Related papers: Ramanujan and Quantum Black Holes
This chapter gives an overview of the quantum aspects of black holes, focusing on the black hole information problem, the counting of black hole entropy in string theory, and the emergence of spacetime in holography. It is aimed at a broad…
This lecture surveys a few loosely related topics, ranging from the scarcity of quantum field theories -- and the role that this has played, and still plays, in physics -- to paradoxes involving black holes in soluble two dimensional string…
It has been suggested that reality works like a quantum computer, but such claims are just words if they are not backed up by sound mathematics. In pursuit of the fundamental equations I look to string theory where physicists led by Mike…
We briefly review some of Ramanujan's contributions to mathematics, including his $1/\pi$ series, his work on modular forms, and his work on partitions. We briefly review his life, including his collaboration with Hardy. Finally, we give a…
This review gives an introduction to various attempts to understand the quantum nature of black holes. The first part focuses on thermodynamics of black holes, Hawking radiation, and the interpretation of entropy. The second part is devoted…
The generating function of partitions with repeated (resp. distinct) parts such that each odd part is less than twice the smallest part is shown to be the third order mock theta function $\omega(q)$ (resp. $\nu(-q)$). Similar results for…
These lectures present a general critical assessment of various frameworks for quantum gravity, with particular emphasis on string theory. The topics discussed cover field-theoretical approaches to quantum gravity, anomalies, bosonic and…
String theory is a promising candidate for a fundamental quantum theory of all interactions including Einstein gravity. Some solutions in string theory can be interpreted as black holes. Using the semi-analytic method and WKB method,the…
The dominant contribution to the semicanonical partition function of dyonic black holes of N=4 string theory is computed for generic charges, generalizing recent results of Shih and Yin. The result is compared to the black hole free energy…
Quantum entanglement lies at the heart of quantum information theory, with applications to quantum computing, teleportation, cryptography and communication. In the apparently separate world of quantum gravity, the Hawking effect of…
During the past decades, theorists have been studying quantum mechanical systems that are believed to describe black holes. We review one of the simplest examples. It involves a collection of interacting oscillators and Majorana fermions.…
This paper reviews the role of black holes in the context of fundamental physics. After recalling some basic results stemming from Planckian string calculations, I present three examples of how stringy effects can improve the curvature…
Computations in the calculable small coupling regime of string theories and the general consensus that no new physics has to be invoked in continuing to the large coupling (black hole) regime, suggest the following picture. Quantum states…
A very brief review is given of some of the developments leading to our current understanding of black holes in string theory. This is followed by a discussion of two possible misconceptions in this subject - one involving the stability of…
Recently, Garthwaite-Penniston have shown that the coefficients of Ramanujan's mock theta function $\omega$ satisfy infinitely many congruences of Ramanujan-type. In this work we give the first explicit examples of congruences for…
The black hole solutions to Einstein's vacuum field equations are also solutions to the equations of motion of the low energy limit of superstring theory. At the same time, string theory boasts a much broader and richer collection of black…
In this paper we add to the literature on the combinatorial nature of the mock theta functions, a collection of curious $q$-hypergeometric series introduced by Ramanujan in his last letter to Hardy in 1920, which we now know to be important…
The explanation of black hole entropy as statistical entropy is one of the big successes of string theory. In this article we review recent progress in this subject, focussing on understanding quantum effects on black hole entropy.…
The aim of these lectures is to give an introduction to several topics which lie at the intersection of string theory, gravity theory and gravity phenomenology. One successively reviews: (i) the "membrane" approach to the dissipative…
I review the recent progress in providing a statistical foundation for black hole thermodynamics. In the context of string theory, one can now identify and count quantum states associated with black holes. One can also compute the analog of…