In this paper, we study a new metric for slowly rotating charged Gauss-Bonnet black holes in higher-dimensional anti-de Sitter space. Taking the angular momentum parameter a up to second order, the slowly rotating charged black hole solutions are obtained by working directly in the action.
This paper presents a new metric and studies slowly rotating Gauss-Bonnet black holes with a nonvanishing angular momentum in five dimensional anti-de Sitter spaces. Taking the angular momentum parameter a up to second order, the slowly rotating black hole solutions are obtained by working directly in the action. In addition, it also finds that this method is applicable in higher order Lovelock gravity.
We explore static spherically symmetric stars in Gauss-Bonnet gravity without a cosmological constant, and present an exact internal solution which attaches to the exterior vacuum solution outside stars. It turns out that the presence of the Gauss-Bonnet term with a positive coupling constant completely changes thermal and gravitational energies, and the upper bound of the red shift of spectral lines from the surface of stars. Unlike in general relativity, the upper bound of the red shift is dependent on the density of stars in our case. Moreover, we have proven that two theorems for judging the stability of equilibrium of stars in general relativity can hold in Gauss-Bonnet gravity.
The gravitational effect of spontaneous symmetry breaking vacuum energy density is investigated by subtracting the fiat space-time contribution from the energy in the curved space-time. We find that the remaining effective energy- momentum tensor is too small to cause the acceleration of the universe, although it satisfies the characteristics of dark energy. However, it could provide a promising explanation to the puzzle of why the gravitational effect produced by the huge symmetry breaking vacuum energy in the electroweak theory has not been observed, as it has a sufficiently small value （smaller than the observed cosmic energy density by a factor of 1032）.
