1、arXiv:gr-qc/0304023v2 21 May 2003 Neutron Stars in a Varying Speed of Light Theory A. W. Whinnett Astronomy Centre, University of Sussex, Falmer, Brighton, BN1 9QJ, United Kingdom February 7, 2008 Abstract We study neutron stars in a varying speed of light (VSL) theory of gravity in which the local
2、speed of light depends upon the value of a scalar fi eld . We fi nd that the masses and radii of the stars are strongly dependent on the strength of the coupling between and the matter fi eld and that for certain choices of coupling parameters, the maximum neutron star mass can be arbitrarily small.
3、 We also discuss the phenomenon of cosmological evolution of VSL stars (analogous to the gravitational evolution in scalar-tensor theories) and we derive a relation showing how the fractional change in the energy of a star is related to the change in the cosmological value of the scalar fi eld. PACS
4、 numbers: 04.40.Dg, 04.50.+h 1Introduction Recently, there has been interest in the possibility that the speed of light c might have been larger in the past. The primary theoretical reason for considering this possibility is that such a variation in c could solve the horizon and fl atness problems o
5、f big-bang cosmology, without needing to postulate the existence of an infl ationary epoch in the early history of the Universe 1. This purely theoretical work was given added impetus more recently after the discovery by Webb et al. 2 that, according to observations of wavelength shifts in the absor
6、ption lines of distant quasars, the fi ne structure constant := e2/( hc) seems to have been smaller in the past. This is consistent with the assumption that c was larger in the past and, although more recent evidence 3 has constrained variations more strongly than the Webb data, the possibility of a
7、 time varying remains. One can assume that any changes in the value of are due to variations in one or both of h and e. However, the physical consequences of allowing either of these to vary are diff erent from those that arise from a varying c theory. For example, Avelino the generalisation to a ti
8、me-dependent spacetime is as straight forwards as it is in GR. We assume that the spacetime is asymptotically fl at and use the usual 3+1 splitting, denoting spacelike hypersurfaces by and the hypersurface orthogonal unit timelike vectors by Ua. The timelike, 2-dimensional boundary of integration at
9、 spacelike infi nity we denote by Sand its outward pointing, spacelike unit normal by na. Starting with the action (1), decomposing R into the Ricci scalar (3)R of the spacelike hypersurfaces and a divergence term, and integrating by parts several times, gives the VSL Hamiltonian H = Z d3xg e 16G ?(
10、3) R ( + 22)hijij 2 ? + eLm # + 1 8G Z S d2x Be( naa),(38) where is the extrinsic curvature scalar of, and abthe induced metric on, the surface S. The integral over vanishes by virtue of Hamiltons equation H/B = 0, where B is the lapse function, and we are left with the surface term. In general, this diverges and we must subtract a reference term HB. Following 16, we choose HBto have the form HB= 1 8 Z S d2x pB BeBB, (39) where the subscript “B” denotes quantities evaluated when is intrinsically fl at. The Hamil- toni
