The C-metric solution is a solution of the vacuum Einstein's field equations. It describes a pair of black holes undergoing uniform acceleration apart from each other. The analysis on its physical interpretation mainly depends on it's structure function. My supervisor, Dr. Edward Teo, came out a factorizable form of the structure function. This would eventually simplify all the analysis. In this project, we attempt to investigate the coordinate transformation from the old structure function into the factorizable version. We will generalize this to the case with charge, rotation, dilaton as well as the cosmological constant.

The superposition of the uncharged C-Metrics has been well studied [gr-qc/0105044]. However, the problem on superposition of the charged C-Metrics is still not solved yet. My supervisor, Edward Teo, came out a factorizable form of the structure function in the C-Metric solution. With this new structure function, we manage to obtain the same physical interpretation of the uncharged C-Metric which has been well studied. Moreover, most of our expressions appear to be much simpler than the previous works. In this project, we attempt to obtain a solution of the multiple charged C-Metrics. In particular, we will investigate the feasibility on the Sigbatulin's method to generate the multiple charged C-metric solution by providing the Ernst data on the symmetry axis. In order to simplify our studies, we will first concentrate on the extremal case, i.e. m=q. It would be quite promising if we could obtain the solution in the extremal case.

The aim of this project is to obtain solutions of black holes and black branes in string theory, and to study their properties. This includes C-metric type solutions, which describe pairs of black holes undergoing uniform acceleration away from each other. Pair production rates would be calculated using instanton techniques, and their thermodynamic properties would be studied in detail.