## Lukas Schneiderbauer

**PhD defense,** Friday September 25 at 14.00, in Veröld, room 023

**Semi-Classical Black Hole Holography **

The defense will be streamed: https://www.youtube.com/user/HIvarp/live

**Dissertation title:** Semi-Classical Black Hole Holography

**Opponents:** Dr. Veronika Hubeny, Professor of Physics at UC Davis,USA

Dr. Mukund Rangamany, Professor of Physics at UC Davis, USA

**Advisor:** Dr. Lárus Thorlacius, Professor at the Faculty of Physical Sciences, University of Iceland

**Doctoral committee:** Dr. Bo Sundborg, Professor at the Department of Physics at Stockholm University, Sweden

Dr. Valentina Giangreco M. Puletti, Professor at the Faculty of Physical Sciences, University of Iceland

Dr. Þórður Jónsson, Professor at the Faculty of Physical Sciences, University of Iceland

**Chair of Ceremony:** Dr. Einar Örn Sveinbjörnsson, Professor and the Head of the Faculty of Physical Sciences, University of Iceland

**Abstract:**

This thesis discusses two aspects of semi-classical black holes.

First, a recently improved semi-classical formula for the entanglement entropy of

black hole radiation is examined. This entropy is an indicator of information loss and determines whether black hole evaporation is an information preserving process or destroys quantum information. Assuming information conservation, Page expressed the entanglement entropy as a function of time, which is referred to as the “Page curve.” Using the improved formula for evaporating black hole solutions of a gravitational model introduced by Callan, Giddings, Harvey and Strominger (CGHS) and modified by Russo, Susskind and Thorlacius (RST), we find that the entanglement entropy follows the Page curve and thus is consistent with unitary evolution.

Second, the notion of quantum complexity is explored in the context of black holes. The quantum complexity of a quantum state measures how many “simple operations” are needed to create that state. Susskind conjectured that the quantum complexity of a black hole state corresponds to a certain volume inside the black hole. A modified conjecture equates the quantum complexity with the gravitational action evaluated for a certain region of spacetime which intersects the black hole interior. We test the complexity conjectures for semi-classical black hole solutions in the CGHS/RST model and find that both conjectures yield the expected behavior.