scholarly journals On Noncommutative Corrections of Gravitational Energy in Teleparallel Gravity

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
S. C. Ulhoa ◽  
R. G. G. Amorim
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Teleparallel Gravity ◽  
Gravitational Energy ◽  
Schwarzschild Solution ◽  
Metric Tensor ◽  
Noncommutative Spacetime

We use the theory of teleparallelism equivalent to general relativity based on noncommutative spacetime coordinates. In this context, we write the corrections of the Schwarzschild solution. We propose the existence of a Weitzenböck spacetime that matches the corrected metric tensor. As an important result, we find the corrections of the gravitational energy in the realm of teleparallel gravity due to the noncommutativity of spacetime. Then we interpret such corrections as a manifestation of quantum theory in gravitational field.

“Prehistoric” Quantum Gravity

2020 ◽  
pp. 41-70
Author(s):  
Dean Rickles
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Quantum Gravity ◽  
Philosophical Nature

In this chapter we examine the very earliest work on the problem of quantum gravity (understood very liberally). We show that, even before the concept of the quantization of the gravitational field in 1929, there was a fairly lively investigation of the relationships between gravity and quantum stretching as far back as 1916, and certainly no suggestion that such a theory would not be forthcoming. Indeed, there are, rather, many suggestions explicitly advocating that an integration of quantum theory and general relativity (or gravitation, at least) is essential for future physics, in order to construct a satisfactory foundation. We also see how this belief was guided by a diverse family of underlying agendas and constraints, often of a highly philosophical nature.

scholarly journals The Spectrum of Teleparallel Gravity

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 80 ◽  
Author(s):  
Tomi Koivisto ◽  
Georgios Tsimperis
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Quadratic Form ◽  
Degrees Of Freedom ◽  
Arbitrary Dimension ◽  
Scalar Potential ◽  
Ultra Violet ◽  
Teleparallel Gravity ◽  
Frame Field ◽  
Covariant Derivation

The observer’s frame is the more elementary description of the gravitational field than the metric. The most general covariant, even-parity quadratic form for the frame field in arbitrary dimension generalises the New General Relativity by nine functions of the d’Alembertian operator. The degrees of freedom are clarified by a covariant derivation of the propagator. The consistent and viable models can incorporate an ultra-violet completion of the gravity theory, an additional polarisation of the gravitational wave, and the dynamics of a magnetic scalar potential.

The Development of Relativity and Einstein

2015 ◽  
Vol 10 (3) ◽  
pp. 2874-2885 ◽  
Author(s):  
C. Y. Lo
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Einstein Equation ◽  
Dimensional Space ◽  
Gravitational Energy ◽  
Energy Conditions ◽  
Positive Mass Theorem ◽  
Charge Mass ◽  
Final Theory ◽  
Singularity Theorems

There are errors in general relativity that must be rectified. As Zhou pointed out, Einstein’s covariance principle is proven to be invalid by explicit examples. Linearization is conditionally valid. Pauli's version of the equivalence principle is impossible in mathematics. Einstein's adaptation of the distance in Riemannian geometry is invalid in physics as pointed out by Whitehead. Moreover, it is inconsistent with the calculation on the bending of light, for which a Euclidean-like framework is necessary. Thus, the interpretation of the Hubble redshifts as due to receding velocities of stars is invalid. The Einstein equation has no dynamic solutions just as Gullstrand suspected. All claims on the existence of dynamic solutions for the Einstein equation are due to mistakes in non-linear mathematics. For the existence of a dynamic solution, the Einstein equation must be modified to the Lorentz-Levy-Einstein equation that have additionally a gravitational energy-stress tensor with an anti-gravity coupling. The existence of photons is a consequence of general relativity. Thus, the space-time singularity theorems of Hawking and Penrose are actually irrelevant to physics because their energy conditions cannot be satisfied. The positive mass theorem of Schoen and Yau is misleading because invalid implicit assumptions are used as Hawking and Penrose did. There are three experiments that show formula E = mc2 is invalid, and a piece of heated-up metal has reduced weight just as a charged capacitor. Thus, the weight is temperature dependent. It is found, due to the repulsive charge-mass interaction, gravity is not always attractive to mass. Since the assumption that gravity is always attractive to mass is not valid, the existence of black holes are questionable.  Because of the repulsive charge-mass interaction, the theoretical framework of general relativity must be extended to a five-dimensional relativity of Lo, Goldstein & Napier. Thus Einstein's conjecture of unification is valid. Moreover, the repulsive gravitational force from a charged capacitor is incompatible with the notion of a four-dimensional space. In Quantum theory, currently the charge-mass interaction is neglected. Thus, quantum theory is not a final theory as Einstein claims.

scholarly journals TELEPARALLEL GRAVITATIONAL ENERGY IN THE GAMMA METRIC

2006 ◽  
Vol 15 (05) ◽  
pp. 695-701 ◽  
Author(s):  
MUSTAFA SALTI
Keyword(s):  
General Relativity ◽  
Teleparallel Gravity ◽  
Gravitational Energy ◽  
Coupling Constants ◽  
Dimensionless Coupling ◽  
Weinberg Complex

The Møller energy (due to matter and fields including gravity) distribution of the gamma metric is studied in teleparallel gravity. The result is the same as those obtained in general relativity by Virbhadra in the Weinberg complex and Yang–Radincshi in the Møller definition. Our result is also independent of the three teleparallel dimensionless coupling constants, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model.

ON TOLMAN'S MASS-ENERGY RELATION AND A NEW TOLMAN-TYPE RELATION

1989 ◽  
Vol 04 (02) ◽  
pp. 327-334
Author(s):  
B. M. BARKER ◽  
R. F. O'CONNELL
Keyword(s):  
Gravitational Field ◽  
Coordinate System ◽  
Energy Relation ◽  
Mass Energy ◽  
Schwarzschild Solution ◽  
Metric Tensor ◽  
Harmonic Coordinates ◽  
Isotropic Coordinates ◽  
Special Cases ◽  
Type Relation

Tolman derived the mass-energy relation [Formula: see text] using a particular choice of coordinates, viz. the Schwarzschild solution for the metric tensor in isotropic coordinates for a body of mass m at rest at the origin. Here we show that this relation retains the same form for the case of a very general coordinate system. The latter includes the Schwarzschild and harmonic coordinates as special cases. In addition, we give a new Tolman-type relation [Formula: see text]. The quantities [Formula: see text] and [Formula: see text] are the energy-momentum densities for matter and the gravitational field, respectively.

The point free Colombeau geometry in singular general relativity

2021 ◽  
Author(s):  
Ja. Foukzon ◽  
A.A. Potapov ◽  
E.R. Men'kova
Keyword(s):  
General Relativity ◽  
Physical Interpretation ◽  
Curvature Scalar ◽  
Schwarzschild Spacetime ◽  
Problem Statement ◽  
Colombeau Algebra ◽  
Schwarzschild Solution ◽  
Metric Tensor ◽  
Levi Civita Connection ◽  
Distributional Geometry

The problem statement. We argue that the canonical interpretation of the Schwarzschild spacetime in contemporary general relativity is wrong and that revision is needed. And we argue that the Schwarzschild solution is impossible to treat classically, since the Levi-Cività connection is not available for the whole Schwarzschild spacetime (Sch,gijSch (t r, , ,θϕ)) ; where Sch=×(({r ≥ 2m} {∪ ≤ ≤0 r 2m})×S2) ; but it can only be treated by using an embedding of the classical Schwarzschild metric tensor gijSch; ,i j =1,2,3,4 into Colombeau algebra δ(4,Σ),Σ= ={r 2m} {∪ =r 0} supergeneralized functions. The classical Schwarzschild spacetime could be extended up to the distributional semi-Riemannian manifold endowed on the tangent bundle with the Colombeau distributional metric tensor. The aim. The development of new physical interpretation for the distributional curvature scalar (Rε( )r )ε and square scalar (Rεμν( )r Rμνε, ( )r )ε, (Rερσμν( )r Rρδμνε, ( )r )εis aimed. Results. The Schwarzschild solution using Colombeau distributional geometry without leaving Schwarzschild coordinates (t r, , ,θϕ) is studied. We obtain that the distributional Ricci tensor and the curvature scalar are δ-type, (R rε( ))ε=−m rδ( − 2m) ,>0 . The practical value. As distributional square scalars are essentially nonclassical Colombeau type distributions: (Rεμν( )r Rμνε, ( )r )ε, (Rερσμν( )r Rρσμνε, ( )r )ε∈(3 )\ ′(3 ), this provides a new physical interpretation for the distributional curvature scalar (R rε( ))ε and square scalars (Rεμν( )r Rμνε, ( )r )ε, (Rερσμν( )r Rρδμνε, ( )r )ε.

On the Independent Emergence of Space-time

2020 ◽  
pp. 183-194
Author(s):  
Richard Healey
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Physical Theory ◽  
Space Time ◽  
Structural Quality ◽  
Space Time Structure ◽  
Emergent Structure ◽  
Fundamental Physical

Physics might show that space-time is an emergent structure without describing its ontological basis. Space and time are fundamental to metaphysics and physics. Their union remained fundamental after special relativity doomed each separately to fade away as a mere shadow of the space-time that Einstein later took to exist only as a structural quality of the gravitational field of general relativity. But problems meshing general relativity with quantum theory appear to show that space-time structure is not fundamental but emerges within a quantum theory of gravity. In a pragmatist view, quantum theory is typically applied not to represent target systems but to guide rational credence about events involving other systems. Applied to a gravitational field, quantum theory may guide credence about events in an emergent space-time without itself representing that field. If so, a fundamental physical theory would not describe any ultimate ground of space-time and its contents.

Conceptual Pitfalls in Teaching the Linearized Approximation in Introductory General Relativity

2020 ◽  
Vol 02 (04) ◽  
pp. 2020005
Author(s):  
Valerio Faraoni
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Test Field ◽  
Metric Tensor ◽  
Small Perturbations ◽  
Flat Background ◽  
Course Material ◽  
Generally Covariant

The decomposition of the metric tensor into a flat background plus small perturbations used in linearized general relativity is often a source of confusion for the student because these two parts are only Lorentz-invariant but not generally covariant. The underlying, crucial, conceptual switch from a dynamical gravitational field to a test field on a fixed background is often omitted in presenting this course material. This issue is clarified and an improved presentation is proposed.

THE EQUIVALENCE PROBLEM IN TELEPARALLEL GRAVITY

2002 ◽  
Vol 17 (29) ◽  
pp. 4161-4166
Author(s):  
J. FONSECA
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Equivalence Problem ◽  
Teleparallel Gravity ◽  
Alternative Formulation ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Invariant Description ◽  
Torsion Free

The teleparallel equivalent of general relativity (TEGR) is an alternative formulation of Einstein's equations in the framework of Riemann-Cartan spacetimes. The gravitational field can be described either by the curvature of the torsion-free connection of general relativity (GR) or by the torsion of the curvature-free connection of the TEGR. Both in GR and TEGR the freedom in the choice of coordinates gives rise to the equivalence problem of deciding whether two solutions of the field equations are the same. This problem is solved by means of a invariant description of the gravitational field. We investigate whether the equivalence between GR and TEGR also holds at the level of these invariant descriptions. We show that the GR description assures equivalence in TEGR only in very special situations. These results are illustrated on teleparallel spacetimes with torsion and Gödel metric.

A CONJECTURE REGARDING QUANTIZED GRAVITATIONAL THEORY AND THE SIZE OF ELEMENTARY PARTICLES

1967 ◽  
Vol 45 (7) ◽  
pp. 2383-2384 ◽  
Author(s):  
Gerald Rosen
Keyword(s):  
Elementary Particle ◽  
General Relativity ◽  
Quantum Theory ◽  
Gravitational Theory ◽  
Gravitational Energy ◽  
Elementary Particles ◽  
Particle Structure ◽  
The Real ◽  
Physical Universe ◽  
Order Of Magnitude

For the quantum theory of general relativity in the real physical universe with radius of about 1028 cm, the order-of-magnitude analysis in this work leads to a fundamental and characteristic metrical disturbance, with a size of about 10−12 cm. It is possible that such a characteristic metrical disturbance (and the considerable amount of associated gravitational energy) may play an important role in elementary particle structure.

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