https://doi.org/10.1140/epjp/s13360-025-06162-x
Regular Article
The linear relations between the complex moduli and using the linear relations reduce the stabilization equations for supersymmetric black holes in N=2 theory
Dept of mathematical sciences, Tsinghua University, 100084, Beijing, China
Received:
5
October
2024
Accepted:
19
February
2025
Published online:
14
March
2025
In [Phys. Rev. D 54, 6293 (1996)], the black hole entropy was derived by solving the matrix equation obtained from the stabilization equations for the solution of frozen moduli. In this paper, by directly solving the stabilization equations for the solution of frozen moduli without using the matrix equation, we find linear relations between any two of the three complex moduli at the black hole horizon. So far, no one discusses the linear relations. Via the linear relations, we derive the unique solution of frozen moduli and reduce the stabilization equations in three different ways. For example, the eight stabilization equations in [Phys. Rev. D 54, 6293 (1996)] can be replaced equivalently with three equations, the solution of moduli 
and two linear relations, which are much simpler and more intuitive.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
