scholarly journals Massive Conformal Gravity

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
F. F. Faria
Keyword(s):  
Scalar Field ◽  
Field Approximation ◽  
Weak Field ◽  
Vacuum Field ◽  
Conformal Transformations ◽  
Conformal Gravity ◽  
Field Equations ◽  
Metric Tensor ◽  
Weak Field Approximation ◽  
Massive Theory

We construct a massive theory of gravity that is invariant under conformal transformations. The massive action of the theory depends on the metric tensor and a scalar field, which are considered the only field variables. We find the vacuum field equations of the theory and analyze its weak-field approximation and Newtonian limit.

scholarly journals Gravitational Paramagnetism, Diamagnetism and Gravitational Superconductivity

1996 ◽  
Vol 49 (6) ◽  
pp. 1063 ◽  
Author(s):  
M Agop ◽  
C Gh Buzea ◽  
V Griga ◽  
C Ciubotariu ◽  
C Buzea ◽  
...  
Keyword(s):  
Gravitational Field ◽  
Meissner Effect ◽  
Field Approximation ◽  
Weak Field ◽  
Gauge Model ◽  
Closed Geodesics ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Weak Field Approximation ◽  
Superconducting Parameters

In the weak field approximation to the gravitational field equations, we study gravitational paramagnetism and diamagnetism, the gravitational Meissner effect and gravitational superconductivity. The spontaneous symmetry breaking corresponds to crossing from closed geodesics to open ones, and to the existence of a critical temperature in the frame of a gauge model at finite temperature. In this later case one can obtain expressions giving the dependence of several superconducting parameters on temperature.

scholarly journals HEURISTIC APPROACH TO THE SCHWARZSCHILD GEOMETRY

2005 ◽  
Vol 14 (12) ◽  
pp. 2051-2067 ◽  
Author(s):  
MATT VISSER
Keyword(s):  
Field Approximation ◽  
Weak Field ◽  
Point Particle ◽  
De Sitter ◽  
Field Equations ◽  
Kerr Geometry ◽  
Spacetime Geometry ◽  
Schwarzschild Geometry ◽  
Inertial Frames ◽  
Weak Field Approximation

In this article I present a simple Newtonian heuristic for motivating a weak-field approximation for the spacetime geometry of a point particle. The heuristic is based on Newtonian gravity, the notion of local inertial frames (the Einstein equivalence principle), plus the use of Galilean coordinate transformations to connect the freely falling local inertial frames back to the "fixed stars." Because of the heuristic and quasi-Newtonian manner in which the specific choice of spacetime geometry is motivated, we are at best justified in expecting it to be a weak-field approximation to the true spacetime geometry. However, in the case of a spherically symmetric point mass the result is coincidentally an exact solution of the full vacuum Einstein field equations — it is the Schwarzschild geometry in Painlevé–Gullstrand coordinates. This result is much stronger than the well-known result of Michell and Laplace whereby a Newtonian argument correctly estimates the value of the Schwarzschild radius — using the heuristic presented in this article one obtains the entire Schwarzschild geometry. The heuristic also gives sensible results — a Riemann flat geometry — when applied to a constant gravitational field. Furthermore, a subtle extension of the heuristic correctly reproduces the Reissner–Nordström geometry and even the de Sitter geometry. Unfortunately the heuristic construction is not truly generic. For instance, it is incapable of generating the Kerr geometry or anti-de Sitter space. Despite this limitation, the heuristic does have useful pedagogical value in that it provides a simple and direct plausibility argument (not a derivation) for the Schwarzschild geometry — suitable for classroom use in situations where the full power and technical machinery of general relativity might be inappropriate. The extended heuristic provides more challenging problems — suitable for use at the graduate level.

scholarly journals GRAVITATIONAL FIELD OF A GLOBAL MONOPOLE IN A MODIFIED GRAVITY

2011 ◽  
Vol 03 ◽  
pp. 446-454 ◽  
Author(s):  
T. R. P. CARAMÊS ◽  
E. R. BEZERRA DE MELLO ◽  
M. E. X. GUIMARÃES
Keyword(s):  
Gravitational Field ◽  
Modified Gravity ◽  
Field Approximation ◽  
Weak Field ◽  
Symmetric System ◽  
Radial Coordinate ◽  
Spherically Symmetric ◽  
Global Monopole ◽  
Field Equations ◽  
Metric Tensor

In this paper we analyze the gravitational field of a global monopole in the context of f(R) gravity. More precisely, we show that the field equations obtained are expressed in terms of [Formula: see text]. Since we are dealing with a spherically symmetric system, we assume that F(R) is a function of the radial coordinate only. Moreover, adopting the weak field approximation, we can provide all components of the metric tensor. A comparison with the corresponding results obtained in General Relativity and in the Brans-Dicke theory is also made.

scholarly journals CAN A NONLOCAL MODEL OF GRAVITY REPRODUCE DARK MATTER EFFECTS IN AGREEMENT WITH MOND?

2014 ◽  
Vol 23 (01) ◽  
pp. 1450008 ◽  
Author(s):  
IVAN ARRAUT
Keyword(s):  
Dark Matter ◽  
Cosmological Constant ◽  
Field Approximation ◽  
Weak Field ◽  
Nonlocal Model ◽  
Field Equations ◽  
Matter Effects ◽  
Weak Field Approximation

I analyze the possibility of reproducing MONDian dark matter effects by using a nonlocal model of gravity. The model was used before in order to recreate screening effects for the cosmological constant (Λ) value. Although the model in the weak-field approximation (in static coordinates) can reproduce the field equations in agreement with the AQUAL Lagrangian, the solutions are scale dependent and cannot reproduce the same dynamics in agreement with MOND.

A unified field theory of gravitation and electromagnetism

1962 ◽  
Vol 270 (1343) ◽  
pp. 501-516 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Field Approximation ◽  
Weak Field ◽  
Unified Field Theory ◽  
Field Equations ◽  
Action Function ◽  
Metric Tensor ◽  
Simple Modification ◽  
Unified Field ◽  
Spherically Symmetric Solution

The field equations of the theory are obtained by applying the usual variational principle to a scalar density action function constructed from a symmetrical metric tensor and a symmetrical affine connexion. The equations involve a four-dimensional curl which is identified as the electromagnetic field tensor. By rewriting the field equations it is shown that the theory is equivalent to a simple modification of the Born-Infeld theory. The modification is sufficient to destroy the symmetry between magnetostatics and electrostatics and prevents the existence of solutions corresponding to magnetic poles. Two different formulations of the theory are found, one involving electromagnetic potentials and the other involving only the electromagnetic field. Some aspects of the static spherically symmetric solution are discussed and the field equations are examined in a weak field approximation.

Gravitational waves

2019 ◽  
pp. 72-79
Author(s):  
Steven Carlip
Keyword(s):  
Gravitational Waves ◽  
Gravitational Radiation ◽  
Field Approximation ◽  
Weak Field ◽  
Quadrupole Moments ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Compact Binary ◽  
Speed Of Gravity ◽  
Weak Field Approximation

In the weak field approximation, the Einstein field equations can be solved, and lead to the prediction of gravitational waves. After showing that gravitational radiation depends on changing quadrupole moments, this chapter describes the production, propagation, and detection of gravitational waves. It includes discussions of the speed of gravity, detectors, the “chirp” waveform for a compact binary system, and the nature of astrophysical sources.

The Einstein–Maxwell-particle system in the York canonical basis of ADM tetrad gravity. Part 2. The weak field approximation in the 3-orthogonal gauges and Hamiltonian post-minkowskian gravity: the N-body problem and gravitational waves with asymptotic background 1This paper is one of three companion papers published in the same issue of Can. J. Phys.

2012 ◽  
Vol 90 (11) ◽  
pp. 1077-1130 ◽  
Author(s):  
David Alba ◽  
Luca Lusanna
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Waves ◽  
Particle System ◽  
Canonical Basis ◽  
Field Approximation ◽  
Weak Field ◽  
N Body Problem ◽  
Hamilton Equations ◽  
Weak Field Approximation ◽  
Tetrad Gravity

In this second paper we define a post-minkowskian (PM) weak field approximation leading to a linearization of the Hamilton equations of Arnowitt–Deser–Misner (ADM) tetrad gravity in the York canonical basis in a family of nonharmonic 3-orthogonal Schwinger time gauges. The York time 3K (the relativistic inertial gauge variable, not existing in newtonian gravity, parametrizing the family, and connected to the freedom in clock synchronization, i.e., to the definition of the the shape of the instantaneous 3-spaces) is set equal to an arbitrary numerical function. The matter are considered point particles, with a Grassmann regularization of self-energies, and the electromagnetic field in the radiation gauge: an ultraviolet cutoff allows a consistent linearization, which is shown to be the lowest order of a hamiltonian PM expansion. We solve the constraints and the Hamilton equations for the tidal variables and we find PM gravitational waves with asymptotic background (and the correct quadrupole emission formula) propagating on dynamically determined non-euclidean 3-spaces. The conserved ADM energy and the Grassmann regularization of self-energies imply the correct energy balance. A generalized transverse–traceless gauge can be identified and the main tools for the detection of gravitational waves are reproduced in these nonharmonic gauges. In conclusion, we get a PM solution for the gravitational field and we identify a class of PM Einstein space–times, which will be studied in more detail in a third paper together with the PM equations of motion for the particles and their post-newtonian expansion (but in the absence of the electromagnetic field). Finally we make a discussion on the gauge problem in general relativity to understand which type of experimental observations may lead to a preferred choice for the inertial gauge variable 3K in PM space–times. In the third paper we will show that this choice is connected with the problem of dark matter.

QUANTUM FIELDS WITH MODIFIED DISPERSION RELATIONS IN CURVED SPACES

2011 ◽  
Vol 20 (05) ◽  
pp. 745-756 ◽  
Author(s):  
FRANCISCO DIEGO MAZZITELLI
Keyword(s):  
Vector Field ◽  
General Structure ◽  
Scalar Fields ◽  
Field Approximation ◽  
Weak Field ◽  
Dispersion Relations ◽  
Quantum Fields ◽  
Renormalization Procedure ◽  
Modified Dispersion Relations ◽  
Weak Field Approximation

We discuss the renormalization procedure for quantum scalar fields with modified dispersion relations in curved spacetimes. We consider two different ways of introducing modified dispersion relations: through the interaction with a dynamical temporal vector field, as in the context of the Einstein–Aether theory, and breaking explicitly the covariance of the theory, as in Hǒrava–Lifshitz gravity. Working in the weak field approximation, we show that the general structure of the counterterms depends on the UV behavior of the dispersion relations and on the mechanism chosen to introduce them.

DIMENSIONAL REDUCTION AND THE LANCZOS TENSOR

1989 ◽  
Vol 04 (28) ◽  
pp. 2739-2746 ◽  
Author(s):  
M.D. ROBERTS
Keyword(s):  
Dimensional Reduction ◽  
Weyl Tensor ◽  
Weak Field ◽  
Vacuum Field ◽  
Linear Wave ◽  
Field Equations ◽  
Weak Field Limit ◽  
Magnetic Theory ◽  
Electro Magnetic ◽  
The One

The Lanczos tensor Hαβγ is a potential for the Weyl tensor. Given the symmetries of these tensors it would be expected that the identification Hαβ5=Fαβ would give a reduction of the five dimensional vacuum field equations into equations related to the Einstein Maxwell equation, it is shown that this does not happen; furthermore it is shown that there is no dimensional reduction scheme involving the Lanczos tensor which agrees with the one devised by Kaluza and Klein in the weak field limit. The covariant derivative of the Weyl tensor can be expressed as a type of non-linear wave equation in the Lanczos tensor, the literature contains two incorrect expressions for this equation, here the correct expression is given for the first time. The expression for the Lanczos tensor in the case of weak fields is generalized. Some remarks are made on other approaches to include electro-magnetic theory into the theory of the Lanczos tensor.

Sign in / Sign up

Export Citation Format

Share Document