The Schwarzschild problem in the quadratic theory of gravitation

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined. As the theory is conformally invariant, one can use different but physically equivalent conformal frames to study the equations. Previously these equations were studied in a conformal frame which, though suitable far away from the isolated particle, turns out not to be suitable in the neighbourhood of the particle. In the present paper a solution in a conformal frame is obtained that is suitable for considering regions near the particle. The solution thus obtained differs from the previous one in several respects. For example, it has no coordinate singularity for any non-zero value of the radial variable, unlike the previous solution or the Schwarzschild solution. It is also shown with the use of this solution that in this theory distant matter has an effect on local geometry.

Download Full-text

BIANCHI I SOLUTIONS OF EFFECTIVE QUADRATIC GRAVITY

International Journal of Modern Physics D ◽

10.1142/s021827181250037x ◽

2012 ◽

Vol 21 (04) ◽

pp. 1250037 ◽

Cited By ~ 4

Author(s):

DANIEL MÜLLER ◽

JULIANO A. DE DEUS

Keyword(s):

Numerical Solutions ◽

Relativity Theory ◽

De Sitter ◽

General Relativity Theory ◽

Spatial Metrics ◽

Effective Gravity ◽

Bianchi I ◽

Quadratic Theory ◽

Quadratic Gravity ◽

Planck Time

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model E3 for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity. This work is a generalization for nondiagonal spatial metrics of a previous result obtained by one of us and a collaborator for Bianchi I spaces.

Download Full-text

Post-Newtonian limit: second-order Jefimenko equations

The European Physical Journal C ◽

10.1140/epjc/s10052-020-8229-7 ◽

2020 ◽

Vol 80 (7) ◽

Author(s):

David Pérez Carlos ◽

Augusto Espinoza ◽

Andrew Chubykalo

Keyword(s):

Linear Equations ◽

Space Time ◽

Second Order ◽

Field Equations ◽

Gravitational Fields ◽

Mass Distributions ◽

Minkowski Space Time ◽

Theory Of Gravitation ◽

Gravity Probe ◽

Gravitational Equations

Abstract The purpose of this paper is to get second-order gravitational equations, a correction made to Jefimenko’s linear gravitational equations. These linear equations were first proposed by Oliver Heaviside in [1], making an analogy between the laws of electromagnetism and gravitation. To achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s non-linear gravitational equations, but with different physical interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2–5], in the latter gravitation is considered as a physical tensor field in the Minkowski space-time (as in [6–8]). In Jefimenko’s theory of gravitation, exposed in [9, 10], there are two kinds of gravitational fields, the ordinary gravitational field, due to the presence of masses, at rest, or in motion and other field called Heaviside field due to and acts only on moving masses. The Heaviside field is known in general relativity as Lense-Thirring effect or gravitomagnetism (The Heaviside field is the gravitational analogous of the magnetic field in the electromagnetic theory, its existence was proved employing the Gravity Probe B launched by NASA (See, for example, [11, 12]). It is a type of gravitational induction), interpreted as a distortion of space-time due to the motion of mass distributions, (see, for example [13, 14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

Download Full-text