Vaidya-type dynamical black holes admit homothetic Killing vectors only for linear-in-null-time mass/charge/rotation profiles, and the resulting homothetic Killing horizons carry surface gravities obeying a flux-balance first law.
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Homothetic Killing horizons in generic Vaidya spacetimes
Vaidya-type dynamical black holes admit homothetic Killing vectors only for linear-in-null-time mass/charge/rotation profiles, and the resulting homothetic Killing horizons carry surface gravities obeying a flux-balance first law.