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 COVARIANT REPRESENTATIONS OF THE DE SITTER ISOMETRY GROUP

2013 ◽  
Vol 28 (09) ◽  
pp. 1350033 ◽  
Author(s):  
ION I. COTĂESCU
Keyword(s):  
General Theory ◽  
Isometry Group ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Induced Representations ◽  
Covariant Representations ◽  
Sitter Spacetime ◽  
Technical Details ◽  
First Time

We show that the induced representations of the de Sitter isometry group proposed many years ago by Nachtmann are equivalent to those derived from our general theory of external symmetry. These methods complete each other leading to a coherent theory of covariant fields with spin on the de Sitter spacetime. Some technical details of these representations are presented here for the first time.

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 SINGULARITAS SEMU PADA RUANG-WAKTU REISSNER-NORDSTRÖM

2019 ◽  
Vol 5 (2) ◽  
pp. 82
Author(s):  
I Gusti Ngurah Yudi Handayana ◽  
Lily Maysari Angraini
Keyword(s):  
Charged Particle ◽  
Event Horizon ◽  
Curvature Tensor ◽  
Riemann Tensor ◽  
Geodesic Equation ◽  
Riemann Curvature ◽  
Field Equations ◽  
Riemann Curvature Tensor ◽  
Gravitational Pull ◽  
Real Singularities

ABSTRAKPenelitian ini mengkaji singularitas semu pada metrik Reissner-Nordström, yang merupakan solusi persamaan medan Einstein untuk model partikel bermuatan. Kajian dilakukan dengan menganalisis titik-titik singular pada metrik, menghitung tensor kelengkungan Riemann, serta menghitung scalar Kretschmann pada titik-titik tersebut. Perhitungan dilakukan dengan bantuan program Maxima. Hasilnya, singularitas nyata hanya terjadi pada r = 0, sedangkan singularitas semu terjadi pada . Singularitas semu tersebut merupakan representasi dari horizon peristiwa. Terdapat tiga kemungkinan situasi pada horizon peristiwa. Hal menarik terdapat pada situasi r = M, dimana terjadi keseimbangan antara massa dan muatan yang memungkinkan tarikan gravitasi dan tolakan elektromagnetik saling meniadakan. Penelitian ini juga menghasilkan persamaan geodesik pada titik-titik yang tidak menghasilkan nilai infinite pada skalar Kretschmaan. Kata Kunci : Kelengkungan Riemann, Metrik Reisner-Nordström, Singularitas, Persamaan  Geodesik ABSTRACTThis study examines pseudo singularities on the Reissner-Nordström metric which is a solution to Einstein's field equations for charged particle models. The study was carried out by analyzing the singular points on the metric calculating the Riemann curvature tensor, and calculating Kretschmann's scalar at these points. The results show that real singularities only occur at r = 0, whereas pseudo singularity occurs at . There is a point of pseudo singularity that representing the event horizon. There are two possible situations on the event horizon. Interesting things are in the case r = M, where here is a balance between mass and charge which allows gravitational pull and electromagnetic repulsion to cancel each other. This study also yields the geodesic equation point that not yields infinite value of Kretschmaan scalar. Keywords: Riemann tensor, Reissner-Nordström Metrik, Singularities, Geodesik equation

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 A new formula for conserved charges of Lovelock gravity in AdS space–times and its generalization

2020 ◽  
Vol 35 (20) ◽  
pp. 2050102 ◽  
Author(s):  
Jun-Jin Peng ◽  
Hui-Fa Liu
Keyword(s):  
Curvature Tensor ◽  
Invariant Theory ◽  
Gravity Theory ◽  
De Sitter ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Lovelock Gravity ◽  
Conserved Charges ◽  
Rank Tensor ◽  
New Formula

Within the framework of the Lovelock gravity theory, we propose a new rank-four divergenceless tensor consisting of the Riemann curvature tensor and inheriting its algebraic symmetry characters. Such a tensor can be adopted to define conserved charges of the Lovelock gravity theory in asymptotically anti-de Sitter (AdS) space–times. Besides, inspired with the case of the Lovelock gravity, we put forward another general fourth-rank tensor in the context of an arbitrary diffeomorphism invariant theory of gravity described by the Lagrangian constructed out of the curvature tensor. On basis of the newly-constructed tensor, we further suggest a Komar-like formula for the conserved charges of this generic gravity theory.

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.

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