scholarly journals Existence and Uniqueness of Solutions of the Semiclassical Einstein Equation in Cosmological Models

2021 ◽  
Author(s):  
Paolo Meda ◽  
Nicola Pinamonti ◽  
Daniel Siemssen
Keyword(s):  
Einstein Equation ◽  
Existence And Uniqueness ◽  
Inversion Formula ◽  
Initial Conditions ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Expectation Values ◽  
Uniqueness Of Solutions ◽  
Stress Energy ◽  
Non Local

AbstractWe prove existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar curvature. In the semiclassical approximation, the backreaction of matter to curvature is taken into account by equating the Einstein tensor to the expectation values of the stress-energy tensor in a suitable state. We impose initial conditions for the scale factor at finite time, and we show that a regular state for the quantum matter compatible with these initial conditions can be chosen. Contributions with derivative of the coefficient of the metric higher than the second are present in the expectation values of the stress-energy tensor and the term with the highest derivative appears in a non-local form. This fact forbids a direct analysis of the semiclassical equation, and in particular, standard recursive approaches to approximate the solution fail to converge. In this paper, we show that, after partial integration of the semiclassical Einstein equation in cosmology, the non-local highest derivative appears in the expectation values of the stress-energy tensor through the application of a linear unbounded operator which does not depend on the details of the chosen state. We prove that an inversion formula for this operator can be found, furthermore, the inverse happens to be more regular than the direct operator and it has the form of a retarded product, hence, causality is respected. The found inversion formula applied to the traced Einstein equation has thus the form of a fixed point equation. The proof of local existence and uniqueness of the solution of the semiclassical Einstein equation is then obtained applying the Banach fixed point theorem.

scholarly journals BMS flux algebra in celestial holography

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Laura Donnay ◽  
Romain Ruzziconi
Keyword(s):  
Solution Space ◽  
Coadjoint Representation ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Asymptotically Flat ◽  
Flat Spacetime ◽  
Stress Energy ◽  
Momentum Fluxes ◽  
Non Local ◽  
Asymptotic Symmetries

Abstract Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. The transformation under the action of asymptotic symmetries and the OPEs of the celestial CFT currents are deduced from the BMS flux algebra.

SQUEEZED STATE REPRESENTATION OF QUANTUM FLUCTUATIONS AND SEMICLASSICAL THEORY

1998 ◽  
Vol 13 (03) ◽  
pp. 165-172 ◽  
Author(s):  
P. K. SURESH ◽  
V. C. KURIAKOSE
Keyword(s):  
Anisotropic Pressure ◽  
Energy Tensor ◽  
Semiclassical Theory ◽  
Stress Energy Tensor ◽  
Squeezed State ◽  
State Representation ◽  
Expectation Values ◽  
Squeezed Vacuum ◽  
Stress Energy ◽  
Vacuum States

A squeezed state representation is constructed for each mode of a quantized scalar field in a classical spatially homogeneous anisotropic background cosmology. The expectation values of stress–energy tensor are calculated in squeezed vacuum states. The results for the fluctuations in energy density and anisotropic pressure are also presented.

scholarly journals AN ISOTROPIZATION MECHANISM IN BIANCHI I MODEL

2003 ◽  
Vol 12 (08) ◽  
pp. 1499-1508
Author(s):  
H. H. FLICHE ◽  
R. TRIAY ◽  
M. NOVELLO ◽  
L. R. De FREITAS
Keyword(s):  
Initial Conditions ◽  
Hamiltonian Formalism ◽  
Anisotropic Pressure ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Stress Energy ◽  
Elimination Mechanism ◽  
Pass Through ◽  
The Universe ◽  
Efficient Elimination

We ask whether the problem on the initial conditions in Cosmology can be solved if an efficient elimination mechanism of the anisotropy was present at earlier epochs. We explore the consequences of the existence of an epoch in which the material content of the Universe was represented by an stress-energy tensor possessing anisotropic pressure which depends nonlinearly on the expansion parameter. We show that for selected candidate behaviors the associated shear pass through a maximum and vanishes asymptotically. We use the Hamiltonian formalism to define a constant of motion which enables us to classify the cosmological world-models.

scholarly journals Stress-energy tensor correlators from the world-sheet

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hanno Bertle ◽  
Andrea Dei ◽  
Matthias R. Gaberdiel
Keyword(s):  
Vertex Operator ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
World Sheet ◽  
Stress Energy ◽  
The World

Abstract The large N limit of symmetric orbifold theories was recently argued to have an AdS/CFT dual world-sheet description in terms of an sl(2, ℝ) WZW model. In previous work the world-sheet state corresponding to the symmetric orbifold stress-energy tensor was identified. We calculate certain 2- and 3-point functions of the corresponding vertex operator on the world-sheet, and demonstrate that these amplitudes reproduce exactly what one expects from the dual symmetric orbifold perspective.

ON THE ELECTROMAGNETIC PERTURBATIONS OF A MULTICONICAL SPACETIME

1996 ◽  
Vol 11 (27) ◽  
pp. 2171-2177
Author(s):  
A.N. ALIEV
Keyword(s):  
Cosmic Strings ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Stress Energy ◽  
Electromagnetic Perturbations

The electromagnetic perturbations propagating in the multiconical spacetime of N parallel cosmic strings are described. The expression for vacuum average of the stress-energy tensor is reduced to a form involving only zero-spin-weighted perturbation modes.

scholarly journals Kerr-Newman stress-tensor from minimal coupling

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Ming-Zhi Chung ◽  
Yu-tin Huang ◽  
Jung-Wook Kim
Keyword(s):  
Form Factor ◽  
Stress Tensor ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Minimal Coupling ◽  
Massive Spin ◽  
Stress Energy ◽  
Newman Black Hole ◽  
Higher Spin ◽  
The One

Abstract In this paper, we demonstrate that at leading order in post Minkowskian (PM) expansion, the stress-energy tensor of Kerr-Newman black hole can be recovered to all orders in spin from three sets of minimal coupling: the electric and gravitational minimal coupling for higher-spin particles, and the “minimal coupling” for massive spin-2 decay. These couplings are uniquely defined from kinematic consideration alone. This is shown by extracting the classical piece of the one-loop stress-energy tensor form factor, which we provide a basis that is valid to all orders in spin. The 1 PM stress tensor, and the metric in the harmonic gauge, is then recovered from the classical spin limit of the form factor.

scholarly journals Stress Energy Tensor Study in Fluid Mechanics

2019 ◽  
Author(s):  
Roman Baudrimont
Keyword(s):  
General Relativity ◽  
Fluid Mechanics ◽  
Space Time ◽  
Newtonian Fluids ◽  
Third Party ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Perfect Fluids ◽  
Stress Energy

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

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