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Public viva-voce Notification Date: Monday, 16 October 2023 Time: 11:30 AM Venue: Seminar Hall Black hole hair removal and positivity of microstate degeneracy Shanmugapriya P Chennai Mathematical Institute. 16-10-23 Abstract This thesis discusses certain aspects of black hole microstate counting. It is divided into two parts. In the first part, we discuss black hole hair removal in the context of a puzzle involving two black holes with identical near horizon geometry. It is understood that black holes with identical near horizon geometries must have the same microscopic degeneracies. Sen et al studied an apparent counter-example of the above statement in the case of a BMPV black hole in flat space and a BMPV Black hole in Taub NUT space. They proposed black hole hair removal as a resolution to the resulting index mismatch puzzle. Motivated by their work, we explicitly construct hair modes in the non-linear theory and show that black hole hair removal is a resolution to a similar puzzle for these black holes in the \mathcal{N} = 4 CHL orbifold models as well. In the second part of the thesis, we study several microscopic indices for CHL black holes. We can in fact obtain additional information about black holes than just their microscopic degeneracies. These indices appear as Fourier coefficients of appropriate Siegel modular forms. We use these coefficients to show the positivity of microstate degeneracy for low charges. Due to the identification of these indices as an innately positive quantity as degeneracy of states, it in turn adds constraints on the signs of certain coefficients of these Siegel modular forms. All are invited to attend the viva-voce examination.
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