Lie point symmetries of near-horizon geometry equation
Eryk Buk, Jerzy Lewandowski, Adam Szereszewski
TL;DR
This paper identifies the Lie point symmetries of the near-horizon geometry equation in Einstein vacuum and Maxwell-Einstein spacetimes, showing they correspond to diffeomorphisms of null generator spaces.
Contribution
It characterizes the Lie point symmetries of the near-horizon geometry equation for specific spacetimes, extending previous results to include Maxwell-Einstein cases.
Findings
Symmetries are diffeomorphisms of null generator spaces.
Results apply to 4D Einstein vacuum with cosmological constant.
Extended to Maxwell-Einstein spacetimes.
Abstract
All the Lie point symmetries of the near extremal horizon geometry equation, in the case of 4-dimensional Einstein vacuum spacetime with cosmological constant, are the diffeomorphisms of the space of the null generators of the horizon. This result is also generalised to the Maxwell-Einstein spacetime.
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