Abstract
Binary black hole merger has been detected directly by LIGO. But the detail physics of binary black hole merger has not been completely revealed due to the lack of exact solution for the corresponding spacetime. Currently only numerical solutions based on some specific coordinate for binary black hole are available. If we allow to including a cosmological constant into the Einstein equation, there is a Kastor-Traschen (KT) solution describing dynamical multi black holes. Through investigation of the related Bondi-Scahs quantities we find that the corresponding gravitational radiation and electromagnetic radiation both vanish. In addition, we have done gravitational electromagnetic analysis. All these quantitative calculations indicate that KT solution does not admit gravitational radiation nor electromagnetic radiation. Based on this finding we argue that the KT solution only describes black holes touch instead of collision.
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