arXiv subjects

Gilad Gour

Publications and source records attributed to Gilad Gour.

121 records · Page 7Linked to original sources

arXiv2003

Questions of Stability near Black Hole Critical Points

In this letter, we discuss how thermal fluctuations can effect the stability of (generally) charged black holes when close to certain critical points. Our novel treatment utilizes the black hole area spectrum (which is, for definiteness, taken to be evenly spaced) and makes an important distinction between fixed and fluctuating charge systems (with these being modeled, respectively, as a canonical and grand canonical ensemble.) The discussion begins with a summary of a recent technical paper [gr-qc/0305018]. We then go on to consider the issue of stability when the system approaches the critical points of interest. These include the $d$-dimensional analogue of the Hawking-Page phase transition, a phase transition that is relevant to Reissner-Nordstrom black holes and various extremal-limiting cases.

gr-qc↗

arXiv2003

Extensive Entropy Bounds

It is shown that, for systems in which the entropy is an extensive function of the energy and volume, the Bekenstein and the holographic entropy bounds predict new results. More explicitly, the Bekenstein entropy bound leads to the entropy of thermal radiation (the Unruh-Wald bound) and the spherical entropy bound implies the "causal entropy bound". Surprisingly, the first bound shows a close relationship between black hole physics and the Stephan-Boltzmann law (for the energy and entropy flux densities of the radiation emitted by a hot blackbody). Furthermore, we find that the number of different species of massless fields is bounded by $\sim 10^{4}$.

gr-qc↗

arXiv2003

Entropy bounds for charged and rotating systems

It was shown in a previous work that, for systems in which the entropy is an extensive function of the energy and volume, the Bekenstein and the holographic entropy bounds predict new results. In this paper, we go further and derive improved upper bounds to the entropy of {\it extensive} charged and rotating systems. Furthermore, it is shown that for charged and rotating systems (including non-extensive ones), the total energy that appear in both the Bekenstein entropy bound (BEB) and the causal entropy bound (CEB) can be replaced by the {\it internal} energy of the system. In addition, we propose possible corrections to the BEB and the CEB.

gr-qc↗

arXiv2002

Quantum Spectrum for a Kerr-Newman Black Hole

In this paper, we consider the quantum area spectrum for a rotating and charged (Kerr-Newman) black hole. Generalizing a recent study on Kerr black holes (which was inspired by the static-black hole formalism of Barvinsky, Das and Kunstatter), we show that the quantized area operator can be expressed in terms of three quantum numbers (roughly related to the mass, charge and spin sectors). More precisely, we find that $A=8π\hbar[n+{1\over 2}+{p_1\over 2}+p_2]$, where $n$, $p_1$ and $p_2$ are strictly non-negative integers. In this way, we are able to confirm a uniformly spaced spectrum even for a fully general Kerr-Newman black hole. Along the way, we derive certain selection rules and use these to demonstrate that, in spite of appearances, the charge and spin spectra are not completely independent.

gr-qc↗

arXiv2002

Kerr Black Hole as a Quantum Rotator

It has been proposed by Bekenstein and others that the horizon area of a black hole conforms, upon quantization, to a discrete and uniformly spaced spectrum. In this paper, we consider the area spectrum for the highly non-trivial case of a rotating (Kerr) black hole solution. Following a prior work by Barvinsky, Das and Kunstatter, we are able to express the area spectrum in terms of an integer-valued quantum number and an angular-momentum operator. Moreover, by using an analogy between the Kerr black hole and a quantum rotator, we are able to quantize the angular-momentum sector. We find the area spectrum to be $A_{n,J_{cl}}=8π\hbar(n+J_{cl}+1/2)$, where $n$ and $J_{cl}$ are both integers. The quantum number $J_{cl}$ is related to but distinct from the eigenvalue $j$ of the angular momentum of the black hole. Actually, it represents the ``classical'' angular momentum and, for $J_{cl}\gg 1$, $J_{cl}\approx j$.

gr-qc↗

arXiv2002

Algebraic approach to quantum black holes: logarithmic corrections to black hole entropy

The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As shown previously, for a neutral non-rotating black hole, such eigenvalues must be $2^{n}$-fold degenerate if one constructs the black hole stationary states by means of a pair of creation operators subject to a specific algebra. We show that the algebra of these two building blocks exhibits $U(2)\equiv U(1)\times SU(2)$ symmetry, where the area operator generates the U(1) symmetry. The three generators of the SU(2) symmetry represent a {\it global} quantum number (hyperspin) of the black hole, and we show that this hyperspin must be zero. As a result, the degeneracy of the $n$-th area eigenvalue is reduced to $2^{n}/n^{3/2}$ for large $n$, and therefore, the logarithmic correction term $-3/2\log A$ should be added to the Bekenstein-Hawking entropy. We also provide a heuristic approach explaining this result, and an evidence for the existence of {\it two} building blocks.

gr-qc↗

arXiv2002

The quantum absolute phase observable

Defining the observable ${\bf ϕ}$ canonically conjugate to the number observable ${\bf N}$ has long been an open problem in quantum theory. Here we show how to define the absolute phase observable ${\bf Φ}\equiv |{\bfϕ}|$ by suitably restricting the Hilbert space of $x$ and $p$ like variables. This ${\bf Φ}$ is actually the absolute value of the phase and has the correct classical limit. A correction to the ``cosine'' ${\bf C}$ and ``sine'' ${\bf S}$ operators of Carruthers and Nieto is obtained.

quant-ph↗

arXiv2002

Building blocks of a black hole

What is the nature of the energy spectrum of a black hole ? The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As stressed long ago by by Mukhanov, such eigenvalues must be exponentially degenerate with respect to the area quantum number if one is to understand black hole entropy as reflecting degeneracy of the observable states. Here we construct the black hole states by means of a pair of "creation operators" subject to a particular simple algebra, a slight generalization of that for the harmonic oscillator. We then prove rigorously that the n-th area eigenvalue is exactly 2 raised to the n-fold degenerate. Thus black hole entropy qua logarithm of the number of states for fixed horizon area comes out proportional to that area.

gr-qc↗

arXiv2002

The quantum phase problem: steps toward a resolution

Defining the observable ${\bf ϕ}$ canonically conjugate to the number observable ${\bf N}$ has long been an open problem in quantum theory. The problem stems from the fact that ${\bf N}$ is bounded from below. In a previous work we have shown how to define the absolute phase observable ${\bf Φ}\equiv |{\bfϕ}|$ by suitably restricting the Hilbert space of $x$ and $p$ like variables. Here we show that also from the classical point of view, there is no rigorous definition for the phase even though it's absolute value is well defined.

quant-ph↗

arXiv2000

Why is the black hole entropy (almost) linear in the horizon area?

We show that essentially pure classical thermodynamics is sufficient to determine Bekenstein's formula for the black hole's entropy, $S=ηA$. We base our reasoning on the minimal assumption that since black body radiation is describable by classical thermodynamics, so is the complete black hole-Hawking radiation system. Furthermore, we argue that any non-linear correction to the black hole entropy must be quantum mechanical in nature. The proportionality coefficient, $η=1/4\ell_P^2$, must be calculated within a semi-classical or full-fledged quantum mechanical framework.

gr-qc↗

arXiv2000

Quantum Mechanics of a Black Hole

Beginning with Bekenstein, many authors have considered a uniformly spaced discrete quantum spectrum for black hole horizon area. It is also believed that the huge degeneracy of these area levels corresponds to the notion of black hole entropy. Starting from these two assumptions we here infer the algebra of a Schwarzschild black hole's observables. This algebra then serves as motivation for introducing in the system's Hamiltonian an interaction term. The interaction contains the horizon area operator, which is a number operator, and its canonical conjugate, the phase operator. The Hawking radiation from a Schwarzschild black hole is seen to be a consequence of an area-phase interaction. Using this interaction we have reproduced the semi-classical result for the Hawking radiation power. Furthermore, we show that the initial state of the black hole determines the nature of its development. Thus, a state which is an area eigenstate describes a static eternal black hole, but a coherent state describes a radiating black hole. Hence, it is the observer's initial knowledge or uncertainty about the horizon area which determines the evolution.

gr-qc↗

arXiv1999

Will small particles exhibit Brownian motion in the quantum vacuum?

The Brownian motion of small particles interacting with a field at a finite temperature is a well-known and well-understood phenomenon. At zero temperature, even though the thermal fluctuations are absent, quantum fields still possess vacuum fluctuations. It is then interesting to ask whether a small particle that is interacting with a quantum field will exhibit Brownian motion when the quantum field is assumed to be in the vacuum state. In this paper, we study the cases of a small charge and an imperfect mirror interacting with a quantum scalar field in (1+1) dimensions. Treating the quantum field as a classical stochastic variable, we write down a Langevin equation for the particles. We show that the results we obtain from such an approach agree with the results obtained from the fluctuation-dissipation theorem. Unlike the finite temperature case, there exists no special frame of reference at zero temperature and hence it is essential that the particles do not break Lorentz invariance. We find that that the scalar charge breaks Lorentz invariance, whereas the imperfect mirror does not. We conclude that small particles such as the imperfect mirror {\it will} exhibit Brownian motion even in the quantum vacuum, but this effect can be so small that it may prove to be difficult to observe it experimentally.

quant-ph↗

arXiv1999

Schwarzschild black hole as a grand canonical ensemble

For long black holes have been considered as endowed with a definite temperature. Yet when the Schwarzschild black hole is treated as a canonical ensemble three problems arise: incompatibility with the Hawking radiation, divergence of the partition function, and a formally negative mean-square fluctuation of the energy. We solve all three problems by considering the Schwarzschild black hole as a grand canonical ensemble, with the Hamiltonian (the ADM mass) and the horizon surface area, separately, as observable parameters. The horizon area simulates the number of particles in statistical mechanics since its spectrum is assumed to be discrete and equally spaced. We obtain a logarithmic correction to the Bekenstein-Hawking entropy and a Gaussian type distribution for the energy levels.

gr-qc↗