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.

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.

scholarly journals CAN f(R) GRAVITY MIMIC GENERAL RELATIVITY?

2012 ◽  
Vol 10 ◽  
pp. 63-68 ◽  
Author(s):  
JE-AN GU
Keyword(s):  
General Relativity ◽  
Differential Equations ◽  
Early Time ◽  
Einstein Equations ◽  
Modified Theories Of Gravity ◽  
Cosmological Perturbations ◽  
Long Run ◽  
Theories Of Gravity ◽  
The Stability ◽  
Higher Order Differential Equations

We discuss the stability of the general-relativity (GR) limit in modified theories of gravity, particularly the f(R) theory. The problem of approximating the higher-order differential equations in modified gravity with the Einstein equations (2nd-order differential equations) in GR is elaborated. We demonstrate this problem with a heuristic example involving a simple ordinary differential equation. With this example we further present the iteration method that may serve as a better approximation for solving the equation, meanwhile providing a criterion for assessing the validity of the approximation. We then discuss our previous numerical analyses of the early-time evolution of the cosmological perturbations in f(R) gravity, following the similar ideas demonstrated by the heuristic example. The results of the analyses indicated the possible instability of the GR limit that might make the GR approximation inaccurate in describing the evolution of the cosmological perturbations in the long run.

General Relativity

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Field Equation ◽  
Einstein Field Equation ◽  
Kerr Metric ◽  
Gravitational Lenses ◽  
Field Equations ◽  
Spacetime Geometry ◽  
Tests Of General Relativity ◽  
Rotating Black Holes

This chapter presents the physical motivation for general relativity, derives the Einstein field equation and gives concise derivations of the main results of the theory. It begins with the equivalence principle, tidal forces in Newtonian gravity and their connection to curved spacetime geometry. This leads to a derivation of the field equation. Tests of general relativity are considered: Mercury’s perihelion advance, gravitational redshift, the deflection of starlight and gravitational lenses. The exterior and interior Schwarzschild solutions are discussed. Eddington–Finkelstein coordinates are used to describe objects falling into non-rotating black holes. The Kerr metric is used to describe rotating black holes and their astrophysical consequences. Gravitational waves are described and used to explain the orbital decay of binary neutron stars. Their recent detection by LIGO and the beginning of a new era of gravitational wave astronomy is discussed. Finally, the gravitational field equations are derived from the Einstein–Hilbert action.

scholarly journals Gravitational Redshifts and the Mass-Radius Relation

1989 ◽  
Vol 114 ◽  
pp. 401-407
Author(s):  
Gary Wegner
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Solar System ◽  
White Dwarf ◽  
Sufficient Accuracy ◽  
Gravitational Redshift ◽  
Principle Of Equivalence ◽  
Field Equations ◽  
Tests Of General Relativity ◽  
Gravitational Field Equations

The gravitational redshift is one of Einstein’s three original tests of General Relativity and derives from time’s slowing near a massive body. For velocities well below c, this is represented with sufficient accuracy by:As detailed by Will (1981), Schiff’s conjecture argues that the gravitational redshift actually tests the principle of equivalence rather than the gravitational field equations. For low redshifts, solar system tests give highest accuracy. LoPresto & Pierce (1986) have shown that the redshift at the Sun’s limb is good to about ±3%. Rocket experiments produce an accuracy of ±0.02% (Vessot et al. 1980), while for 40 Eri B the best white dwarf, the observed and predicted VRS agree to only about ±_5% (Wegner 1980).

scholarly journals Generalized derivations and general relativity

2013 ◽  
Vol 91 (10) ◽  
pp. 757-763
Author(s):  
Michael Heller ◽  
Tomasz Miller ◽  
Leszek Pysiak ◽  
Wiesław Sasin
Keyword(s):  
General Relativity ◽  
Extra Dimension ◽  
Linear Mapping ◽  
Einstein Equations ◽  
Leibniz Rule ◽  
Generalized Derivations ◽  
Field Equations ◽  
Time Dimension ◽  
Smooth Functions ◽  
Kaluza Klein

We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra [Formula: see text]. Such a derivation, introduced by Brešar in 1991, is given by a linear mapping [Formula: see text] such that there exists a usual derivation, d, of [Formula: see text] satisfying the generalized Leibniz rule u(ab) = u(a)b + ad(b) for all [Formula: see text]. The generalized geometry “is tested” in the case of the algebra of smooth functions on a manifold. We then apply this machinery to study generalized general relativity. We define the Einstein–Hilbert action and deduce from it Einstein’s field equations. We show that for a special class of metrics containing, besides the usual metric components, only one nonzero term, the action reduces to the O’Hanlon action that is the Brans–Dicke action with potential and with the parameter ω equal to zero. We also show that the generalized Einstein equations (with zero energy–stress tensor) are equivalent to those of the Kaluza–Klein theory satisfying a “modified cylinder condition” and having a noncompact extra dimension. This opens a possibility to consider Kaluza–Klein models with a noncompact extra dimension that remains invisible for a macroscopic observer. In our approach, this extra dimension is not an additional physical space–time dimension but appears because of the generalization of the derivation concept.

THE CONFRONTATION BETWEEN GENERAL RELATIVITY AND EXPERIMENT: A 1992 UPDATE

1992 ◽  
Vol 01 (01) ◽  
pp. 13-68 ◽  
Author(s):  
CLIFFORD M. WILL
Keyword(s):  
General Relativity ◽  
Equivalence Principle ◽  
Experimental Tests ◽  
Advanced Technology ◽  
Theoretical Frameworks ◽  
Binary Pulsar ◽  
Tests Of General Relativity ◽  
Lunar Motion ◽  
The Status ◽  
Einstein's Equivalence Principle

The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein’s equivalence principle is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Tests of general relativity have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected to half a percent using the binary pulsar, and new binary pulsar systems promise further improvements. The status of the “fifth force” is discussed, along with the frontiers of experimental relativity, including proposals for testing relativistic gravity with advanced technology and spacecraft.

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