null string (string with zero tension), while the first-order correction incorporates the string dynamics. We apply our formalism to quantum null strings in de Sitter spacetime. After a reparametrization of the worldsheet coordinates, the equations of motion are simplified. The quantum algebra generated by the constraints is considered, ordering the momentum operators to the right of the coordinate operators. No critical dimension appears. It is anticipated, however, that the conformal anomaly will appear when the first-order corrections proportional to T0, are introduced.

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