scholarly journals General Relativistic Aberration Equation and Measurable Angle of Light Ray in Kerr–de Sitter Spacetime

Universe ◽  
2021 ◽  
Vol 7 (6) ◽  
pp. 173
Author(s):  
Hideyoshi Arakida
Keyword(s):  
Cosmological Constant ◽  
Gravitational Lensing ◽  
Transverse Velocity ◽  
Second Order ◽  
Transverse Motion ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
General Relativistic ◽  
The Impact

As an extension of our previous paper, instead of the total deflection angle α, we will mainly focus on the discussion of measurable angle of the light ray ψP at the position of observer P in Kerr–de Sitter spacetime, which includes the cosmological constant Λ. We will investigate the contribution of the radial and transverse motion of the observer which are connected with radial velocity vr and transverse velocity bvϕ (b is the impact parameter) as well as the spin parameter a of the central object which induces the gravito-magnetic field or frame dragging and the cosmological constant Λ. The general relativistic aberration equation is employed to take into account the influence of motion of the observer on the measurable angle ψP. The measurable angle ψP derived in this paper can be applicable to the observer placed within the curved and finite-distance region in the spacetime. The equation of light trajectory will be obtained in such a sense that the background is de Sitter spacetime instead of Minkowski one. As an example, supposing the cosmological gravitational lensing effect, we assume that the lens object is the typical galaxy and the observer is in motion with respect to the lensing object at a recession velocity vr=bvϕ=vH=H0D (where H0 is a Hubble constant and D means the distance between the observer and the lens object). The static terms O(Λbm,Λba) are basically comparable with the second order deflection term O(m2), and they are almost one order smaller that the Kerr deflection −4ma/b2. The velocity-dependent terms O(Λbmvr,Λbavr) for radial motion and O(Λb2mvϕ,Λb2avϕ) for transverse motion are at most two orders of magnitude smaller than the second order deflection O(m2). We also find that even when the radial and transverse velocity have the same sign, asymptotic behavior as ϕ approaches 0 is different from each other, and each diverges to opposite infinity.

scholarly journals Relationship between Bondi–Sachs quantities and source of gravitational radiation in asymptotically de Sitter spacetime

2018 ◽  
Vol 27 (04) ◽  
pp. 1850046 ◽  
Author(s):  
Xiaokai He ◽  
Jiliang Jing ◽  
Zhoujian Cao
Keyword(s):  
Cosmological Constant ◽  
Gravitational Wave ◽  
Gravitational Radiation ◽  
The Other ◽  
Perturbation Approach ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Sitter Spacetime ◽  
Explicit Expressions

Gravitational radiation plays an important role in astrophysics. Based on the fact that our universe is expanding, the gravitational radiation when a positive cosmological constant is presented has been studied along with two different ways recently, one is the Bondi–Sachs (BS) framework in which the result is shown by BS quantities in the asymptotic null structure, the other is the perturbation approach in which the result is presented by the quadrupoles of source. Therefore, it is worth to interpret the quantities in asymptotic null structure in terms of the information of the source. In this paper, we investigate this problem and find the explicit expressions of BS quantities in terms of the quadrupoles of source in asymptotically de Sitter spacetime. We also estimate how far away the source is, the cosmological constant may affect the detection of the gravitational wave.

scholarly journals ON DETERMINATION OF THE GEOMETRIC COSMOLOGICAL CONSTANT FROM THE OPERA EXPERIMENT OF SUPERLUMINAL NEUTRINOS

2012 ◽  
Vol 27 (11) ◽  
pp. 1250041 ◽  
Author(s):  
MU-LIN YAN ◽  
SEN HU ◽  
WEI HUANG ◽  
NENG-CHAO XIAO
Keyword(s):  
Dark Energy ◽  
Cosmological Constant ◽  
Fundamental Constant ◽  
Zero Point ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Point Energy ◽  
Sitter Spacetime ◽  
Effective Cosmological Constant

The recent OPERA experiment of superluminal neutrinos has deep consequences in cosmology. In cosmology a fundamental constant is the cosmological constant. From observations one can estimate the effective cosmological constant Λ eff which is the sum of the quantum zero point energy Λ dark energy and the geometric cosmological constant Λ. The OPERA experiment can be applied to determine the geometric cosmological constant Λ. It is the first study to distinguish the contributions of Λ and Λ dark energy from each other by experiment. The determination is based on an explanation of the OPERA experiment in the framework of Special Relativity with de Sitter spacetime symmetry.

scholarly journals Schwinger pair production and the extended uncertainty principle: can heuristic derivations be trusted?

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Yen Chin Ong
Keyword(s):  
Cosmological Constant ◽  
Pair Production ◽  
Uncertainty Principle ◽  
Correction Term ◽  
Correct Result ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Extended Uncertainty ◽  
Background Curvature

Abstract The rate of Schwinger pair production due to an external electric field can be derived heuristically from the uncertainty principle. In the presence of a cosmological constant, it has been argued in the literature that the uncertainty principle receives a correction due to the background curvature, which is known as the “extended uncertainty principle” (EUP). We show that EUP does indeed lead to the correct result for Schwinger pair production rate in anti-de Sitter spacetime (the case for de Sitter spacetime is similar), provided that the EUP correction term is negative (positive for the de Sitter case). We compare the results with previous works in the EUP literature, which are not all consistent. Our result further highlights an important issue in the literature of generalizations of the uncertainty principle: how much can heuristic derivations be trusted?

scholarly journals Dark energy and quantum gravity

2019 ◽  
Vol 28 (14) ◽  
pp. 1944018 ◽  
Author(s):  
Per Berglund ◽  
Tristan Hübsch ◽  
Djordje Minić
Keyword(s):  
Dark Energy ◽  
String Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Particle Physics ◽  
Dual Space ◽  
Planck Scale ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime

Realizing dark energy and the observed de Sitter spacetime in quantum gravity has proven to be obstructed in almost every usual approach. We argue that additional degrees of freedom of the left- and right-movers in string theory and a resulting doubled, noncommutatively generalized geometric formulation thereof can lead to an effective model of dark energy consistent with de Sitter spacetime. In this approach, the curvature of the canonically conjugate dual space provides for the dark energy inducing a positive cosmological constant in the observed spacetime, whereas the size of the above dual space is the gravitational constant in the same observed de Sitter spacetime. As a hallmark relation owing to a unique feature of string theory which relates short distances to long distances, the cosmological constant scale, the Planck scale and the effective TeV-sized particle physics scale must satisfy a see-saw-like formula — precisely the generic prediction of certain stringy cosmic brane type models.

scholarly journals EXTENDED UNCERTAINTY PRINCIPLE AND THE GEOMETRY OF (ANTI)-DE SITTER SPACE

2010 ◽  
Vol 25 (20) ◽  
pp. 1697-1703 ◽  
Author(s):  
S. MIGNEMI
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Sitter Spacetime ◽  
Heisenberg Uncertainty ◽  
Sitter Background ◽  
Extended Uncertainty

It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.

scholarly journals Holographic de Sitter spacetime and quantum corrections to the cosmological constant

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Shuichi Yokoyama
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Conformal Symmetry ◽  
Flow Equation ◽  
Vector Model ◽  
Quantum Corrections ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Dynamical Aspect

Abstract A dynamical aspect of quantum gravity on de Sitter spacetime is investigated by holography and the de Sitter/conformal field theory correspondence. We show that de Sitter spacetime emerges from a free Sp($N$) vector model by complexifying the ghost fields and course-graining them by flow equation in parallel to the imaginary axis. We confirm that the emergence of de Sitter spacetime is ensured by conformal symmetry. We also compute the quantum corrections to the cosmological constant up to the next-to-leading order of the $1/N$ expansion in a proposed holographic approach. As a result the sub-leading corrections have the opposite sign to the classical value. This implies that a quantum gravity on de Sitter spacetime is perturbatively stable and quantum effects make the universe flatter and the cosmological constant smaller.

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