Thermodynamics and area in Minkowski space: Heat capacity of entanglement

Tracing over the degrees of freedom inside (or outside) a sub-volume V of Minkowski space in a given quantum state |psi>, results in a statistical ensemble described by a density matrix rho. This enables one to relate quantum fluctuations in V when in the state |psi>, to statistical fluctuations in the ensemble described by rho. These fluctuations scale linearly with the surface area of V. If V is half of space, then rho is the density matrix of a canonical ensemble in Rindler space. This enables us to `derive' area scaling of thermodynamic quantities in Rindler space from area scaling of quantum fluctuations in half of Minkowski space. When considering shapes other than half of Minkowski space, even though area scaling persists, rho does not have an interpretation as a density matrix of a canonical ensemble in a curved, or geometrically non-trivial, background.Comment: 17 page

The Problem of Time and Quantum Black Holes

We discuss the derivation of the so-called semi-classical equations for both mini-superspace and dilaton gravity. We find that there is no systematic derivation of a semi-classical theory in which quantum mechanics is formulated in a space-time that is a solution of Einstein's equation, with the expectation value of the matter stress tensor on the right-hand side. The issues involved are related to the well-known problems associated with the interpretation of the Wheeler-deWitt equation in quantum gravity, including the problem of time. We explore the de Broglie-Bohm interpretation of quantum mechanics (and field theory) as a way of spontaneously breaking general covariance, and thereby giving meaning to the equations that many authors have been using to analyze black hole evaporation. We comment on the implications for the ``information loss" problem.Comment: 30 pages, COLO-HEP-33

Quantum Black Holes in Two Dimensions

We show that a whole class of quantum actions for dilaton-gravity, which reduce to the CGHS theory in the classical limit, can be written as a Liouville-like theory. In a sub-class of this, the field space singularity observed by several authors is absent, regardless of the number of matter fields, and in addition it is such that the dilaton-gravity functional integration range (the real line) transforms into itself for the Liouville theory fields. We also discuss some problems associated with the usual calculation of Hawking radiation, which stem from the neglect of back reaction. We give an alternative argument incorporating back reaction but find that the rate is still asymptotically constant. The latter is due to the fact that the quantum theory does not seem to have a lower bound in energy and Hawking radiation takes positive Bondi (or ADM) mass solutions to arbitrarily large negative mass.Comment: 28 pages, phyzzx, revised discussion of Hawking radiatio

Evaporating Black Holes and Entropy

We study the Hawking radiation for the geometry of an evaporating 1+1 dimensional black hole. We compute Bogoliubov coefficients and the stress tensor. We use a recent result of Srednicki to estimate the entropy of entanglement produced in the evaporation process, for the 1+1 dimensional hole and for the 3+1 dimensional hole. It is found that the one space dimensional result of Srednicki is the pertinent one to use, in both cases.Comment: 29 pages, one figure (available from authors), Latex. (Mailer errors removed.

Semi-infinite Throat as the End-state Geometry of two-dimensional Black Hole Evaporation

We study a modified two-dimensional dilaton gravity theory which is exactly solvable in the semiclassical approximation including back-reaction. The vacuum solutions of this modified theory are asymptotically flat static space-times. Infalling matter forms a black hole if its energy is above a certain threshold. The black hole singularity is initially hidden behind a timelike apparent horizon. As the black hole evaporates by emitting Hawking radiation, the singularity meets the shrinking horizon in finite retarded time to become naked. A natural boundary condition exists at the naked singularity such that for general infalling matter-configuration the evaporating black hole geometries can be matched continuously to a unique static end-state geometry. This end-state geometry is asymptotically flat at its right spatial infinity, while its left spatial infinity is a semi-infinite throat extending into the strong coupling region.Comment: Tex + compressed uuencoded ps version with one figure included, 11

Numerical Analysis of Black Hole Evaporation

Black hole formation/evaporation in two-dimensional dilaton gravity can be described, in the limit where the number $N$ of matter fields becomes large, by a set of second-order partial differential equations. In this paper we solve these equations numerically. It is shown that, contrary to some previous suggestions, black holes evaporate completely a finite time after formation. A boundary condition is required to evolve the system beyond the naked singularity at the evaporation endpoint. It is argued that this may be naturally chosen so as to restore the system to the vacuum. The analysis also applies to the low-energy scattering of $S$-wave fermions by four-dimensional extremal, magnetic, dilatonic black holes.Comment: 10 pages, 9 figures in separate uuencoded fil

Effects of heavy modes on vacuum stability in supersymmetric theories

We study the effects induced by heavy fields on the masses of light fields in supersymmetric theories, under the assumption that the heavy mass scale is much higher than the supersymmetry breaking scale. We show that the square-masses of light scalar fields can get two different types of significant corrections when a heavy multiplet is integrated out. The first is an indirect level-repulsion effect, which may arise from heavy chiral multiplets and is always negative. The second is a direct coupling contribution, which may arise from heavy vector multiplets and can have any sign. We then apply these results to the sGoldstino mass and study the implications for the vacuum metastability condition. We find that the correction from heavy chiral multiplets is always negative and tends to compromise vacuum metastability, whereas the contribution from heavy vector multiplets is always positive and tends on the contrary to reinforce it. These two effects are controlled respectively by Yukawa couplings and gauge charges, which mix one heavy and two light fields respectively in the superpotential and the Kahler potential. Finally we also comment on similar effects induced in soft scalar masses when the heavy multiplets couple both to the visible and the hidden sector.Comment: LaTex, 24 pages, no figures; v2 some comments and references adde

The No-Hair Conjecture in 2D Dilaton Supergravity

We study two dimensional dilaton gravity and supergravity following hamiltonian methods. Firstly, we consider the structure of constraints of 2D dilaton gravity and then the 2D dilaton supergravity is obtained taking the squere root of the bosonic constraints. We integrate exactly the equations of motion in both cases and we show that the solutions of the equation of motion of 2D dilaton supergravity differs from the solutions of 2D dilaton gravity only by boundary conditions on the fermionic variables, i.e. the black holes of 2D dilaton supergravity theory are exactly the same black holes of 2D bosonic dilaton gravity modulo supersymmetry transformations. This result is the bidimensional analogue of the no-hair theorem for supergravity.Comment: Plain Tex, 19pp, IPNO-TH 93/2

Mothers of Soldiers in Wartime: A National News Narrative

National news media represent mothers of US combat soldiers in the Iraq War as archetypal good mothers, that is, mothers who continue their maternal work even after their children are deployed. However, not all mothers are depicted as the archetypal patriotic mother, i.e., a good mother who is also stoic and silent about the war and her child\u27s role in it. Mothers of soldiers are portrayed as good mothers who sometimes also voice their attitudes about the war effort. The maternal attitudes ranged from complete support for the war to opposition to the war but support for the soldiers. The findings suggest a picture of wartime motherhood that is more nuanced than the historical image of the patriotic mother suggests

Nonsingular Lagrangians for Two Dimensional Black Holes

We introduce a large class of modifications of the standard lagrangian for two dimensional dilaton gravity, whose general solutions are nonsingular black holes. A subclass of these lagrangians have extremal solutions which are nonsingular analogues of the extremal Reissner-Nordstrom spacetime. It is possible that quantum deformations of these extremal solutions are the endpoint of Hawking evaporation when the models are coupled to matter, and that the resulting evolution may be studied entirely within the framework of the semiclassical approximation. Numerical work to verify this conjecture is in progress. We point out however that the solutions with non-negative mass always contain Cauchy horizons, and may be sensitive to small perturbations.Comment: 27 pages, three figures, RU-92-61. (Replaced version contains some corrections to incorrect equations. The zero temperature extremal geometry (the conjectured end-point of the Hawking evaporation) is not as stated in the previous version, but rather is a nonsingular analogue of the zero temperature $M^2 = Q^2$ Reissner-Nordstrom space-time.