Related papers: Ramanujan and Quantum Black Holes
Phase-locking governs the phase noise in classical clocks through effects described in precise mathematical terms. We seek here a quantum counterpart of these effects by working in a finite Hilbert space. We use a coprimality condition to…
In his second notebook, Ramanujan recorded total of 23 P-Q modular equations involving theta-functions $f(-q)$, $\varphi(q)$ and $\psi(q)$. In this paper, modular equations analogous to those recorded by Ramanujan are obtained involving…
We give a review of classical, thermodynamic and quantum properties of black holes relevant to fundamental physics.
A relativistic framework for the description of bound states consisting of a large number of quantum constituents is presented, and applied to black-hole interiors. At the parton level, the constituent distribution, number and energy…
Consistency of quantum mechanics in black hole physics requires unusual Lorentz transformation properties of the size and shape of physical systems with momentum beyond the Planck scale. A simple parton model illustrates the kind of…
It has recently been suggested that black holes may be described as condensates of weakly interacting gravitons at a critical point, exhibiting strong quantum effects. In this paper, we study a model system of attractive bosons in one…
In previous papers we have shown how strings in a two-dimensional target space reconcile quantum mechanics with general relativity, thanks to an infinite set of conserved quantum numbers, ``W-hair'', associated with topological soliton-like…
This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of G\"ollnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at…
The modeling of black holes is an important desideratum for any quantum theory of gravity. Not only is a classical black hole metric sought, but also agreement with the laws of black hole thermodynamics. In this paper, we describe how these…
This is a brief introduction to quantum aspects of black holes, addressed at an astrophysics-oriented audience. The topics are: The laws of black-hole mechanics, Hawking radiation, interpretation of entropy, and primordial black holes.
Eigenvectors of the discrete Fourier transform can be expressed using Ramanujan theta functions. New theta function identities, Ramanujan theta function identities, and generating functions for the quadratic numbers are a consequence.
In these lectures we review the quantum physics of large Schwarzschild black holes. Hawking's information paradox, the theory of the stretched horizon and the principle of black hole complementarity are covered. We then discuss how the…
One of the main goals of contemporary theoretical physics is to find the quantum theory of gravity. There are various working hypotheses, mostly operating in the regime of high-energy physics well above the reach of particle accelerators.…
The effective action for string theory which takes into account non-minimal coupling of moduli admits multi-black hole solutions. The euclidean continuation of these solutions can be interpreted as an instanton mediating the splitting and…
I review the present theoretical attempts to understand the quantum properties of spacetime. In particular, I illustrate the main achievements and the main difficulties in: string theory, loop quantum gravity, discrete quantum gravity…
We discuss the interior of a black hole in quantum gravity, in which black holes form and evaporate unitarily. The interior spacetime appears in the sense of complementarity because of special features revealed by the microscopic degrees of…
The black hole information paradox forces us into a strange situation: we must find a way to break the semiclassical approximation in a domain where no quantum gravity effects would normally be expected. Traditional quantizations of gravity…
We propose a method to test the effects of quantum fluctuations on black holes by analyzing the effects of thermal fluctuations on dumb holes, the analogues for black holes. The proposal is based on the Jacobson formalism, where the…
For any positive integers $s$ and $t$, let $Q_{t}^{s}(n)$ denotes the number of partitions of a positive integer $n$ into distinct parts such that no part is congruent to $s$ or $t-s$ modulo $t$. We prove some Ramanujan-type congruences for…
This paper discusses the existence of black holes from the foundations of quantum mechanics. It is found that quantum mechanics rule out a possible gravitational collapse.