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Jump to: Review

336 KiB

Open AccessArticle

Theoretical Tools for Relativistic Gravimetry, Gradiometry and Chronometric Geodesy and Application to a Parameterized Post-Newtonian Metric

by Pacôme Delva and Jan Geršl

Universe 2017, 3(1), 24; https://doi.org/10.3390/universe3010024 - 13 Mar 2017

Cited by 8 | Viewed by 4479

Abstract

An extensive review of past work on relativistic gravimetry, gradiometry and chronometric geodesy is given. Then, general theoretical tools are presented and applied for the case of a stationary parameterized post-Newtonian metric. The special case of a stationary clock on the surface of [...] Read more.

An extensive review of past work on relativistic gravimetry, gradiometry and chronometric geodesy is given. Then, general theoretical tools are presented and applied for the case of a stationary parameterized post-Newtonian metric. The special case of a stationary clock on the surface of the Earth is studied. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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328 KiB

Open AccessArticle

Convexity and the Euclidean Metric of Space-Time

by Nikolaos Kalogeropoulos

Universe 2017, 3(1), 8; https://doi.org/10.3390/universe3010008 - 8 Feb 2017

Cited by 2 | Viewed by 4289

Abstract

We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli [...] Read more.

We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

450 KiB

Open AccessArticle

Strategies to Ascertain the Sign of the Spatial Curvature

by Pedro C. Ferreira and Diego Pavón

Universe 2016, 2(4), 27; https://doi.org/10.3390/universe2040027 - 24 Nov 2016

Cited by 3 | Viewed by 4030

Abstract

The second law of thermodynamics, in the presence of gravity, is known to hold at small scales, as in the case of black holes and self-gravitating radiation spheres. Using the Friedmann–Lemaître–Robertson–Walker metric and the history of the Hubble factor, we argue that this [...] Read more.

The second law of thermodynamics, in the presence of gravity, is known to hold at small scales, as in the case of black holes and self-gravitating radiation spheres. Using the Friedmann–Lemaître–Robertson–Walker metric and the history of the Hubble factor, we argue that this law also holds at cosmological scales. Based on this, we study the connection between the deceleration parameter and the spatial curvature of the metric,

Ω_{k}

, and set limits on the latter, valid for any homogeneous and isotropic cosmological model. Likewise, we devise strategies to determine the sign of the spatial curvature index k. Finally, assuming the lambda cold dark matter model is correct, we find that the acceleration of the cosmic expansion is increasing today. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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241 KiB

Open AccessFeature PaperArticle

A Solution of the Mitra Paradox

by Øyvind Grøn

Universe 2016, 2(4), 26; https://doi.org/10.3390/universe2040026 - 4 Nov 2016

Cited by 1 | Viewed by 4623

Abstract

The “Mitra paradox” refers to the fact that while the de Sitter spacetime appears non-static in a freely falling reference frame, it looks static with reference to a fixed reference frame. The coordinate-independent nature of the paradox may be gauged from the fact [...] Read more.

The “Mitra paradox” refers to the fact that while the de Sitter spacetime appears non-static in a freely falling reference frame, it looks static with reference to a fixed reference frame. The coordinate-independent nature of the paradox may be gauged from the fact that the relevant expansion scalar,

θ = \sqrt{3 Λ}

, is finite if

Λ > 0

. The trivial resolution of the paradox would obviously be to set

Λ = 0

. However, here it is assumed that

Λ > 0

, and the paradox is resolved by invoking the concept of “expansion of space”. This is a reference-dependent concept, and it is pointed out that the solution of the Mitra paradox is obtained by taking into account the properties of the reference frame in which the coordinates are co-moving. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

278 KiB

Open AccessArticle

On the Effect of the Cosmological Expansion on the Gravitational Lensing by a Point Mass

by Oliver F. Piattella

Universe 2016, 2(4), 25; https://doi.org/10.3390/universe2040025 - 18 Oct 2016

Cited by 13 | Viewed by 3720

Abstract

We analyse the effect of the cosmological expansion on the deflection of light caused by a point mass, adopting the McVittie metric as the geometrical description of a point-like lens embedded in an expanding universe. In the case of a generic, non-constant Hubble [...] Read more.

We analyse the effect of the cosmological expansion on the deflection of light caused by a point mass, adopting the McVittie metric as the geometrical description of a point-like lens embedded in an expanding universe. In the case of a generic, non-constant Hubble parameter, H, we derive and approximately solve the null geodesic equations, finding an expression for the bending angle δ, which we expand in powers of the mass-to-closest approach distance ratio and of the impact parameter-to-lens distance ratio. It turns out that the leading order of the aforementioned expansion is the same as the one calculated for the Schwarzschild metric and that cosmological corrections contribute to δ only at sub-dominant orders. We explicitly calculate these cosmological corrections for the case of the H constant and find that they provide a correction of order 10⁻¹¹ on the lens mass estimate. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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964 KiB

Open AccessFeature PaperArticle

General Relativity and Cosmology: Unsolved Questions and Future Directions

by Ivan Debono and George F. Smoot

Universe 2016, 2(4), 23; https://doi.org/10.3390/universe2040023 - 28 Sep 2016

Cited by 154 | Viewed by 47259

Abstract

For the last 100 years, General Relativity (GR) has taken over the gravitational theory mantle held by Newtonian Gravity for the previous 200 years. This article reviews the status of GR in terms of its self-consistency, completeness, and the evidence provided by observations, [...] Read more.

For the last 100 years, General Relativity (GR) has taken over the gravitational theory mantle held by Newtonian Gravity for the previous 200 years. This article reviews the status of GR in terms of its self-consistency, completeness, and the evidence provided by observations, which have allowed GR to remain the champion of gravitational theories against several other classes of competing theories. We pay particular attention to the role of GR and gravity in cosmology, one of the areas in which one gravity dominates and new phenomena and effects challenge the orthodoxy. We also review other areas where there are likely conflicts pointing to the need to replace or revise GR to represent correctly observations and consistent theoretical framework. Observations have long been key both to the theoretical liveliness and viability of GR. We conclude with a discussion of the likely developments over the next 100 years. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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767 KiB

Open AccessArticle

Warm Inflation

by Øyvind Grøn

Universe 2016, 2(3), 20; https://doi.org/10.3390/universe2030020 - 6 Sep 2016

Cited by 10 | Viewed by 4495

Abstract

I show here that there are some interesting differences between the predictions of warm and cold inflation models focusing in particular upon the scalar spectral index

n_{s}

and the tensor-to-scalar ratio r. The first thing to be noted is that the [...] Read more.

I show here that there are some interesting differences between the predictions of warm and cold inflation models focusing in particular upon the scalar spectral index

n_{s}

and the tensor-to-scalar ratio r. The first thing to be noted is that the warm inflation models in general predict a vanishingly small value of r. Cold inflationary models with the potential

V = M^{4} {(ϕ / M_{P})}^{p}

and a number of e-folds

N = 60

predict

δ_{n s C} \equiv 1 - n_{s} \approx (p + 2) / 120

, where

n_{s}

is the scalar spectral index, while the corresponding warm inflation models with constant value of the dissipation parameter

Γ

predict

δ_{n s W} = [(20 + p) / (4 + p)] / 120

. For example, for

p = 2

this gives

δ_{n s W} = 1.1 δ_{n s C}

. The warm polynomial model with

Γ = V

seems to be in conflict with the Planck data. However, the warm natural inflation model can be adjusted to be in agreement with the Planck data. It has, however, more adjustable parameters in the expressions for the spectral parameters than the corresponding cold inflation model, and is hence a weaker model with less predictive force. However, it should be noted that the warm inflation models take into account physical processes such as dissipation of inflaton energy to radiation energy, which is neglected in the cold inflationary models. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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256 KiB

Open AccessArticle

The Teleparallel Equivalent of General Relativity and the Gravitational Centre of Mass

by José Wadih Maluf

Universe 2016, 2(3), 19; https://doi.org/10.3390/universe2030019 - 31 Aug 2016

Cited by 13 | Viewed by 3629

Abstract

We present a brief review of the teleparallel equivalent of general relativity and analyse the expression for the centre of mass density of the gravitational field. This expression has not been sufficiently discussed in the literature. One motivation for the present analysis is [...] Read more.

We present a brief review of the teleparallel equivalent of general relativity and analyse the expression for the centre of mass density of the gravitational field. This expression has not been sufficiently discussed in the literature. One motivation for the present analysis is the investigation of the localization of dark energy in the three-dimensional space, induced by a cosmological constant in a simple Schwarzschild-de Sitter space-time. We also investigate the gravitational centre of mass density in a particular model of dark matter, in the space-time of a point massive particle and in an arbitrary space-time with axial symmetry. The results are plausible, and lead to the notion of gravitational centre of mass (COM) distribution function. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

249 KiB

Open AccessArticle

Symplectic Structure of Intrinsic Time Gravity

by Eyo Eyo Ita and Amos S. Kubeka

Universe 2016, 2(3), 18; https://doi.org/10.3390/universe2030018 - 30 Aug 2016

Cited by 1 | Viewed by 3543

Abstract

The Poisson structure of intrinsic time gravity is analysed. With the starting point comprising a unimodular three-metric with traceless momentum, a trace-induced anomaly results upon quantization. This leads to a revision of the choice of momentum variable to the (mixed index) traceless momentric. [...] Read more.

The Poisson structure of intrinsic time gravity is analysed. With the starting point comprising a unimodular three-metric with traceless momentum, a trace-induced anomaly results upon quantization. This leads to a revision of the choice of momentum variable to the (mixed index) traceless momentric. This latter choice unitarily implements the fundamental commutation relations, which now take on the form of an affine algebra with SU(3) Lie algebra amongst the momentric variables. The resulting relations unitarily implement tracelessness upon quantization. The associated Poisson brackets and Hamiltonian dynamics are studied. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

566 KiB

Open AccessArticle

What Is the Validity Domain of Einstein’s Equations? Distributional Solutions over Singularities and Topological Links in Geometrodynamics

by Elias Zafiris

Universe 2016, 2(3), 17; https://doi.org/10.3390/universe2030017 - 29 Aug 2016

Cited by 3 | Viewed by 4470

Abstract

The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime [...] Read more.

The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

241 KiB

Open AccessArticle

Charged and Electromagnetic Fields from Relativistic Quantum Geometry

by Marcos R. A. Arcodía and Mauricio Bellini

Universe 2016, 2(2), 13; https://doi.org/10.3390/universe2020013 - 21 Jun 2016

Cited by 6 | Viewed by 3874

Abstract

In the recently introduced Relativistic Quantum Geometry (RQG) formalism, the possibility was explored that the variation of the tensor metric can be done in a Weylian integrable manifold using a geometric displacement, from a Riemannian to a Weylian integrable manifold, described by the [...] Read more.

In the recently introduced Relativistic Quantum Geometry (RQG) formalism, the possibility was explored that the variation of the tensor metric can be done in a Weylian integrable manifold using a geometric displacement, from a Riemannian to a Weylian integrable manifold, described by the dynamics of an auxiliary geometrical scalar field θ, in order that the Einstein tensor (and the Einstein equations) can be represented on a Weyl-like manifold. In this framework we study jointly the dynamics of electromagnetic fields produced by quantum complex vector fields, which describes charges without charges. We demonstrate that complex fields act as a source of tetra-vector fields which describe an extended Maxwell dynamics. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

269 KiB

Open AccessArticle

Virial Theorem in Nonlocal Newtonian Gravity

by Bahram Mashhoon

Universe 2016, 2(2), 9; https://doi.org/10.3390/universe2020009 - 30 May 2016

Cited by 4 | Viewed by 3840

Abstract

Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of [...] Read more.

Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for “isolated” astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy’s baryonic diameter

D_{0}

—namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time—is predicted to be larger than the effective dark matter fraction

f_{D M}

times a universal length that is the basic nonlocality length scale

λ_{0} \approx 3 \pm 2

kpc. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

285 KiB

Open AccessArticle

Effect of the Cosmological Constant on Light Deflection: Time Transfer Function Approach

by Hideyoshi Arakida

Universe 2016, 2(1), 5; https://doi.org/10.3390/universe2010005 - 14 Mar 2016

Cited by 10 | Viewed by 3989

Abstract

We revisit the role of the cosmological constant Λ in the deflection of light by means of the Schwarzschild–de Sitter/Kottler metric. In order to obtain the total deflection angle α, the time transfer function approach is adopted, instead of the commonly used [...] Read more.

We revisit the role of the cosmological constant Λ in the deflection of light by means of the Schwarzschild–de Sitter/Kottler metric. In order to obtain the total deflection angle α, the time transfer function approach is adopted, instead of the commonly used approach of solving the geodesic equation of photon. We show that the cosmological constant does appear in expression of the deflection angle, and it diminishes light bending due to the mass of the central body M. However, in contrast to previous results, for instance, that by Rindler and Ishak (Phys. Rev. D. 2007), the leading order effect due to the cosmological constant does not couple with the mass of the central body M. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

340 KiB

Open AccessArticle

Autoparallel vs. Geodesic Trajectories in a Model of Torsion Gravity

by Luis Acedo

Universe 2015, 1(3), 422-445; https://doi.org/10.3390/universe1030422 - 25 Nov 2015

Cited by 8 | Viewed by 5360

Abstract

We consider a parametrized torsion gravity model for Riemann–Cartan geometry around a rotating axisymmetric massive body. In this model, the source of torsion is given by a circulating vector potential following the celestial parallels around the rotating object. Ours is a variant of [...] Read more.

We consider a parametrized torsion gravity model for Riemann–Cartan geometry around a rotating axisymmetric massive body. In this model, the source of torsion is given by a circulating vector potential following the celestial parallels around the rotating object. Ours is a variant of the Mao, Tegmark, Guth and Cabi (MTGC model) in which the total angular momentum is proposed as a source of torsion. We study the motion of bodies around the rotating object in terms of autoparallel trajectories and determine the leading perturbations of the orbital elements by using standard celestial mechanics techniques. We find that this torsion model implies new gravitational physical consequences in the Solar system and, in particular, secular variations of the semi-major axis of the planetary orbits. Perturbations on the longitude of the ascending node and the perihelion of the planets are already under discussion in the astronomical community, and if confirmed as truly non-zero effects at a statistically significant level, we might be at the dawn of an era of torsion phenomenology in the Solar system. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

387 KiB

Open AccessArticle

Editorial for the Special Issue 100 Years of Chronogeometrodynamics: The Status of the Einstein’s Theory of Gravitation in Its Centennial Year

by Lorenzo Iorio

Universe 2015, 1(1), 38-81; https://doi.org/10.3390/universe1010038 - 27 Apr 2015

Cited by 98 | Viewed by 8274

Abstract

The present Editorial introduces the Special Issue dedicated by the journal Universe to the General Theory of Relativity, the beautiful theory of gravitation of Einstein, a century after its birth. It reviews some of its key features in a historical perspective, and, in [...] Read more.

The present Editorial introduces the Special Issue dedicated by the journal Universe to the General Theory of Relativity, the beautiful theory of gravitation of Einstein, a century after its birth. It reviews some of its key features in a historical perspective, and, in welcoming distinguished researchers from all over the world to contribute it, some of the main topics at the forefront of the current research are outlined. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

Review

Jump to: Research

211 KiB

Open AccessReview

The Singularity Problem in Brane Cosmology

by Ignatios Antoniadis and Spiros Cotsakis

Universe 2017, 3(1), 15; https://doi.org/10.3390/universe3010015 - 16 Feb 2017

Cited by 2 | Viewed by 3634

Abstract

We review results about the development and asymptotic nature of singularities in “brane–bulk” systems. These arise for warped metrics obeying the five-dimensional Einstein equations with fluid-like sources, and including a brane four-metric that is either Minkowski, de Sitter, or Anti-de Sitter. We characterize [...] Read more.

We review results about the development and asymptotic nature of singularities in “brane–bulk” systems. These arise for warped metrics obeying the five-dimensional Einstein equations with fluid-like sources, and including a brane four-metric that is either Minkowski, de Sitter, or Anti-de Sitter. We characterize all singular Minkowski brane solutions, and look for regular solutions with nonzero curvature. We briefly comment on matching solutions, energy conditions, and finite Planck mass criteria for admissibility, and we briefly discuss the connection of these results to ambient theory. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

564 KiB

Open AccessReview

Tests of Lorentz Symmetry in the Gravitational Sector

by Aurélien Hees, Quentin G. Bailey, Adrien Bourgoin, Hélène Pihan-Le Bars, Christine Guerlin and Christophe Le Poncin-Lafitte

Universe 2016, 2(4), 30; https://doi.org/10.3390/universe2040030 - 1 Dec 2016

Cited by 75 | Viewed by 6875

Abstract

Lorentz symmetry is one of the pillars of both General Relativity and the Standard Model of particle physics. Motivated by ideas about quantum gravity, unification theories and violations of CPT symmetry, a significant effort has been put the last decades into testing Lorentz [...] Read more.

Lorentz symmetry is one of the pillars of both General Relativity and the Standard Model of particle physics. Motivated by ideas about quantum gravity, unification theories and violations of CPT symmetry, a significant effort has been put the last decades into testing Lorentz symmetry. This review focuses on Lorentz symmetry tests performed in the gravitational sector. We briefly review the basics of the pure gravitational sector of the Standard-Model Extension (SME) framework, a formalism developed in order to systematically parametrize hypothetical violations of the Lorentz invariance. Furthermore, we discuss the latest constraints obtained within this formalism including analyses of the following measurements: atomic gravimetry, Lunar Laser Ranging, Very Long Baseline Interferometry, planetary ephemerides, Gravity Probe B, binary pulsars, high energy cosmic rays, … In addition, we propose a combined analysis of all these results. We also discuss possible improvements on current analyses and present some sensitivity analyses for future observations. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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5467 KiB

Open AccessFeature PaperReview

A Brief History of Gravitational Waves

by Jorge L. Cervantes-Cota, Salvador Galindo-Uribarri and George F. Smoot

Universe 2016, 2(3), 22; https://doi.org/10.3390/universe2030022 - 13 Sep 2016

Cited by 50 | Viewed by 27260

Abstract

This review describes the discovery of gravitational waves. We recount the journey of predicting and finding those waves, since its beginning in the early twentieth century, their prediction by Einstein in 1916, theoretical and experimental blunders, efforts towards their detection, and finally the [...] Read more.

This review describes the discovery of gravitational waves. We recount the journey of predicting and finding those waves, since its beginning in the early twentieth century, their prediction by Einstein in 1916, theoretical and experimental blunders, efforts towards their detection, and finally the subsequent successful discovery. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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586 KiB

Open AccessReview

Testing General Relativity with the Radio Science Experiment of the BepiColombo mission to Mercury

by Giulia Schettino and Giacomo Tommei

Universe 2016, 2(3), 21; https://doi.org/10.3390/universe2030021 - 12 Sep 2016

Cited by 17 | Viewed by 6820

Abstract

The relativity experiment is part of the Mercury Orbiter Radio science Experiment (MORE) on-board the ESA/JAXA BepiColombo mission to Mercury. Thanks to very precise radio tracking from the Earth and accelerometer, it will be possible to perform an accurate test of General Relativity, [...] Read more.

The relativity experiment is part of the Mercury Orbiter Radio science Experiment (MORE) on-board the ESA/JAXA BepiColombo mission to Mercury. Thanks to very precise radio tracking from the Earth and accelerometer, it will be possible to perform an accurate test of General Relativity, by constraining a number of post-Newtonian and related parameters with an unprecedented level of accuracy. The Celestial Mechanics Group of the University of Pisa developed a new dedicated software, ORBIT14, to perform the simulations and to determine simultaneously all the parameters of interest within a global least squares fit. After highlighting some critical issues, we report on the results of a full set of simulations, carried out in the most up-to-date mission scenario. For each parameter we discuss the achievable accuracy, in terms of a formal analysis through the covariance matrix and, furthermore, by the introduction of an alternative, more representative, estimation of the errors. We show that, for example, an accuracy of some parts in

10^{- 6}

for the Eddington parameter β and of

10^{- 5}

for the Nordtvedt parameter η can be attained, while accuracies at the level of

5 \times 10^{- 7}

and

1 \times 10^{- 7}

can be achieved for the preferred frames parameters

α_{1}

and

α_{2}

, respectively. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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294 KiB

Open AccessReview

Einstein and Beyond: A Critical Perspective on General Relativity

by Ram Gopal Vishwakarma

Universe 2016, 2(2), 11; https://doi.org/10.3390/universe2020011 - 30 May 2016

Cited by 47 | Viewed by 5904

Abstract

An alternative approach to Einstein’s theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor [...] Read more.

An alternative approach to Einstein’s theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor

T^{i k}

and unphysical solutions. The new approach emanates from a critical analysis of these problems, providing a novel insight that the matter fields, together with the ensuing gravitational field, are already present inherently in the spacetime without taking recourse to

T^{i k}

. Supported by lots of evidence, the new insight revolutionizes our views on the representation of the source of gravitation and establishes the spacetime itself as the source, which becomes crucial for understanding the unresolved issues in a unified manner. This leads to a new paradigm in GR by establishing equation

R^{i k} = 0

as the field equation of gravitation plus inertia in the very presence of matter. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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4104 KiB

Open AccessReview

The Scales of Gravitational Lensing

by Francesco De Paolis, Mosè Giordano, Gabriele Ingrosso, Luigi Manni, Achille Nucita and Francesco Strafella

Universe 2016, 2(1), 6; https://doi.org/10.3390/universe2010006 - 14 Mar 2016

Cited by 14 | Viewed by 7090

Abstract

After exactly a century since the formulation of the general theory of relativity, the phenomenon of gravitational lensing is still an extremely powerful method for investigating in astrophysics and cosmology. Indeed, it is adopted to study the distribution of the stellar component in [...] Read more.

After exactly a century since the formulation of the general theory of relativity, the phenomenon of gravitational lensing is still an extremely powerful method for investigating in astrophysics and cosmology. Indeed, it is adopted to study the distribution of the stellar component in the Milky Way, to study dark matter and dark energy on very large scales and even to discover exoplanets. Moreover, thanks to technological developments, it will allow the measure of the physical parameters (mass, angular momentum and electric charge) of supermassive black holes in the center of ours and nearby galaxies. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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Graphical abstract

867 KiB

Open AccessFeature PaperReview

The Status of Cosmic Topology after Planck Data

by Jean-Pierre Luminet

Universe 2016, 2(1), 1; https://doi.org/10.3390/universe2010001 - 15 Jan 2016

Cited by 28 | Viewed by 7881

Abstract

In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background (hereafter CMB) obtained by WMAP and Planck telescopes. Cosmic Topology involves both global [...] Read more.

In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background (hereafter CMB) obtained by WMAP and Planck telescopes. Cosmic Topology involves both global topological features and more local geometrical properties such as curvature. It deals with questions such as whether space is finite or infinite, simply-connected or multi-connected, and smaller or greater than its observable counterpart. A striking feature of some relativistic, multi-connected small universe models is to create multiples images of faraway cosmic sources. While the last CMB (Planck) data fit well the simplest model of a zero-curvature, infinite space model, they remain consistent with more complex shapes such as the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. We review the theoretical and observational status of the field. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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