## Publicly Accessible Penn Dissertations

#### Title

Subtracted Geometry

2016

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Physics & Astronomy

Mirjam Cvetic

#### Abstract

In this thesis we study a special class of black hole geometries called subtracted geometries. Subtracted geometry black holes are obtained when one omits certain terms from the warp factor of the metric of general charged rotating black holes. The omission of these terms allows one to write the wave equation of the black hole in a completely separable way and one can explicitly see that the wave equation of a massless scalar field in this slightly altered background of a general multi-charged rotating black hole acquires an $SL(2,\mathbb{R}) \times \times SL(2,\mathbb{R}) \times SO(3)$ symmetry. The ”subtracted limit” is considered an appropriate limit for studying the internal structure of the non-subtracted black holes because

new 'subtracted' black holes have the same horizon area and periodicity of the angular and time coordinates in the near horizon regions as the original black hole geometry it was constructed from. The new geometry is asymptotically conical and is physically similar to that of a black hole in

an asymptotically confining box. We use the different nice properties of these geometries to understand various classically and quantum mechanically important features of general charged rotating black holes.

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