Red-shifts near black holes

A simple ordinary differential equation is derived governing the red-shifts of wave-fronts propagating through a non-stationary spherically symmetric space-time. Approach to an event horizon corresponds to approach to a fixed point; in general, the phase portrait of the equation illuminates the qualitative features of the geometry. In particular, the asymptotics of the red-shift as a horizon is approached, a critical ingredient of Hawking's prediction of radiation from black holes, are easily brought out. This asympotic behavior has elements in common with the universal behavior near phase transitions in statistical physics. The validity of the Unruh vacuum for the Hawking process can be understood in terms of this universality. The concept of surface gravity is extended to to non-stationary spherically symmetric black holes. Finally, it is shown that in the non-stationary case, Hawking's predicted flux of radiation from a black hole would be modified.Comment: 20 pages, plain Tex, IOP macros, 4 eps figures, accepted by CQ

Kant's philosophy of the aesthetic and the philosophy of praxis

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 Association for Economic and Social Analysis.This essay seeks to reconstruct the terms for a more productive engagement with Kant than is typical within contemporary academic cultural Marxism, which sees him as the cornerstone of a bourgeois model of the aesthetic. The essay argues that, in the Critique of Judgment, the aesthetic stands in as a substitute for the missing realm of human praxis. This argument is developed in relation to Kant's concept of reflective judgment that is in turn related to a methodological shift toward inductive and analogical procedures that help Kant overcome the dualisms of the first two Critiques. This reassessment of Kant's aesthetic is further clarified by comparing it with and offering a critique of Terry Eagleton's assessment of the Kantian aesthetic as synonymous with ideology

NMA Survey of CO and HCN Emission from Nearby Active Galaxies

High resolution (a few arcseconds) observations of CO(1-0) and HCN(1-0) emission from nearby Seyfert galaxies have been conducted with the Nobeyama Millimeter Array. Based on the observed CO distributions and kinematics,we suggest that a small scale (a few 100 pc - a few kpc) distortion of the underlying potential seems to be necessary for Seyfert activity, although it is not a sufficient condition. We also find that the Toomre's Q values in the centers of Seyfert galaxies tend to be larger than unity, indicating the circumnuclear molecular gas disks around Seyfert nuclei would be gravitationally stable. The HCN/CO integrated intensity ratios (R_HCN/CO) range over an order of magnitude, from 0.086 to 0.6. The Seyfert galaxies with high R_HCN/CO may have an extended (r ~ 100 pc scale) envelope of obscuring material. The presence of kpc scale jet/ outflow might be also related to the extremely high R_HCN/CO.Comment: To appear in the Proceedings of the 3rd Cologne-Zermatt Symposium, ``The Physics and Chemistry of the Interstellar Medium'

Starbursting Nuclear CO Disks of Early-type Spiral Galaxies

We have initiated the first CO interferometer survey of early-type spiral galaxies (S0-Sab). We observed five early-type spiral galaxies with HII nuclei (indicating circumnuclear starburst activities). These observations indicate gas masses for the central kiloparsec of \sim 1-5% of the dynamical masses. Such low gas mass fractions suggest that large-scale gravitational instability in the gas is unlikely to be the driving cause for the starburst activities. The Toomre Q values were >1 (mostly >3) within the central kiloparsec, indicating that the gas disks are globally gravitationally stable. The area filling factor of the gas disks is estimated to be about 0.05. This small value indicates the existence of lumpy structure, i.e. molecular clouds, in the globally-gravitationally stable disks. The typical surface density of the molecular clouds is as high as \sim 3000 Msun pc^{-2}. We reconsider the nature of the Toomre Q criterion, and conclude that the Q derived from CO observations indicates neither star formation nor molecular cloud formation. This argument should be valid not only for the circumnuclear disks but also for any region in galactic disks. We tentatively explore an alternative model, i.e. cloud-cloud collisions, as an initiating mechanism of star formation.Comment: 7pages, including 2 figures ; A&A accepted (19 Oct. 2004

The implications of noninertial motion on covariant quantum spin

It is shown that the Pauli-Lubanski spin vector defined in terms of curvilinear co-ordinates does not satisfy Lorentz invariance for spin-1/2 particles in noninertial motion along a curved trajectory. The possibility of detecting this violation in muon decay experiments is explored, where the noninertial contribution to the decay rate becomes large for muon beams with large momenta and trajectories with radius of curvature approaching the muon's Compton wavelength scale. A new spacelike spin vector is derived from the Pauli-Lubanski vector that satisfies Lorentz invariance for both inertial and noninertial motion. In addition, this spin vector suggests a generalization for the classification of spin-1/2 particles, and has interesting properties that are applicable for both massive and massless particles.Comment: REVTeX file; 7 pages; 2 figures; slightly revised with new abstract; accepted for publication in Classical and Quantum Gravit

Functional Evolution of Free Quantum Fields

We consider the problem of evolving a quantum field between any two (in general, curved) Cauchy surfaces. Classically, this dynamical evolution is represented by a canonical transformation on the phase space for the field theory. We show that this canonical transformation cannot, in general, be unitarily implemented on the Fock space for free quantum fields on flat spacetimes of dimension greater than 2. We do this by considering time evolution of a free Klein-Gordon field on a flat spacetime (with toroidal Cauchy surfaces) starting from a flat initial surface and ending on a generic final surface. The associated Bogolubov transformation is computed; it does not correspond to a unitary transformation on the Fock space. This means that functional evolution of the quantum state as originally envisioned by Tomonaga, Schwinger, and Dirac is not a viable concept. Nevertheless, we demonstrate that functional evolution of the quantum state can be satisfactorily described using the formalism of algebraic quantum field theory. We discuss possible implications of our results for canonical quantum gravity.Comment: 21 pages, RevTeX, minor improvements in exposition, to appear in Classical and Quantum Gravit

The Energy Density in the Casimir Effect

We compute the expectations of the squares of the electric and magnetic fields in the vacuum region outside a half-space filled with a uniform dispersive dielectric. We find a positive energy density of the electromagnetic field which diverges at the interface despite the inclusion of dispersion in the calculation. We also investigate the mean squared fields and the energy density in the vacuum region between two parallel half-spaces. Of particular interest is the sign of the energy density. We find that the energy density is described by two terms: a negative position independent (Casimir) term, and a positive position dependent term with a minimum value at the center of the vacuum region. We argue that in some cases, including physically realizable ones, the negative term can dominate in a given region between the two half-spaces, so the overall energy density can be negative in this region.Comment: 16 pages, 4 figures; 3 references and some new material in Sect. 4.4 adde

Molecular Gas in Spiral Galaxies

In this review, I highlight a number of recent surveys of molecular gas in nearby spiral galaxies. Through such surveys, more complete observations of the distribution and kinematics of molecular gas have become available for galaxies with a wider range of properties (e.g., brightness, Hubble type, strength of spiral or bar structure). These studies show the promise of both interferometers and single-dish telescopes in advancing our general understanding of molecular gas in spiral galaxies. In particular, I highlight the contributions of the recent BIMA Survey of Nearby Galaxies (SONG).Comment: 8 pages, 1 figure. To appear in the proceedings of the 4th Cologne-Bonn-Zermatt-Symposium, "The Dense Interstellar Medium in Galaxies", which was held in Zermatt, Switzerland in September 200