Hawking radiation as instantons

International Journal of Modern Physics D, 2004

We develop a Hamiltonian formalism which can be used to discuss the physics of a massless scalar field in a gravitational background of a Schwarzschild black hole. Using this formalism we show that the time evolution of the system is unitary and yet all known results such as the existence of Hawking radiation can be readily understood. We then point out that the Hamiltonian formalism leads to interesting observations about black hole entropy and the information paradox.

Physical Review D, 2015

We consider a novel approach to address the black hole information paradox (BHIP). The idea is based on adapting, to the situation at hand, the modified versions of quantum theory involving spontaneous stochastic dynamical collapse of quantum states, which have been considered in attempts to deal with shortcomings of the standard Copenhagen interpretation of quantum mechanics, in particular, the issue known as "the measurement problem". The new basic hypothesis is that the modified quantum behavior is enhanced in the region of high curvature so that the information encoded in the initial quantum state of the matter fields is rapidly erased as the black hole singularity is approached. We show that in this manner the complete evaporation of the black hole via Hawking radiation can be understood as involving no paradox. Calculations are performed using a modified version of quantum theory known as "Continuous Spontaneous Localization" (CSL), which was originally developed in the context of many particle non-relativistic quantum mechanics. We use a version of CSL tailored to quantum field theory and applied in the context of the two dimensional Callan-Giddings-Harvey-Strominger (CGHS) model. Although the role of quantum gravity in this picture is restricted to the resolution of the singularity, related studies suggest that there might be further connections.

2002

This talk is about results obtained by Kirill Melnikov and myself pertaining to the canonical quantization of a massless scalar field in the presence of a Schwarzschild black hole. After a brief summary of what we did and how we reproduce the familiar Hawking temperature and energy flux, I focus attention on how our discussion differs from other treatments. In particular I show that we can define a system which fakes an equilibrium thermodynamic object whose entropy is given by the A/4 (where A is the area of the black hole horizon), but for which the assignment of a classical entropy to the system is incorrect. Finally I briefly discuss a discretized version of the theory which seems to indicate that things work in a surprising way near r = 0.

International Journal of Modern Physics D

We develop a Hamiltonian formalism which can be used to discuss the physics of a massless scalar field in a gravitational background of a Schwarzschild black hole. Using this formalism we show that the time evolution of the system is unitary and yet all known results such as the existence of Hawking radiation can be readily understood. We then point out that the Hamiltonian formalism leads to interesting observations about black hole entropy and the information paradox.

Physics Letters B, 2009

It was found in [Phys.Lett.B 675 (2009) 98] that information is conserved in the process of black hole evaporation, by using the tunneling formulism and considering the correlations between emitted particles. In this Letter, we shall include quantum gravity effects, by taking into account of the log-area correction to Bekenstein-Hawking entropy. The correlation between successively emitted particles is calculated, with Planck-scale corrections. By considering the black hole evaporation process, entropy conservation is checked, and the existence of black hole remnant is emphasized. We conclude in this case information can leak out through the radiation and black hole evaporation is still a unitary process.

International Journal of Modern Physics D, 2003

There are numerous derivations of the Hawking effect available in the literature. They emphasise different features of the process, and sometimes make markedly different physical assumptions. This article presents a "minimalist" argument, and strips the derivation of as much excess baggage as possible. All that is really necessary is quantum physics plus a slowly evolving future apparent horizon (not an event horizon). In particular, neither the Einstein equations nor Bekenstein entropy are necessary (nor even useful) in deriving Hawking radiation.

2005

The formation and evaporation of a black hole can be viewed as a scattering process in Quantum Gravity. Semiclassical arguments indicate that the process should be non-unitary, and that all the information of the original quantum state forming the black hole should be lost after the black hole has completely evaporated, except for its mass, charge and angular momentum. This would imply a violation of basic principles of quantum mechanics. We review some proposed resolutions to the problem, including developments in string theory and a recent proposal by Hawking. We also suggest a novel approach which makes use of some ingredients of earlier proposals. [Based on Talks given at ERE2004 "Beyond General Relativity", Miraflores de la Sierra, Madrid (Sept 2004), and at CERN (Oct 2004)].

General Relativity and Gravitation, 2015

The two-point function 2. The Hadamard Ansatz 3. The non-Hadamard behavior B. Proof of well defined foliation C. Useful integrals to define ζ D. The SSC Formalism and the Sudden Collapse of the quantum state References I. INTRODUCTION The surprising discovery of black hole radiation by S. Hawking [3] in the 1970's, has had an enormous influence in our ideas concerning the interface of quantum theory and gravitation. For instance, it has changed our perception regarding the laws of black hole thermodynamics, which, before that discovery, could have been regarded as mere analogies to our current view that they represent simply the ordinary thermodynamical laws, as they apply to situations involving black holes (see for instance[51]). This, in turn, has led to the quest to understand, on statistical mechanical terms, and within different proposals for a theory of quantum gravity, the area of the black hole horizon as a measure of the black hole entropy. In fact, the most popular programs in this regard, String Theory and Loop Quantum Gravity, have important success in this front. Furthermore, the fact that as the black hole radiates it must lose mass leads to some tension between the picture that emerges from the gravitational side and the basic tenants of quantum theory. This tension was first pointed out by Hawking [4] and has even been described by many theorists as the "Black Hole Information Paradox" (BHIP). The root of the tension is that, according to the picture that emerges from the gravitational side, it seems that one can start with a pure initial quantum state characterizing the system at some initial stage, which then evolves into something that, at the quantum level, can only be characterized as a highly mixed quantum state, while, the standard quantum mechanical considerations would lead one to expect a fully unitary evolution. There is even some debate as to whether or not this issue should be considered as paradoxical.

We study the Dirac equation in black hole spacetimes and vacuum, stationary axisymmetric spacetimes in general. We solve the Dirac equation in such spacetimes via a factorization ansatz which we then apply to the Schwarzschild and Kerr spacetime. The thermal Hawking-Unruh flux is confirmed for the case of Schwarzschild. The Dirac equation is then studied in the Eddington-Finkelstein spacetime where it is suggested that the semi-classical gravitational back-reaction may be computed in the one particle case only and may represent the emission of gravitational waves. In particular the mode solutions to the Dirac equation, are completely regular at the horizon in this case and the infalling particle encounters nothing unusual at the horizon. Finally, we speculate on the Information Loss problem in a more general context beyond the semi-classical approximation.

2006

In our previous papers the first step was made to the construction of a global wave function on the configuration space of a self-gravitating shell. The asymptotic behaviour of analytical wave functions at the infinities was analyzed. As a result, a discrete mass spectrum of a quantum black hole and a discrete spectrum for the Hawking radiation were found. In the present paper we study a global quasiclassical solution inside and outside the horizon. The result is rather unexpected: for a quasiclassical solution with two waves of equal amplitudes under the horizon we obtain, in the outer region of the black hole, ingoing and outgoing waves with the amplitudes Zin and Zout such that Z 2 in /Z 2 out = exp{−δA/(4m 2 pl)} where A is the black hole horizon area. This result exactly coincides with the main result of the Hartle and Hawking consideration [21], from which one can derive the value of the black hole temperature and entropy.