scholarly journals Fierz–Pauli theory reloaded: from a theory of a symmetric tensor field to linearized massive gravity

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Giulio Gambuti ◽  
Nicola Maggiore
Keyword(s):  
General Relativity ◽  
Tensor Field ◽  
Degrees Of Freedom ◽  
Mass Parameter ◽  
Symmetric Tensor ◽  
Field Approximation ◽  
Massive Gravity ◽  
Alternative Theory ◽  
Theoretical Treatment ◽  
Massless Limit

AbstractModifying gravity at large distances by means of a massive graviton may explain the observed acceleration of the Universe without Dark Energy. The standard paradigm for Massive Gravity is the Fierz–Pauli theory, which, nonetheless, displays well known flaws in its massless limit. The most serious one is represented by the vDVZ discontinuity, which consists in a disagreement between the massless limit of the Fierz–Pauli theory and General Relativity. Our approach is based on a field-theoretical treatment of Massive Gravity: General Relativity, in the weak field approximation, is treated as a gauge theory of a symmetric rank-2 tensor field. This leads us to propose an alternative theory of linearized Massive Gravity, describing five degrees of freedom of the graviton, with a good massless limit, without vDVZ discontinuity, and depending on one mass parameter only, in agreement with the Fierz–Pauli theory.

CAN THE GRAVITON HAVE A MASS?

2011 ◽  
Vol 20 (14) ◽  
pp. 2803-2807 ◽  
Author(s):  
KAZUYA KOYAMA ◽  
GUSTAVO NIZ ◽  
GIANMASSIMO TASINATO
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Massive Gravity ◽  
Late Time ◽  
Graviton Mass ◽  
Massless Limit ◽  
Mass Source ◽  
Free Theory ◽  
Acceleration Of The Universe ◽  
The Universe

In this essay, we address two long-standing problems of massive gravity: The ghost mode found by Boulware and Deser, and the incompatibility with General Relativity in the massless limit, better known as the vDVZ discontinuity. We present a recent candidate for a ghost-free theory, and show how Einstein's gravity is recovered within a certain macroscopic radius from a mass source, via the Vainshtein mechanism. We also exhibit an exact solution which could account for the late time acceleration of the Universe by means of a small graviton mass.

scholarly journals A Teleparallel Type Theory for Massless Spin 2 Fields

2020 ◽  
Author(s):  
José Wadih Maluf ◽  
Sérgio Costa Ulhoa
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
Type Theory ◽  
Degrees Of Freedom ◽  
Symmetric Tensor ◽  
Flat Space ◽  
Space Time ◽  
Two Degrees Of Freedom ◽  
Curved Space ◽  
Massless Spin

We present the Lagrangian and Hamiltonian formulations of a theory for spin 2 fields. The construction is developed in flat space-time. The construction in curved space-time is conceptually straightforward, although it is not unique. The theory is based on a symmetric tensor $S_{\mu\nu}$, contains two degrees of freedom of radiation, is motivated by the teleparallel formulation of general relativity, and displays a certain resemblance with Maxwell's theory for the electromagnetic field.

Fixing redundant degrees of teleparallel equivalent of general relativity

2017 ◽  
Vol 14 (11) ◽  
pp. 1750154
Author(s):  
Gamal G. L. Nashed ◽  
B. Elkhatib
Keyword(s):  
General Relativity ◽  
Lorentz Transformation ◽  
Arbitrary Function ◽  
Degrees Of Freedom ◽  
Symmetric Tensor ◽  
Cylindrical Symmetry ◽  
Radial Coordinate ◽  
Field Equations ◽  
Local Lorentz Transformation ◽  
Teleparallel Theory

It is well known that the field equation of teleparallel theory which is equivalent to general relativity completely agrees with the field equations of general relativity. However, teleparallel equivalent of general relativity has six redundant degrees of freedom which spoil the true physics. These extra degrees are related to the local Lorentz transformation. In this study, we give three different tetrad fields having cylindrical symmetry and depend only on the radial coordinate. One of these tetrads contains an arbitrary function, which is responsible to reproduce the other solutions, which come from local Lorentz transformation. We show by explicate calculations that this arbitrary function spoils the calculations of the conserved charges. We formulate a skew-symmetric tensor whose vanishing value puts a constraint on this arbitrary function. This constraint fixed the redundant degrees of freedom which characterize the teleparallel equivalent of general relativity.

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

scholarly journals Phase Transitions of the BTZ Black Hole in New Massive Gravity

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Yun Soo Myung
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Phase Transitions ◽  
Fourth Order ◽  
Mass Parameter ◽  
Massive Gravity ◽  
Curvature Radius ◽  
Btz Black Hole

We investigate thermodynamics of the BTZ black hole in new massive gravity explicitly. Form2l2>1/2withm2being the mass parameter of fourth-order terms andl2AdS3curvature radius, the Hawking-Page phase transition occurs between the BTZ black hole and AdS (thermal) soliton. Form2l2<1/2, however, this transition unlikely occurs but a phase transition between the BTZ black hole and the massless BTZ black hole is possible to occur. We may call the latter the inverse Hawking-Page phase transition and this transition is favored in the new massive gravity.

Can a tensorial analogue of gravitational force explain away the galactic rotation curves without dark matter?

2021 ◽  
Author(s):  
Ram Gopal Vishwakarma
Keyword(s):  
Dark Matter ◽  
Tensor Field ◽  
Gravitational Force ◽  
Direct Detection ◽  
Alternative Theory ◽  
Galactic Rotation ◽  
Rotation Curves ◽  
Modern Physics ◽  
Flat Rotation Curves ◽  
Relativistic Analogue

The dark matter problem is one of the most pressing problems in modern physics. As there is no well-established claim from a direct detection experiment supporting the existence of the illusive dark matter that has been postulated to explain the flat rotation curves of galaxies, and since the whole issue of an alternative theory of gravity remains controversial, it may be worth to reconsider the familiar ground of general relativity (GR) itself for a possible way out. It has recently been discovered that a skew-symmetric rank-three tensor field — the Lanczos tensor field — that generates the Weyl tensor differentially, provides a proper relativistic analogue of the Newtonian gravitational force. By taking account of its conformal invariance, the Lanczos tensor leads to a modified acceleration law which can explain, within the framework of GR itself, the flat rotation curves of galaxies without the need for any dark matter whatsoever.

scholarly journals A Note On Umbilics of a Closed Surface

1959 ◽  
Vol 15 ◽  
pp. 219-223
Author(s):  
Minoru Kurita
Keyword(s):  
Riemannian Manifold ◽  
Euclidean Space ◽  
Tensor Field ◽  
Symmetric Tensor ◽  
Closed Surface ◽  
Dimension 2 ◽  
Direction Field

In this paper we investigate indices of umbilics of a closed surface in the euclidean space. Most part of the discussion is concerned with a symmetric tensor field of degree 2, or rather a direction field, on a Riemannian manifold of dimension 2.

scholarly journals Torsion or not torsion, that is the question

2016 ◽  
Vol 25 (12) ◽  
pp. 1644013 ◽  
Author(s):  
Yuri Bonder
Keyword(s):  
General Relativity ◽  
Degrees Of Freedom ◽  
Empirical Support ◽  
Experimental Tests ◽  
Spin Polarized ◽  
Empirical Tests ◽  
New Interactions

A hypothesis of general relativity (GR) is that spacetime torsion vanishes identically. This assumption has no empirical support; in fact, a nonvanishing torsion is compatible with all the experimental tests of GR. The first part of this essay specifies the framework that is suitable to test the vanishing-torsion hypothesis, and an interesting relation with the gravitational degrees of freedom is suggested. In the second part, some original empirical tests are proposed based on the observation that torsion induces new interactions between different spin-polarized particles.

scholarly journals Augustine of Hippo’s Philosophy of Time Meets General Relativity

KronoScope ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 71-89 ◽  
Author(s):  
Ettore Minguzzi
Keyword(s):  
General Relativity ◽  
Cosmological Model ◽  
Degrees Of Freedom ◽  
Big Bang ◽  
Null Hypersurface ◽  
Philosophy Of Time ◽  
The Big Bang ◽  
The Universe

Abstract This paper proposes a cosmological model that uses a causality argument to solve the homogeneity and entropy problems of cosmology. In this model, a chronology violating region of spacetime causally precedes the remainder of the Universe, and a theorem establishes the existence of time functions precisely outside the chronology violating region. This model is shown to nicely reproduce Augustine of Hippo’s thought on time and the beginning of the Universe. In the model, the spacelike boundary representing the Big Bang is replaced by a null hypersurface at which the gravitational degrees of freedom are almost frozen while the matter and radiation content is highly homogeneous and thermalized.

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