Charged Black Holes in String Theory with Gauss-Bonnet Correction in Various Dimensions

We study charged black hole solutions in Einstein-Gauss-Bonnet theory with the dilaton field which is the low-energy effective theory of the heterotic string. The spacetime is D-dimensional and assumed to be static and spherically symmetric with the $(D-2)$-dimensional constant curvature space and asymptotically flat. The system of the basic equations is complex and the solutions are obtained numerically. We identify the allowed parameter region where the black hole solutions exist, and show configurations of the field functions in D=4 -- 6 and 10. We also show the relations of the physical quantities of the black holes such as the horizon radius, the mass, the temperature, and so on, and find several results. The forms of the allowed parameter regions are different depending on the dimension. There is no extreme black hole solution with T=0 that can be obtained by taking the limit of the non-extreme solutions within the parameter range we chose. Entropy of the black holes in the dilatonic theory is always larger than that in the non-dilatonic theory. Our analysis includes the higher order term of the dilaton field which is not in our previous works. Its effect remarkably appears in five dimensions and is given in the appendix. By our analysis it is found that the properties of the black hole solutions strongly depend on the dimension, charge, existence of the dilaton field. Hence both the detailed analyses of the individual systems and the investigations from the systematic point of view are important.Comment: 23 pages, 14 figures. Typos corrected, references added, accepted in PR

Global Structure of Black Holes in String Theory with Gauss-Bonnet Correction in Various Dimensions

We study global structures of black hole solutions in Einstein gravity with Gauss-Bonnet term coupled to dilaton in various dimensions. In particular we focus on the problem whether the singularity is weakened due to the Gauss-Bonnet term and dilaton. We find that there appears the non-central singularity between horizon and the center in many cases, where the metric does not diverge but the Kretschmann invariant does diverge. Hence this is a singularity, but we find the singularity is much milder than the Schwarzschild solution and the non-dilatonic one. We discuss the origin of this "fat" singularity. In other cases, we encounter singularity at the center which is much stronger than the usual one. We find that our black hole solutions have three different types of the global structures; the Schwarzschild, Schwarzschild-AdS and "regular AdS black hole" types.Comment: 22 pages, 6 figure

Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions III -- Asymptotically AdS Black Holes with k=±1k=\pm 1 --

We study black hole solutions in the Einstein-Gauss-Bonnet gravity with the dilaton and a negative ``cosmological constant''. We derive the field equations for the static spherically symmetric ($k=1$) and hyperbolically symmetric ($k=-1$) spacetime in general $D$ dimensions. The system has some scaling symmetries which are used in our analysis of the solutions. We find exact solutions, i.e., regular AdS solution for $k=1$ and a massless black hole solution for $k=-1$. Nontrivial asymptotically AdS solutions are obtained numerically in D=4 -- 6 and 10 dimensional spacetimes. For spherically symmetric solutions, there is the minimum horizon radius below which no solution exists in D=4 -- 6. However in D=10, there is not such lower bound but the solution continues to exist to zero horizon size. For hyperbolically symmetric solution, there is the minimum horizon radius in all dimensions. Our solution can be used for investigations of the boundary theory through AdS/CFT correspondence.Comment: 25 pages, 16 figure

String creation in D6-brane background

The production of string charge during a crossing of certain oriented D-branes is studied. We compute the string charge in the system of a probe D2-brane and a background D6-brane by use of the equations of motion in the ten-dimensions. We confirm the creation of string charge as inflow from the background D6-brane.Comment: 11 pages, 1 figure, typos correcte

Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions II -- Asymptotically AdS Topological Black Holes --

We study asymptotically AdS topological black hole solutions with k=0 (plane symmetric) in the Einstein gravity with Gauss-Bonnet term, the dilaton and a "cosmological constant" in various dimensions. We derive the field equations for suitable ansatz for general D dimensions. We determine the parameter regions including dilaton couplings where such solutions exist and construct black hole solutions of various masses numerically in D=4,5,6 and 10 dimensional spacetime with (D-2)-dimensional hypersurface of zero curvature.Comment: 24 pages, 8 figures, PTPTeX, typos correcte

Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions I -- Asymptotically Flat Black Holes --

We study spherically symmetric, asymptotically flat black hole solutions in the low-energy effective heterotic string theory, which is the Einstein gravity with Gauss-Bonnet term and the dilaton, in various dimensions. We derive the field equations for suitable ansatz for general D dimensions and construct black hole solutions of various masses numerically in D=4,5,6 and 10 dimensional spacetime with (D-2)-dimensional hypersurface with positive constant curvature. A detailed comparison with the non-dilatonic solutions is made. We also examine the thermodynamic properties of the solutions. It is found that the dilaton has significant effects on the black hole solutions, and we discuss physical consequences.Comment: 30 pages, 7 figures, PTPTeX, references added, accepted for publication in PT