Massive NGT and spherically symmetric systems

Abstract

The arguments leading to the introduction of the massive Nonsymmetric Gravitational action are reviewed [1,2], leading to an action that gives asymptotically well-behaved perturbations on GR backgrounds. Through the analysis of spherically symmetric perturbations about GR (Schwarzschild) and NGT (Wyman-type) static backgrounds, it is shown that spherically symmetric systems are not guaranteed to be static, and hence Birkhoff's theorem is not valid in NGT. This implies that in general one must consider time dependent exteriors when looking at spherically symmetric systems in NGT. For the surviving monopole mode considered here there is no energy flux as it is short ranged by construction. Further work on the spherically symmetric case will be motivated through a discussion of the possibility that there remain additional modes that do not show up in weak field situations, but nonetheless exist in the full theory and may again result in bad global asymptotics. A presentation of the action and field equations in a general frame is given in the course of the paper, providing an alternative approach to dealing with the algebraic complications inherent in NGT, as well as offering a more general framework for discussing the physics of the antisymmetric sector.

Einstein Gravity in Almost Kähler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics

“…In this paper, for simplicity, we shall work with a general d-connection D which is compatible toǧ, i.e. satisfies the conditions (37), or (36), and can be generated by a distorsion tensor B from D (39), or from n D (35). We note that for certain canonical constructions the d-objects D, • D, D, n D and B are completely defined by the coefficients of a d-metricǧ = g + a and N on V.…”

“…The authors agreed that one can be elaborated such models with nonzero mass term for the nonsymmetric part of metric (treated as an absolutely symmetric torsion induced by an effective B-field like in string gravity, but in four dimensions). That solved the problems formally created by absence of gauge invariance found by Damour, Deser and McCarthy [34], see explicit constructions and detailed discussions in [23,35]. It was also emphasized that, as a matter of principle, the 1 A pair (V, N ), where V is a manifold and N is a nonintegrable distribution on V, is called a nonholonomic manifold; we note that in our works we use left "up" and "low" symbols as formal labels for certain geometric objects and that the spacetime signature may be encoded into formal frame (vielbein) coefficients, some of them being proportional to the imaginary unity i, when i 2 = −1.…”

“…One should be noted that in a number of works on gravity with nonsymmetric metrics the short term NGT is used [35,36] (instead of nonsymmetric gravity theory/-ies, see details in [22][23][24]38]). This may result in some misunderstanding with the "noncommutative gravity theory" developed in some approaches to noncommutative geometry and applications.…”

The Dynamical Instability of Static, Spherically Symmetric Solutions in Nonsymmetric Gravitational Theories

“…Here we will give the (coordinate frame) action for NGT as presented in [12] S ngt = d 4 x √ −g −g µν R ns µν − g µν ∇ [µ [W ] ν] + 1 2 αg µν W µ W ν + l µ Λ µ + 1 4 µ 2 g [µν] g [µν] . (2.1)…”

“…The action (2.1) and field equations (2.3) and (2.4) encompass those of the 'massive' theory [13,12,14,15] when α = 3/4, 'old' NGT [2] with vanishing source current for α = 0 and µ = 0 (which is equivalent to UFT [16,3]), and recovers GR in the limit that all antisymmetric components of the fundamental tensor are set to zero [12,17]. The general form of the spherically-symmetric fundamental tensor [18] consists of the general form of a spherically symmetric metric with the additional antisymmetric components g [01] = ω(t, r) and g [23] = f (t, r) sin(θ); in this work we consider the Wyman sector [4,5] defined by choosing g [01] = 0.…”