- Marginally DTTSs in the Brill-Lindquist two-black-hole initial data
- In our recent work, we defined a new concept, a marginally Dynamically Transversely Trapping Surface (a marginally DTTS), to characterize strong gravity regions. A marginally DTTS is reduced to the photon sphere r=3M in the Schwarzschild spacetime. A marginally DTTS has close analogy with a marginally trapped surface (or, an apparent horizon), which is reduced to the horizon r=2M in the Schwarzschild spacetime.
- The Brill-Lindquist initial data is vacuum time-symmetric initial data with conformally flat spatial structure,
 .
- The equation for Ψ is reduced to the Laplace equation of a flat space, and if we choose the solution
 ,
- the initial data represent the system of two black holes momentarily at rest. Here are the pictures of marginally DTTSs in the initial data:
- Marginally trapped surfaces (or, apparent horizons) in the Brill-Lindquist two-black-hole initial data
- For comparison, I show the pictures of marginally trapped surfaces in the same initial data. Similarity between marginally DTTSs and marginally trapped surfaces can be recognized.
- Marginally DTTSs in the system of two black holes in a Majumdar-Papapetrou spacetime
- We also studied marginally DTTSs in the system of two black holes in the Majumdar-Papapetrou spacetime. The Majumdar-Papapetrou spacetime is a static spacetime with a metric,
 .
- Electromagnetic fields are present in this spacetime
and the four-potential is given by
 .
- The equation for U is reduced to the Laplace equation of a flat space, and if we choose the solution
 ,
- the system reperesents two black holes, which are kept static due to balance between gravitational attractiive interaction and electromagnetic repulsive interaction.
- Here are pictures of marginally DTTSs in the system of two black holes in a Majumdar-Papapetrou spacetime.
See our paper arXiv:1909.08420[gr-qc] for details.
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