scholarly journals OPERATIONAL GEOMETRY ON DE SITTER SPACETIME

2012 ◽  
Vol 27 (23) ◽  
pp. 1250130 ◽  
Author(s):  
P. AGUILAR ◽  
Y. BONDER ◽  
C. CHRYSSOMALAKOS ◽  
D. SUDARSKY
Keyword(s):  
Quantum Theory ◽  
Operational Definition ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Spacetime Geometry ◽  
Point Particles ◽  
Sitter Spacetime ◽  
Classical Point Particles ◽  
Definition Of ◽  
Classical Point

Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though, leading us to consider the implications of using realistic probes in defining an effective spacetime geometry. As an example, we consider de Sitter spacetime and employ the centroid of various composite probes to obtain its effective sectional curvature, which is found to depend on the probe's internal energy, spatial extension, and spin. Possible refinements of our approach are pointed out and remarks are made on the relevance of our results to the quest for a quantum theory of gravity.

scholarly journals On the algebraic quantization of a massive scalar field in anti-de Sitter spacetime

2018 ◽  
Vol 30 (02) ◽  
pp. 1850004 ◽  
Author(s):  
Claudio Dappiaggi ◽  
Hugo R. C. Ferreira
Keyword(s):  
Scalar Field ◽  
De Sitter Spacetime ◽  
Massive Scalar ◽  
De Sitter ◽  
Functional Formalism ◽  
Arbitrary Boundary ◽  
Massive Scalar Field ◽  
Sitter Spacetime ◽  
Hadamard States ◽  
Definition Of

We discuss the algebraic quantization of a real, massive scalar field in the Poincaré patch of the [Formula: see text]-dimensional anti-de Sitter spacetime, with arbitrary boundary conditions. By using the functional formalism, we show that it is always possible to associate to such system an algebra of observables enjoying the standard properties of causality, time-slice axiom and F-locality. In addition, we characterize the wavefront set of the ground state associated to the system under investigation. As a consequence, we are able to generalize the definition of Hadamard states and construct a global algebra of Wick polynomials.

BACK REACTION IN SCHWARZSCHILD–de SITTER SPACETIME WITH A MASSLESS QUANTUM FIELD

2006 ◽  
Vol 21 (02) ◽  
pp. 169-179
Author(s):  
P. I. KURIAKOSE ◽  
V. C. KURIAKOSE
Keyword(s):  
Black Hole ◽  
Effective Potential ◽  
Thermal Equilibrium ◽  
Back Reaction ◽  
De Sitter Spacetime ◽  
Quantum Field ◽  
De Sitter ◽  
Spacetime Geometry ◽  
Sitter Spacetime ◽  
Massless Quantum

Back reaction in the Schwarzschild–de Sitter black hole in thermal equilibrium with conformal massless quantum field is discussed using the method of York. The presence of quantum field and back reaction ensures the entropy of dressed black hole. In the perturbed spacetime geometry, the nature of the effective potential and the orbits of massless and massive particles are also investigated.

scholarly journals Riemann curvature of a boosted spacetime geometry

2016 ◽  
Vol 13 (01) ◽  
pp. 1650002
Author(s):  
Emmanuele Battista ◽  
Giampiero Esposito ◽  
Paolo Scudellaro ◽  
Francesco Tramontano
Keyword(s):  
Curvature Tensor ◽  
Initial Conditions ◽  
Geodesic Equation ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Spacetime Geometry ◽  
Sitter Spacetime ◽  
First Time

The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild–de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild–de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature, through Dirac’s [Formula: see text] distribution and its derivatives, is numerically evaluated for this class of spacetimes. Moreover, the analysis of the Kretschmann invariant and the geodesic equation shows that the spacetime possesses a “scalar curvature singularity” within a 3-sphere and it is possible to define what we here call “boosted horizon”, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. This seems to suggest that such “boosted geometries” are ruled by a sort of “antigravity effect” since all geodesics seem to refuse to enter the “boosted horizon” and are “reflected” by it, even though their initial conditions are aimed at driving the particles toward the “boosted horizon” itself. Eventually, the equivalence with the coordinate shift method is invoked in order to demonstrate that all [Formula: see text] terms appearing in the Riemann curvature tensor give vanishing contribution in distributional sense.

scholarly journals ON BELTRAMI MODEL OF de SITTER SPACETIME

2004 ◽  
Vol 19 (22) ◽  
pp. 1701-1709 ◽  
Author(s):  
HAN-YING GUO ◽  
CHAO-GUANG HUANG ◽  
ZHAN XU ◽  
BIN ZHOU
Keyword(s):  
Large Scale ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Spatial Curvature ◽  
Relativity Principle ◽  
Sitter Spacetime ◽  
Test Particles ◽  
Light Signals ◽  
Definition Of ◽  
Shed Light

Based on some important properties of dS space, we present a Beltrami model ℬΛ that may shed light on the observable puzzle of dS space and the paradox between the special relativity principle and cosmological principle. In ℬΛ, there are inertial-type coordinates and inertial-type observers. Thus, the classical observables can be defined for test particles and light signals. In addition, by choosing the definition of simultaneity the Beltrami metric is transformed to the Robertson–Walker-like metric. It is of positive spatial curvature of order Λ. This has already been shown by the CMB power spectrum from WMAP and should be further confirmed by its data in large scale.

scholarly journals Entropy in locally-de Sitter spacetimes

2015 ◽  
Vol 24 (14) ◽  
pp. 1550099 ◽  
Author(s):  
A. Araujo ◽  
J. G. Pereira
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
A Priori ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Schwarzschild Solution ◽  
Sitter Group ◽  
Quotient Spaces ◽  
Sitter Spacetime ◽  
Definition Of

As quotient spaces, Minkowski and de Sitter are fundamental spacetimes in the sense that they are known a priori, independently of Einstein equation. They represent different nongravitational backgrounds for the construction of physical theories. If general relativity is constructed on a de Sitter spacetime, the underlying kinematics will no longer be ruled by Poincaré, but by the de Sitter group. In this case the definition of diffeomorphism changes, producing concomitant changes in the notions of energy and entropy. These changes are explicitly discussed for the case of the Schwarzschild solution, in which the black hole and the de Sitter horizons show up as a unique entangled system. Such entanglement, together with energy conservation, create a constraint between the black hole activity and the evolution of the de Sitter radius, providing a new scenario for the study of cosmology.

Localization of energy for a regular black hole solution in an asymptotically de Sitter spacetime geometry

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Irina Radinschi ◽  
Theophanes Grammenos ◽  
Andromahi Spanou
Keyword(s):  
Black Hole ◽  
Black Hole Solution ◽  
Mass Parameter ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Regular Black Hole ◽  
Spacetime Geometry ◽  
Sitter Spacetime ◽  
Momentum Distributions ◽  
Energy And Momentum

AbstractThe energy and momentum distributions of a regular black hole in a four-dimensional, asymptotically de Sitter spacetime geometry are computed, whereby the Einstein, Landau-Lifshitz, Weinberg and Møller energy-momentum complexes are utilized. It is found, for all prescriptions applied, that the momentum distribution vanishes, while the energy distribution depends on the mass parameter M, the electric charge Q, and the cosmological constant Λ. In addition, various limiting cases are discussed.

scholarly journals Unimodular vs nilpotent superfield approach to pure dS supergravity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sukruti Bansal ◽  
Silvia Nagy ◽  
Antonio Padilla ◽  
Ivonne Zavala
Keyword(s):  
String Theory ◽  
General Framework ◽  
Recent Progress ◽  
High Energy ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
New Approach ◽  
Sitter Spacetime ◽  
Novel Approach ◽  
De Sitter Vacua

Abstract Recent progress in understanding de Sitter spacetime in supergravity and string theory has led to the development of a four dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua, also called de Sitter supergravity. One approach makes use of constrained (nilpotent) superfields, while an alternative one couples supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action. These two approaches have been shown to give rise to the same 4D action. A novel approach to de Sitter vacua in supergravity involves the generalisation of unimodular gravity to supergravity using a super-Stückelberg mechanism. In this paper, we make a connection between this new approach and the previous two which are in the context of nilpotent superfields and the goldstino brane. We show that upon appropriate field redefinitions, the 4D actions match up to the cubic order in the fields. This points at the possible existence of a more general framework to obtain de Sitter spacetimes from high-energy theories.

scholarly journals Wavefunctions in dS/CFT revisited: principal series and double-trace deformations

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hiroshi Isono ◽  
Hoiki Madison Liu ◽  
Toshifumi Noumi
Keyword(s):  
Principal Series ◽  
Light Fields ◽  
Quadratic Term ◽  
De Sitter Spacetime ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Complementary Series ◽  
Point Function ◽  
Sitter Spacetime ◽  
Simple Scaling

Abstract We study wavefunctions of heavy scalars on de Sitter spacetime and their implications to dS/CFT correspondence. In contrast to light fields in the complementary series, heavy fields in the principal series oscillate outside the cosmological horizon. As a consequence, the quadratic term in the wavefunction does not follow a simple scaling and so it is hard to identify it with a conformal two-point function. In this paper, we demonstrate that it should be interpreted as a two-point function on a cyclic RG flow which is obtained by double-trace deformations of the dual CFT. This is analogous to the situation in nonrelativistic AdS/CFT with a bulk scalar whose mass squared is below the Breitenlohner-Freedman (BF) bound. We also provide a new dS/CFT dictionary relating de Sitter two-point functions and conformal two-point functions in the would-be dual CFT.

scholarly journals Interacting quantum fields in various charts of anti–de Sitter spacetime

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
E. T. Akhmedov ◽  
A. A. Artemev ◽  
I. V. Kochergin
Keyword(s):  
De Sitter Spacetime ◽  
Quantum Fields ◽  
De Sitter ◽  
Sitter Spacetime
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