scholarly journals Asymptotic structure with vanishing cosmological constant

2021 ◽  
Author(s):  
Francisco Fernández-Álvarez ◽  
Jose M M Senovilla
Keyword(s):  
Gravitational Field ◽  
Cosmological Constant ◽  
Weyl Tensor ◽  
Space Time ◽  
Geometrical Construction ◽  
Asymptotic Structure ◽  
Weyl Curvature ◽  
Factors Associated ◽  
General Energy ◽  
New Criterion

Abstract This is the first of two papers [1] devoted to the asymptotic structure of space-time in the presence of a non-negative cosmological constant Λ. This first paper is concerned with the case of Λ = 0. Our approach is fully based on the tidal nature of the gravitational field and therefore on the ‘tidal energies’ built with the Weyl curvature. In particular, we use the (radiant) asymptotic supermomenta computed from the rescaled Weyl tensor at infinity to provide a novel characterisation of radiation escaping from, or entering into, the space-time. Our new criterion is easy to implement and shown to be fully equivalent to the classical one based on the news tensor. One of its virtues is that its formulation can be easily adapted to the case with Λ > 0 covered in the second paper. We derive the general energy-momentum-loss formulae including the matter terms and all factors associated to the choices of arbitrary foliation and of super- translation. We also revisit and present a full reformulation of the traditional peeling behaviour with a neat geometrical construction that leads, in particular, to an asymptotic alignment of the supermomenta in accordance with the radiation criterion.

scholarly journals Hamiltonian expression of curvature tensors in the York canonical basis: (II) Weyl tensor, Weyl scalars, Weyl eigenvalues and the problem of the observables of the gravitational field

2014 ◽  
Vol 11 (06) ◽  
pp. 1450053 ◽  
Author(s):  
Luca Lusanna ◽  
Mattia Villani
Keyword(s):  
Gravitational Field ◽  
Weyl Tensor ◽  
Canonical Basis ◽  
Riemann Tensor ◽  
Space Time ◽  
Minkowskian Space ◽  
Canonical Gravity ◽  
The Family ◽  
Tetrad Gravity ◽  
Curvature Tensors

We find the Hamiltonian expression in the York basis of canonical ADM tetrad gravity of the 4-Weyl tensor of the asymptotically Minkowskian space-time. Like for the 4-Riemann tensor we find a radar tensor (whose components are 4-scalars due to the use of radar 4-coordinates), which coincides with the 4-Weyl tensor on-shell on the solutions of Einstein's equations. Then, by using the Hamiltonian null tetrads, we find the Hamiltonian expression of the Weyl scalars of the Newman–Penrose approach and of the four eigenvalues of the 4-Weyl tensor. After having introduced the Dirac observables (DOs) of canonical gravity, whose determination requires the solution of the super-Hamiltonian and super-momentum constraints, we discuss the connection of the DOs with the notion of 4-scalar Bergmann observables (BOs). Due to the use of radar 4-coordinates these two types of observables coincide in our formulation of canonical ADM tetrad gravity. However, contrary to Bergmann proposal, the Weyl eigenvalues are shown not to be BOs, so that their relevance is only in their use (first suggested by Bergmann and Komar) for giving a physical identification as point-events of the mathematical points of the space-time 4-manifold. Finally we give the expression of the Weyl scalars in the Hamiltonian post-Minkowskian linearization of canonical ADM tetrad gravity in the family of (non-harmonic) 3-orthogonal Schwinger time gauges.

scholarly journals Entropic gravity from noncommutative black holes

2017 ◽  
Vol 15 (01) ◽  
pp. 1850004 ◽  
Author(s):  
Rafael C. Nunes ◽  
Hooman Moradpour ◽  
Edésio M. Barboza ◽  
Everton M. C. Abreu ◽  
Jorge Ananias Neto
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Field ◽  
Cosmological Constant ◽  
Black Hole Entropy ◽  
Space Time ◽  
Isotropic Universe ◽  
Entropic Gravity ◽  
The Universe

In this paper, we investigated the effects of a noncommutative (NC) space-time on the dynamics of the Universe. We generalize the black hole entropy for a NC black hole. Then, using the entropic gravity formalism, we will show that the noncommutativity changes the strength of the gravitational field. By applying this result to a homogeneous and isotropic Universe containing nonrelativistic matter and a cosmological constant, we show that the modified scenario by the noncommutativity of the space-time is a better fit to the obtained data than the standard one at 68% CL.

scholarly journals Space-Time Second-Quantization Effects and the Quantum Origin of Cosmological Constant in Covariant Quantum Gravity

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 287 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Gravitational Field ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Proper Time ◽  
Theoretical Background ◽  
Space Time ◽  
Einstein Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Covariant Quantum

Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant proper-time parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend generally also on the realization of the quantum probability density for the quantum gravitational field tensor. The emerging physical picture predicts a generally non-stationary quantum cosmological constant which originates from fluctuations (i.e., gradients) of vacuum quantum gravitational energy density and is consistent with the existence of quantum massive gravitons.

The spin-zero Duffin-Kemmer-Petiau equation in a cosmic-string space-time with the Cornell interaction

2016 ◽  
Vol 31 (36) ◽  
pp. 1650191 ◽  
Author(s):  
M. de Montigny ◽  
M. Hosseinpour ◽  
H. Hassanabadi
Keyword(s):  
Gravitational Field ◽  
Coordinate System ◽  
Cosmic String ◽  
Topological Defects ◽  
Space Time ◽  
Dkp Equation

In this paper, we study the covariant Duffin-Kemmer-Petiau (DKP) equation in the cosmic-string space-time and consider the interaction of a DKP field with the gravitational field produced by topological defects in order to examine the influence of topology on this system. We solve the spin-zero DKP oscillator in the presence of the Cornell interaction with a rotating coordinate system in an exact analytical manner for nodeless and one-node states by proposing a proper ansatz solution.

Pseudo-Z symmetric space-times with divergence-free Weyl tensor and pp-waves

2016 ◽  
Vol 13 (02) ◽  
pp. 1650015 ◽  
Author(s):  
Carlo Alberto Mantica ◽  
Young Jin Suh
Keyword(s):  
Symmetric Space ◽  
Weyl Tensor ◽  
Killing Vector ◽  
Complete Classification ◽  
Space Time ◽  
Conformal Killing ◽  
Conformally Flat ◽  
Conformal Curvature ◽  
Wave Space ◽  
Divergence Free

In this paper we present some new results about [Formula: see text]-dimensional pseudo-Z symmetric space-times. First we show that if the tensor Z satisfies the Codazzi condition then its rank is one, the space-time is a quasi-Einstein manifold, and the associated 1-form results to be null and recurrent. In the case in which such covector can be rescaled to a covariantly constant we obtain a Brinkmann-wave. Anyway the metric results to be a subclass of the Kundt metric. Next we investigate pseudo-Z symmetric space-times with harmonic conformal curvature tensor: a complete classification of such spaces is obtained. They are necessarily quasi-Einstein and represent a perfect fluid space-time in the case of time-like associated covector; in the case of null associated covector they represent a pure radiation field. Further if the associated covector is locally a gradient we get a Brinkmann-wave space-time for [Formula: see text] and a pp-wave space-time in [Formula: see text]. In all cases an algebraic classification for the Weyl tensor is provided for [Formula: see text] and higher dimensions. Then conformally flat pseudo-Z symmetric space-times are investigated. In the case of null associated covector the space-time reduces to a plane wave and results to be generalized quasi-Einstein. In the case of time-like associated covector we show that under the condition of divergence-free Weyl tensor the space-time admits a proper concircular vector that can be rescaled to a time like vector of concurrent form and is a conformal Killing vector. A recent result then shows that the metric is necessarily a generalized Robertson–Walker space-time. In particular we show that a conformally flat [Formula: see text], [Formula: see text], space-time is conformal to the Robertson–Walker space-time.

Новый критерий оптимальности пространственно-временных матриц

2020 ◽  
Author(s):  
A.A. Reznev ◽  
V.B. Kreyndelin
Keyword(s):  
Computational Complexity ◽  
Large Scale ◽  
Noise Immunity ◽  
Optimality Criterion ◽  
Mimo Systems ◽  
Optimality Criteria ◽  
Space Time ◽  
Space Time Codes ◽  
Golden Code ◽  
New Criterion

The application of optimality criteria for the study of space-time codes is considered. Known rank and determinant criteria are described. The computational complexity of determinant criteria is presented taking into account some estimation of the real CPUs specifications. An algorithm for calculating a new optimality criterion is described. The computational complexity of the new optimality criterion is evaluated. The new criterion is applied to the study of the space-time Golden matrix. The obtained criterion value is used to modify the Golden code. The modeling for Golden code demonstrates that criterion works and gives us better levels for noise immunity. The proposed optimality criterion is acceptable in terms of computational complexity even for a large number of antennas, which is typical for large-scale MIMO systems. Рассматривается применение критериев оптимальности для исследования пространственно-временных кодов.Описаны известные ранговый и детерминантный критерии. Для детерминантного критерия оценена вычислительная сложность с учетом определения специальных высокопроизводительных процессоров. Описан алгоритм расчета нового критерия оптимальности. Проведена оценка вычислительной сложности нового критерия оптимальности. Новый критерий применен для исследования пространственно-временной матрицы Голден. Полученное значение критерия использовано для модификациикода Голден. Продемонстрированы кривые помехоустойчивости для кода Голден и кода Голден с модифицированным параметром, получен энергетический выигрыш. Предложенный критерий оптимальности приемлем с точки зрения вычислительнойсложности даже при большом числе антенн, характерном для систем широкомасштабного MIMO.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

SPACE–TIME ENERGY–MOMENTUM, THE OBSERVER AND UNCERTAINTY IN GENERAL RELATIVITY

2010 ◽  
Vol 19 (14) ◽  
pp. 2353-2359 ◽  
Author(s):  
F. I. COOPERSTOCK ◽  
M. J. DUPRE
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Uncertainty Principle ◽  
Ricci Tensor ◽  
Space Time ◽  
Energy Integral ◽  
New Approach ◽  
Extended Space ◽  
Energy And Momentum

In this essay, we introduce a new approach to energy–momentum in general relativity. Space–time, as opposed to space, is recognized as the necessary arena for its examination, leading us to define new extended space–time energy and momentum constructs. From local and global considerations, we conclude that the Ricci tensor is the required element for a localized expression of energy–momentum to include the gravitational field. We present and rationalize a fully invariant extended expression for space–time energy, guided by Tolman's well-known energy integral for an arbitrary bounded stationary system. This raises fundamental issues which we discuss. The role of the observer emerges naturally and we are led to an extension of the uncertainty principle to general relativity, of particular relevance to ultra-strong gravity.

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