Abstract
We show that the structure of the Higgs vacuum could be revealed in gravitational experiments which probe the Schwarzschild geometry to only one order inMG/r beyond that needed for the classical tests of general relativity.
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While not central to the present paper, we should point out in passing that in a recent series of papers the authors have considered the possibility that there may in fact actually be something questionable about Einstein gravity. The specific references are Mannheim, P. D.: 1990,Gen. Rel. Grav. 22, 289.
Mannheim, P. D. and Kazanas, D.: 1989,Astrophys. J. 342, 635.
Kazanas, D. and Mannheim, P. D.: 1991,Astrophys. J. Suppl. (to be published). In this set of papers the authors considered the possibility that gravity is described by the fourth order conformal invariant Weyl theory rather than by the standard second order Einstein theory. In their study the authors found that the static vacuum solution (i.e., the completely empty vacuum solution) to the theory agrees with that of the Einstein theory on stellar scales, but that there are major differences on galactic scales. The Higgs vacuum effects considered in the present paper would also be present in the Weyl theory too, but these effects would not be expected to be radically modified by Weyl gravity on stellar distance scales.
While our theory thus contains both tensor and scalar long range macroscopic classical fields it nonetheless is not in the category of scalar-tensor theories which have been advanced in the literature from time to time as potential alternative candidate theories of gravity to Einstein relativity itself. Our theory is strictly Einstein with its only special feature being that there is a macroscopic Higgs field which makes contributions to the energy-momentum tensor. The origin of this Higgs field could for instance be from the spontaneous breaking of the fundamental interactions or it could be of cosmological origin perhaps being a remnant scalar field from the inflationary universe era. Unlike the situation in the alternate scalar-tensor theories of gravity, our scalar field is not in and of itself intrinsically gravitational, and, moreover, its couplings to ordinary matter are completely standard. With regard to possible observational consequences we note that by and large the alternate scalar-tensor theories of gravity already disagree with observation at the currently available level of orderr −2 in the standard coordinate metric coefficientB(r) of Equation (1) and orderr −1 inA(r) (see, e.g.,Theory and Experiment in Gravitational Physics, by C. M. Will, Cambridge University Press, New York (1981) for an extensive review), whereas, as we will see below, our theory only departs from the Einstein-Schwarzschild metric in the next order.
Buchdahl, H. A.: 1959,Phys. Rev. 115, 1325.
Yilmaz, H.: 1958,Phys. Rev. 111, 1417.
For phenomenological purposes we note in passing that the 4MGr 20 /3r 3 term in Equation (17) could in principle be much larger than theM 3 G 3/3r 3 term. It only needs to be smaller thanM 2 G 2/r 2 for the theory to be compatible with current experimental information. Likewise, in Equation (18) the 4r 20 /r 2 term only needs to be smaller than the 2MG/r term. For the standard solar system testsr 0 could thus conceivably be quite large and could even be fairly close in order of magnitude to the actual radius of the Sun without our theory being in conflict with experiment. The parameterr 0 could then actually be a real radius of a system and it does not seem to have to be constrained to be as small as the Schwarzschild radius of the same system. To obtain any additional theoretical information on the parameterr 0 requires the solving of the so far intractable interior gravitational problem in the presence of Higgs fields. Additionally, we note that we may eventually be able to obtain some information regarding the magnitude of the parameters of our model via the current experimental set of fifth force searches, since our non-Schwarzschild terms could be the origin of any (so far unobserved of course) deviations from Newton. (For details see P. D. Mannheim,Astrophys Space Sci. 181, 55.
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Mannheim, P.D., Kazanas, D. Probing the Higgs vacuum with general relativity. Astrophys Space Sci 185, 167–179 (1991). https://doi.org/10.1007/BF00643185
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DOI: https://doi.org/10.1007/BF00643185