Related papers: Three Lectures on Complexity and Black Holes
In this thesis properties and the origin of black hole entropy are investigated from various points of view. First, laws of black hole thermodynamics are reviewed. In particular, the first and generalized second laws are investigated in…
Hawking showed that a black hole formed by collapse will emit radiation and eventually disappear. We address the challenge to define an objective notion of physical entropy which increases throughout this process in a way consistent with…
An important conjecture within the AdS/CFT correspondence relates holographic spacetime to the quantum computational complexity of the dual quantum field theory. However, the quantitative understanding of this relation is still an open…
These notes are an elaboration on: (i) a short course that I gave at the IPhT-Saclay in May-June 2012; (ii) a previous letter on reversibility in quantum mechanics. They present an introductory, but hopefully coherent, view of the main…
This is a revised and shortened version of a MSc thesis submitted to the University of Sussex, UK. An introduction into the pre-string physics of black holes and related thermodynamics is given. Then, starting with an introduction of how…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
We review black hole entropy with special reference to euclidean quantum gravity, the brick wall approach and loop quantum gravity.
Early in 2011 Sam Evens acting on behalf of the organizers of the summer school on quantization at Notre Dame asked me to give a short series of lectures on geometric quantization. These lectures were meant to prepare a group of graduate…
Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the…
The thermodynamic and euclidean functional integral approaches to black hole entropy are discussed. The existence of some freedom in the definition of the entropy is pointed out and the possibility of a departure from the semiclassical…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
I review elements of the foundations of black-hole theory with attention to problematic issues, and describe some techniques which either seem to help with the difficulties or at least investigate their scope. The definition of black holes…
This SpringerBrief is based on a masters course on black hole thermodynamics and the black hole information problem taught by Dieter L\"ust during the summer term 2017 at the Ludwig-Maximilians-Universit\"at in Munich; it was written by…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
Thirty years of a deepening information paradox suggest the need to revise our basic physical framework. Multiple indicators point toward reassessment of the principle of locality: lack of a precise definition in quantum gravity, behavior…
We define the analytic continuation of the number of black hole microstates in Loop Quantum Gravity to complex values of the Barbero-Immirzi parameter $\gamma$. This construction deeply relies on the link between black holes and…
Supersymmetric black holes provide an excellent theoretical laboratory to test ideas about quantum gravity in general and black hole entropy in particular. When four-dimensional supergravity is interpreted as the low-energy approximation of…
The comparison of geometrical properties of black holes with classical thermodynamic variables reveals surprising parallels between the laws of black hole mechanics and the laws of thermodynamics. Since Hawking's discovery that black holes…
We portray the structure of quantum gravity emerging from recent progress in understanding the quantum mechanics of an evaporating black hole. Quantum gravity admits two different descriptions, based on Euclidean gravitational path integral…
We discuss some recent results on black hole thermodynamics within the context of effective gravitational actions including higher-curvature interactions. Wald's derivation of the First Law demonstrates that black hole entropy can always be…