scholarly journals Causal Gödel-type metrics in non-local gravity theories

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
J. R. Nascimento ◽  
A. Yu. Petrov ◽  
P. J. Porfírio
Keyword(s):  
General Relativity ◽  
Entire Functions ◽  
Classical Solutions ◽  
Local Models ◽  
Field Equations ◽  
Local Gravity ◽  
Transcendental Entire Functions ◽  
Non Local ◽  
Theories Of Gravity ◽  
Non Locality

AbstractIt is well known that non-local theories of gravity have been a flourish arena of studies for many reasons, for instance, the UV incompleteness of General Relativity (GR). In this paper we check the consistency of ST-homogeneous Gödel-type metrics within the non-local gravity framework. The non-local models considered here are ghost-free but not necessarily renormalizable since we focus on the classical solutions of the field equations. Furthermore, the non-locality is displayed in the action through transcendental entire functions of the d’Alembert operator $$\Box $$ □ that are mathematically represented by a power series of the $$\Box $$ □ operator. We find two exact solutions for the field equations correspondent to the degenerate ($$\omega =0$$ ω = 0 ) and hyperbolic ($$m^{2}=4\omega ^2$$ m 2 = 4 ω 2 ) classes of ST-homogeneous Gödel-type metrics.

scholarly journals Non-local curvature and Gauss–Bonnet cosmologies by Noether symmetries

2020 ◽  
Vol 135 (12) ◽  
Author(s):  
Francesco Bajardi ◽  
Salvatore Capozziello ◽  
Daniele Vernieri
Keyword(s):  
Noether Symmetries ◽  
Field Equations ◽  
Local Curvature ◽  
Symmetry Approach ◽  
Local Gravity ◽  
Cosmological Solutions ◽  
Related Point ◽  
Functional Forms ◽  
Non Local ◽  
Scalar Invariants

AbstractNon-local gravity cosmologies are considered under the standard of Noether symmetry approach. In particular, we focus on non-local theories whose gravitational actions depend on curvature and Gauss–Bonnet scalar invariants. Specific functional forms of the related point-like Lagrangians are selected by Noether symmetries, and we solve the corresponding field equations finding out exact cosmological solutions.

scholarly journals Revisiting cosmologies in teleparallelism

2021 ◽  
Author(s):  
Fabio D'Ambrosio ◽  
Lavinia Heisenberg ◽  
Simon Kuhn
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Symmetry Reduction ◽  
Affine Geometry ◽  
Linear Extensions ◽  
Field Equations ◽  
Torsion Scalar ◽  
Friedmann Equations ◽  
General Field ◽  
Theories Of Gravity

Abstract We discuss the most general field equations for cosmological spacetimes for theories of gravity based on non-linear extensions of the non-metricity scalar and the torsion scalar. Our approach is based on a systematic symmetry-reduction of the metric-affine geometry which underlies these theories. While for the simplest conceivable case the connection disappears from the field equations and one obtains the Friedmann equations of General Relativity, we show that in $f(\mathbb{Q})$ cosmology the connection generically modifies the metric field equations and that some of the connection components become dynamical. We show that $f(\mathbb{Q})$ cosmology contains the exact General Relativity solutions and also exact solutions which go beyond. In $f(\mathbb{T})$~cosmology, however, the connection is completely fixed and not dynamical.

scholarly journals A new golden age: testing general relativity with cosmology

2011 ◽  
Vol 369 (1957) ◽  
pp. 4941-4946
Author(s):  
Rachel Bean ◽  
Pedro G. Ferreira ◽  
Andy Taylor
Keyword(s):  
General Relativity ◽  
Large Scale ◽  
Large Scale Structure ◽  
Einstein Gravity ◽  
Field Equations ◽  
The Past ◽  
Cosmological Observations ◽  
Wide Range ◽  
Theories Of Gravity ◽  
The Universe

Gravity drives the evolution of the Universe and is at the heart of its complexity. Einstein's field equations can be used to work out the detailed dynamics of space and time and to calculate the emergence of large-scale structure in the distribution of galaxies and radiation. Over the past few years, it has become clear that cosmological observations can be used not only to constrain different world models within the context of Einstein gravity but also to constrain the theory of gravity itself. In this article, we look at different aspects of this new field in which cosmology is used to test theories of gravity with a wide range of observations.

scholarly journals Palatini formulation of non-local gravity

2017 ◽  
Vol 14 (02) ◽  
pp. 1750019 ◽  
Author(s):  
F. Briscese ◽  
M. L. Pucheu
Keyword(s):  
General Relativity ◽  
Gravity Model ◽  
Local Model ◽  
Dynamical Equations ◽  
Palatini Formalism ◽  
Local Gravity ◽  
Non Local ◽  
Vacuum Solutions

We derive the dynamical equations for a non-local gravity model in the Palatini formalism and we discuss some of the properties of this model. We have show that, in some specific case, the vacuum solutions of general relativity are also vacuum solutions of the non-local model, so we conclude that, at least in this case, the singularities of Einstein’s gravity are not removed.

scholarly journals Is gravity actually the curvature of spacetime?

2019 ◽  
Vol 28 (14) ◽  
pp. 1944021
Author(s):  
Sebastian Bahamonde ◽  
Mir Faizal
Keyword(s):  
General Relativity ◽  
Casimir Effect ◽  
Boundary Effect ◽  
Experimental Tests ◽  
Classical Field ◽  
Einstein Equations ◽  
Field Equations ◽  
Tests Of General Relativity ◽  
Boundary Terms ◽  
Theories Of Gravity

The Einstein equations, apart from being the classical field equations of General Relativity, are also the classical field equations of two other theories of gravity. As the experimental tests of General Relativity are done using the Einstein equations, we do not really know if gravity is the curvature of a torsionless spacetime or torsion of a curvatureless spacetime or if it occurs due to the nonmetricity of a curvatureless and torsionless spacetime. However, as the classical actions of all these theories differ from each other by the boundary terms, and the Casimir effect is a boundary effect, we propose that a novel gravitational Casimir effect between superconductors can be used to test which of these theories actually describe gravity.

scholarly journals NON-LOCALITY OF QUANTUM MECHANICS AND THE LOCALITY OF GENERAL RELATIVITY

2002 ◽  
Vol 17 (15n17) ◽  
pp. 1097-1106 ◽  
Author(s):  
JEEVA ANANDAN
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Non Local ◽  
Frame Work ◽  
Time Description ◽  
Aharonov Bohm ◽  
Space Description ◽  
Non Locality

The conflict between the locality of general relativity, reflected in its space-time description, and the non-locality of quantum mechanics, contained in its Hilbert space description, is discussed. Gauge covariant non-local observables that depend on gauge fields and gravity as well as the wave function are used in order to try to understand and minimize this conflict within the frame-work of these two theories. Applications are made to the Aharonov-Bohm effect and its generalizations to non Abelian gauge fields and gravity.

scholarly journals THE CAUCHY PROBLEM FOR f(R)-GRAVITY: AN OVERVIEW

2012 ◽  
Vol 09 (01) ◽  
pp. 1250006 ◽  
Author(s):  
S. CAPOZZIELLO ◽  
S. VIGNOLO
Keyword(s):  
Cauchy Problem ◽  
General Relativity ◽  
Scalar Fields ◽  
Conformal Transformations ◽  
Field Equations ◽  
The Cauchy Problem ◽  
Theories Of Gravity ◽  
Matter Fields

We review the Cauchy problem for f(R) theories of gravity, in metric and metric-affine formulations, pointing out analogies and differences with respect to General Relativity. The role of conformal transformations, effective scalar fields and sources in the field equations is discussed in view of the well-formulation and the well-position of the problem. Finally, criteria of viability of the f(R)-models are considered according to the various matter fields acting as sources.

scholarly journals Non-Locality and Late-Time Cosmic Acceleration from an Ultraviolet Complete Theory †

Universe ◽  
2018 ◽  
Vol 4 (8) ◽  
pp. 82 ◽  
Author(s):  
Gaurav Narain ◽  
Tianjun Li
Keyword(s):  
Dark Energy ◽  
Local Treatment ◽  
Scalar Fields ◽  
Cosmic Acceleration ◽  
Late Time ◽  
Scale Invariant ◽  
Higher Derivative ◽  
Local Gravity ◽  
Non Local ◽  
Non Locality

A local phenomenological model that reduces to a non-local gravitational theory giving dark energy is proposed. The non-local gravity action is known to fit the data as well as Λ-CDM thereby demanding a more fundamental local treatment. It is seen that the scale-invariant higher-derivative scalar-tensor theory of gravity, which is known to be ultraviolet perturbative renormalizable to all loops and where ghosts become innocuous, generates non-locality at low energies. The local action comprises of two real scalar fields coupled non-minimally with the higher-derivative gravity action. When one of the scalar acquiring the Vacuum Expectation Value (VEV) induces Einstein–Hilbert gravity, generates mass for fields, and gets decoupled from system, it leaves behind a residual theory which in turn leads to a non-local gravity generating dark energy effects.

scholarly journals PLANE SYMMETRIC SOLUTIONS IN f(R) GRAVITY

2010 ◽  
Vol 25 (15) ◽  
pp. 1281-1288 ◽  
Author(s):  
M. SHARIF ◽  
M. FARASAT SHAMIR
Keyword(s):  
General Relativity ◽  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Modified Theories Of Gravity ◽  
Field Equations ◽  
Plane Symmetric ◽  
Symmetric Vacuum ◽  
Theories Of Gravity ◽  
Static Plane ◽  
Vacuum Solutions

The modified theories of gravity, especially the f(R) theory, have attracted much attention in recent years. In this context, we explore static plane symmetric vacuum solutions using the metric approach of this theory. The field equations are solved using the assumption of constant scalar curvature which may be zero or nonzero. We have found a total of three plane symmetric solutions. The correspondence of these solutions with the well-known solutions in General Relativity is given.

General Relativity

2019 ◽  
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
High Energy Physics ◽  
Hamiltonian Formulation ◽  
Experimental Tests ◽  
High Energy ◽  
Gravitational Energy ◽  
Field Equations ◽  
Physics First ◽  
Condensed Matter Theory ◽  
Introductory Textbooks

This work is a short textbook on general relativity and gravitation, aimed at readers with a broad range of interests in physics, from cosmology to gravitational radiation to high energy physics to condensed matter theory. It is an introductory text, but it has also been written as a jumping-off point for readers who plan to study more specialized topics. As a textbook, it is designed to be usable in a one-quarter course (about 25 hours of instruction), and should be suitable for both graduate students and advanced undergraduates. The pedagogical approach is “physics first”: readers move very quickly to the calculation of observational predictions, and only return to the mathematical foundations after the physics is established. The book is mathematically correct—even nonspecialists need to know some differential geometry to be able to read papers—but informal. In addition to the “standard” topics covered by most introductory textbooks, it contains short introductions to more advanced topics: for instance, why field equations are second order, how to treat gravitational energy, what is required for a Hamiltonian formulation of general relativity. A concluding chapter discusses directions for further study, from mathematical relativity to experimental tests to quantum gravity.

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