Curvature collineations and the determination of the metric from the curvature in general relativity

1983 ◽  
Vol 15 (6) ◽  
pp. 581-589 ◽  
Author(s):  
G. S. Hall
Keyword(s):  
General Relativity ◽  
Curvature Collineations

scholarly journals Theory of Nonlocal Point Transformations in General Relativity

2016 ◽  
Vol 2016 ◽  
pp. 1-32 ◽  
Author(s):  
Massimo Tessarotto ◽  
Claudio Cremaschini
Keyword(s):  
General Relativity ◽  
Field Equations ◽  
Traditional Concept ◽  
Curved Space ◽  
Point Transformations ◽  
Functional Setting ◽  
Mathematical Foundations ◽  
The Relationship ◽  
Metric Tensors

A discussion of the functional setting customarily adopted in General Relativity (GR) is proposed. This is based on the introduction of the notion of nonlocal point transformations (NLPTs). While allowing the extension of the traditional concept of GR-reference frame, NLPTs are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems. For this purpose in the paper the mathematical foundations of NLPT-theory are laid down and basic physical implications are considered. In particular, explicit applications of the theory are proposed, which concern(1)a solution to the so-called Einstein teleparallel problem in the framework of NLPT-theory;(2)the determination of the tensor transformation laws holding for the acceleration 4-tensor with respect to the group of NLPTs and the identification of NLPT-acceleration effects, namely, the relationship established via general NLPT between particle 4-acceleration tensors existing in different curved space-times;(3)the construction of the nonlocal transformation law connecting different diagonal metric tensors solution to the Einstein field equations; and(4)the diagonalization of nondiagonal metric tensors.

Chronometric measurements in geodesy and geophysics

2020 ◽  
Author(s):  
Pacôme Delva ◽  
Guillaume Lion
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
High Spatial Resolution ◽  
Relativistic Effects ◽  
Atomic Clocks ◽  
Fundamental Physics ◽  
Geodynamic Processes ◽  
New Ideas ◽  
Mass Transfers

<p>At the beginning of the 20th century the theories of special and general relativity were developed by Einstein and his contemporaries. These physical theories revolutionize our conceptions of time and of the measurement of time. The atomic clocks, which appeared in the 1950s, are so accurate and stable that it is now essential to take into account many relativistic effects. The development and worldwide comparisons of such atomic clocks allowed for some of the most stringent of fundamental physics, as well as new ideas for the search of dark matter. On a more applied level, when taking general relativity for granted, distant comparisons of atomic clocks can be used for navigation and positioning, as well as the determination of the geopotential. I will show how the chronometric observables can fit and be used within the context of classical geodesy and geophysics, presenting various applications: determination of the geopotential with high spatial resolution, vertical reference system, and discussing the possible applications associated to the geodynamic processes related to mass transfers.</p>

NUCLEOSYNTHESIS BOUNDS ON JORDAN-BRANS-DICKE THEORIES OF GRAVITY

1992 ◽  
Vol 07 (05) ◽  
pp. 447-456 ◽  
Author(s):  
J.A. CASAS ◽  
J. GARCÍA-BELLIDO ◽  
M. QUIRÓS
Keyword(s):  
General Relativity ◽  
Observational Data ◽  
Light Elements ◽  
Theory Comparison ◽  
Theories Of Gravity

We reexamine the nucleosynthesis predictions for the simplest class of scalar-tensor theories of gravity, the Jordan-Brans-Dicke theory. Comparison with present observational data on light elements’ abundances provides bounds on the ω-parameter which are as strong as the post-Newtonian ones, or even stronger, depending on the value of Ωh2. Future improvements in the determination of the 4 He and D +3He abundances will increase this bound dramatically. We argue that a future (hypothetical) experimental deviation from general relativity prediction could be restored by a Jordan-Brans-Dicke theory.

scholarly journals Simultaneous determination of mass parameter and radial marker in Schwarzschild geometry

2021 ◽  
Author(s):  
Victor Varela ◽  
Lorenzo Leal
Keyword(s):  
General Relativity ◽  
Simultaneous Determination ◽  
Euclidean Geometry ◽  
Proper Time ◽  
Mass Parameter ◽  
Thought Experiments ◽  
Newtonian Gravity ◽  
Algebraic Equations ◽  
Schwarzschild Geometry

Abstract We show that mass parameter and radial marker values can be indirectly measured in thought experiments performed in Schwarzschild spacetime, without using the Newtonian limit of general relativity or approximations based on Euclidean geometry. Our approach involves different proper time quantifications as well as solutions to systems of algebraic equations, and aims to strengthen the conceptual independence of general relativity from Newtonian gravity.

scholarly journals Determining PPN γ with Gaia's astrometric core solution

2009 ◽  
Vol 5 (S261) ◽  
pp. 315-319 ◽  
Author(s):  
David Hobbs ◽  
Berry Holl ◽  
Lennart Lindegren ◽  
Frédéric Raison ◽  
Sergei Klioner ◽  
...  
Keyword(s):  
General Relativity ◽  
Statistical Correlation ◽  
Small Scale ◽  
Tests Of General Relativity ◽  
Satellite Attitude ◽  
Cassini Mission ◽  
Core Solution ◽  
Space Astrometry ◽  
Better Than

AbstractThe ESA space astrometry mission Gaia, due for launch in early 2012, will in addition to its huge output of fundamental astrometric and astrophysical data also provide stringent tests of general relativity. In this paper we present an updated analysis of Gaia's capacity to measure the PPN parameter γ as part of its core astrometric solution. The analysis is based on small-scale astrometric solutions taking into account the simultaneous determination of stellar astrometric parameters and the satellite attitude. In particular, the statistical correlation between PPN γ and the stellar parallaxes is considered. Extrapolating the results to a full-scale solution using some 100 million stars, we find that PPN γ could be obtained to about 10−6, which is significantly better than today's best estimate from the Cassini mission of 2 × 10−5.

scholarly journals Neutron stars in Palatini $$R+\alpha R^2$$ and $$R+\alpha R^2+\beta Q$$ theories

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Georg Herzog ◽  
Hèlios Sanchis-Alepuz
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Neutron Stars ◽  
Equations Of State ◽  
Stellar Structure ◽  
Modified Theories Of Gravity ◽  
State Uncertainty ◽  
Structure Equations ◽  
Theories Of Gravity

AbstractWe study solutions of the stellar structure equations for spherically symmetric objects in modified theories of gravity, where the Einstein-Hilbert Lagrangian is replaced by $$f(R)=R+\alpha R^2$$ f ( R ) = R + α R 2 and $$f(R,Q)=R+\alpha R^2+\beta Q$$ f ( R , Q ) = R + α R 2 + β Q , with R being the Ricci scalar curvature, $$Q=R_{\mu \nu }R^{\mu \nu }$$ Q = R μ ν R μ ν and $$R_{\mu \nu }$$ R μ ν the Ricci tensor. We work in the Palatini formalism, where the metric and the connection are assumed to be independent dynamical variables. We focus on stellar solutions in the mass-radius region associated to neutron stars. We illustrate the potential impact of the $$R^2$$ R 2 and Q terms by studying a range of viable values of $$\alpha $$ α and $$\beta $$ β . Similarly, we use different equations of state (SLy, FPS, HS(DD2) and HS(TMA)) as a simple way to account for the equation of state uncertainty. Our results show that for certain combinations of the $$\alpha $$ α and $$\beta $$ β parameters and equation of state, the effect of modifications of general relativity on the properties of stars is sizeable. Therefore, with increasing accuracy in the determination of the equation of state for neutron stars, astrophysical observations may serve as discriminators of modifications of General Relativity.

Primordial quantum perturbations

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Slow Roll ◽  
Inflationary Models

This chapter shows that fluctuations of quantum origin are generated during inflation and that this process supplies initial conditions compatible with the observations. These fluctuations are therefore an important prediction of inflationary models. The chapter thus begins with a study of perturbations during inflation, proceeding in a similar manner to the previous chapter by finding the perturbation of the energy–momentum tensor of the scalar field. Another method of deriving the equations of motion of the perturbations is to start from the action of general relativity coupled to a scalar field, and expand to second order in the metric and scalar field perturbations. The chapter then proceeds with the determination of the initial conditions and the slow-roll inflation.

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