Static spherically symmetric solutions in a new algebraically extended theory of gravity

Kelly, Patrick; Mann, Robert B.

doi:10.1088/0264-9381/4/6/018

Cited by 10 publications

(2 citation statements)

References 29 publications

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“…Thus the model is sick already at quadratic order, having "ghost" kinematics, even though its flat space limit is the required H 2 theory. This much was noticed in [16]; earlier it had separately been noted that these theories had no asymptotically flat static spherically symmetric solution [17]. To elucidate further the sickness of the model when expanded on a curved background, let us consider the field equations, which decompose into symmetric and antisymmetric pieces as follows:…”

Section: Problems With the Basic Modelsmentioning

confidence: 99%

Nonsymmetric gravity theories: Inconsistencies and a cure

1993

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Motivated by the apparent dependence of string σ-models on the sum of spacetime metric and antisymmetric tensor fields, we reconsider gravity theories constructed from a nonsymmetric metric. We first show that all such "geometrical" theories homogeneous in second derivatives violate standard physical requirements: ghost-freedom, absence of algebraic inconsistencies or continuity of degree-of-freedom content. This no-go result applies in particular to the old unified theory of Einstein and its recent avatars. However, we find that the addition of nonderivative, "cosmological" terms formally restores consistency by giving a mass to the antisymmetric tensor field, thereby transmuting it into a fifth-force-like massive vector but with novel possible matter couplings. The resulting macroscopic models also exhibit "van der Waals"-type gravitational effects, and may provide useful phenomenological foils to general relativity.

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Section: Problems With the Basic Modelsmentioning

confidence: 99%

Nonsymmetric gravity theories: Inconsistencies and a cure

1993

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“…This theory was extended by Kalinowski [28] to include spin-torsion coupling. A different theory, based on the same geometry but with different fundamental variables, has been constructed by Kelly and Mann [29]. Zai-Zhe [30] has proposed a non-symmetric gauge theory of gravitation.…”

Section: Introductionmentioning

confidence: 99%

Generalised affine geometry and algebraically extended relativity-a new approach to spin-torsion coupling

Soleng¹

1989

Class. Quantum Grav.

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A geometric theory of gravitation with spin-torsion coupling is proposed. The theory could be interpreted either as general relativity based on a generalised affine connection, or alternatively as an algebraically extended general relativity over the algebra of hypercomplex numbers. According to the algebraically extended interpretation the torsion tensor must be totally antisymmetric. In this case the authors also have a geometric symmetry corresponding to spin-reversal invariance. The simplest Lagrangian density within this theory is that of the Einstein-Cartan theory, but where torsion is determined by an antisymmetric torsion potential. The conservation laws of the theory correspond to conservation of energy-momentum and spin-angular momentum.

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New ghost-free extensions of general relativity

Mann

1989

Class. Quantum Grav.

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The method of algebraic extension is shown to yield a large class of gravitational theories which are extensions of general relativity. Requiring positivity of energy in the flat-space limit of such theories provides some constraints, but a large set of theories of potential phenomenological interest survives this condition. Explicit examples of such theories include the non-symmetric gravitational theory of Moffat, algebraically extended Hilbert gravity and a one-parameter family of theories with dynamical torsion. In general such theories do not alter general relativistic post-Newtonian predictions for time delay experiments; rather they alter the non-linearities of the post-Newtonian gravitational potential. Such effects may be probed by measuring periastron shifts, as in the eclipsing binary systems Di Her and AS Cam, as well as in the binary pulsar PSR 1913+16.

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Static spherically symmetric solutions in a new algebraically extended theory of gravity

Cited by 10 publications

References 29 publications

Nonsymmetric gravity theories: Inconsistencies and a cure

Nonsymmetric gravity theories: Inconsistencies and a cure

Generalised affine geometry and algebraically extended relativity-a new approach to spin-torsion coupling

New ghost-free extensions of general relativity

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