Remarks on theoretical problems in nonsymmetric gravitational theory

Abstract

Damour, Deser, and McCarthy have claimed that the nonsymmetric gravitational theory (NGT) is untenable due to curvature coupled ghost modes and bad asymptotic behavior. This claim is false for it is based on the incorrect assertion that only non-falling-off solutions can be found for the field equations, and that the nonexistence of an exact gauge symmetry for the skew sector leads to a flux of negative energy. We show that the NGT has solutions compatible with physical boundary conditions and that the flux of gravitational radiation in NGT is finite in magnitude and positive in sign.PACS number(s) : 04.50.fhThe nonsymmetric gravitational theory (NGT) has been extensively studied over a period of years [1,2] and these studies have shown that the theory is a mathematically consistent alternative t o Einstein's gravitational theory [general relativity (GR)]. Other possible versions of nonsymmetric gravitational theories [3,4] have either been shown t o possess.ghost poles in the linear approximation or not t o contain static spherically symmetric solutions, which have a Schwarzschild-like behavior a t large distances, unless the parameter describing the Schwarzschild mass is forced to be negative definite [4].The NGT Lagrangian without sources is of the form 121 :and where a semicolon denotes covariant differentiation with respect to the connection I?;,. Equations (7) and (8) are constrained, in turn, by the identities The field equations are further constrained by the four Bianchi identities: where The empty space field equations which follow from (1) are These field equations represent 12 independent equations for the 12 independent field variables g, , [there exist four arbitrary coordinate transformations: dxlP = ( 8 x 1~/ a x a ) d z a , which can be used to remove 4 of the 16 ~P V ' S I . Equation ( 5 ) can be decomposed into the two sets of equations R{[P"],U) = R[,"] (r'),u + R [ W U I (~) ,~ + R[UPl ( r ) , " = 07where G,,(r) = R,, ( r ) -g,,R(I').Employing Eq. (6) to eliminate I? in favor of g,,, Eqs. (4), (7), and (8) represent 18 equations for g,,. Taking into account the six identities (lo), ( l l ) , and (12)) this set of equations provides 12 independent field equations for the 12 independent field variables, g,,. At no stage have we had to refer to the vector WP. WP does not describe dynamical degrees of freedom, in keeping with the fact that it corresponds t o a Lagrange multiplier. Of course, one could use Eq. (9) t o solve for W, in terms of the previously determined g,, but this would serve no useful purpose.In a weak-field approximation obtained from expanding g, , about the Minkowski spacetime metric qPv, where E << 1, the field equations take the form, to lowest order, 4422 N . J. CORNISH AND J. W. MOFFAT -47where = 8P8, and h = qCYPh,p. We see that the symmetric part of the field equations decouples from the skew part, and that it is identical to that of GR. The skew equations take the form of Kalb-Ramond-Kimura equations [5] in a permanently fixed gauge [although (15) are, strictly speaking...

Nonsymmetric gravitational theory

“…An analysis of the properties of gravitational radiation in the nonsymmetric gravitational theory (NGT) is given, based on the field equations with sources. In previous work 1 , an analysis of the radiation problem in NGT, showed that the flux of gravitational radiation was the same as the leading order contribution in general relativity (GR). This result was shown to follow from the axisymmetric, time-dependent vacuum field equations in a first-order expansion about a curved GR background 2 .…”

Relativistic Exponential Gravitation and Exponential Potential of Electric Charge

“…We mention some Nonsymmetrical Gravitational Theories (38)(39)(40)(41)(42)(43)(44)(45) (NGT), that do not exhibit black holes. These NGT theories are based on nonsymmetric metric tensors.…”

Gravitational waves from an axi-symmetric source in the Nonsymmetric Gravitational Theory

“…Secondly, the literature already contains several incorrect treatments of gravitational radiation in NGT [3][4][5], and since more incorrect treatments are currently being published [6], it is important that the record be set straight. The reasons why erroneous results were arrived at by these other authors are explained in [7].…”