Spin-2 Amplitudes in Black-Hole Evaporation

Quantum amplitudes for $s=2$ gravitational-wave perturbations of Einstein/scalar collapse to a black hole are treated by analogy with $s=1$ Maxwell perturbations. The spin-2 perturbations split into parts with odd and even parity. We use the Regge-Wheeler gauge; at a certain point we make a gauge transformation to an asymptotically-flat gauge, such that the metric perturbations have the expected falloff behaviour at large radii. By analogy with $s=1$, for $s=2$ natural 'coordinate' variables are given by the magnetic part $H_{ij} (i,j=1,2,3)$ of the Weyl tensor, which can be taken as boundary data on a final space-like hypersurface $\Sigma_F$. For simplicity, we take the data on the initial surface $\Sigma_I$ to be exactly spherically-symmetric. The (large) Lorentzian proper-time interval between $\Sigma_I$ and $\Sigma_F$, measured at spatial infinity, is denoted by $T$. We follow Feynman's $+i\epsilon$ prescription and rotate $T$ into the complex: $T\to{\mid}T{\mid} \exp(-i\theta)$, for $0<\theta\leq\pi/2$. The corresponding complexified {\it classical} boundary-value problem is expected to be well-posed. The Lorentzian quantum amplitude is recovered by taking the limit as $\theta\to 0_+$. For boundary data well below the Planck scale, and for a locally supersymmetric theory, this involves only the semi-classical amplitude $\exp(iS^{(2)}_{\rm class}$, where $S^{(2)}_{\rm class}$ denotes the second-variation classical action. The relations between the $s=1$ and $s=2$ natural boundary data, involving supersymmetry, are investigated using 2-component spinor language in terms of the Maxwell field strength $\phi_{AB}=\phi_{(AB)}$ and the Weyl spinor $\Psi_{ABCD}=\Psi_{(ABCD)}$

Cretaceous-to-recent record of elevated 3He/4He along the Hawaiian-Emperor volcanic chain

Helium isotopes are a robust geochemical tracer of a primordial mantle component in hot spot volcanism. The high 3He/4He (up to 35 RA, where RA is the atmospheric 3He/4He ratio of 1.39 × 10−6) of some Hawaiian Island volcanism is perhaps the classic example. New results for picrites and basalts from the Hawaiian-Emperor seamount chain indicate that the hot spot has produced high 3He/4He lavas for at least the last 76 million years. Picrites erupted at 76 Ma have 3He/4He (10–14 RA), which is at the lower end of the range for the Hawaiian Islands but still above the range of modern mid-ocean ridge basalt (MORB; 6–10 RA). This was at a time when hot spot volcanism was occurring on thin lithosphere close to a spreading ridge and producing lava compositions otherwise nearly indistinguishable from MORB. After the hot spot and spreading center diverged during the Late Cretaceous, the hot spot produced lavas with significantly higher 3He/4He (up to 24 RA). Although 3He/4He ratios stabilized at relatively high values by 65 Ma, other chemical characteristics such as La/Yb and 87Sr/86Sr did not reach and stabilize at Hawaiian-Island-like values until ~45 Ma. Our limited 3He/4He record for the Hawaiian hot spot shows a poor correlation with plume flux estimates (calculated from bathymetry and residual gravity anomalies [Van Ark and Lin, 2004]). If 3He is a proxy for the quantity of primordial mantle material within the plume, then the lack of correlation between 3He/4He and calculated plume flux suggests that variation in primordial mantle flux is not the primary factor controlling total plume flux

Relic Radiation from an Evaporating Black Hole

We present a non-string-theoretic calculation of the microcanonical entropy of relic integer-spin Hawking radiation -- at fixed total energy $E$. The only conserved macroscopic quantity is the total energy $E$ (the total energy of the relic radiation). Data for a boundary-value approach, with massless, integer-spin perturbations, are set on initial and final space-like hypersurfaces. In the resulting 1-dimensional statistical-mechanics problem, the real part of the (complex) time separation at spatial infinity, $T = {\mid}T{\mid}\exp(-i\delta), \delta >0$, is the variable conjugate to the total energy. We count the number of weak-field configurations on the final space-like hypersurface with energy $E$. One recovers the Cardy formula and the Bekenstein-Hawking entropy, if Re(T) is of the order of the black-hole life- time, leading to a statistical interpretation of black-hole entropy. The microcanonical entropy includes a logarithmic correction to the black-hole area law, which is {\it universal} (independent of black-hole parameters). Here, the discreteness of the energy levels is crucial. This approach is compared with that of string theory for the transition to the fundamental-string r\'egime in the final stages of evaporation. The squared coupling, $g^2$, regulating the transition to a highly-excited string state and {\it vice versa}, can be related to the angle, $\delta$, of complex-time rotation above. The strong-coupling r\'egime corresponds to a Euclidean black hole, while the physical limit of a Lorentzian space-time (as $\delta \to 0_+$) corresponds to the weak-coupling r\'egime. This resembles the transition to a highly-excited string-like state which subsequently decays into massless particles, thereby avoiding the naked singularity.Comment: To appear in International Journal of Modern Physics

Black hole evaporation in a spherically symmetric non-commutative space-time

Recent work in the literature has studied the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat space-time and weak radiation at a very late time. The relevant quantum amplitudes have been evaluated for bosonic and fermionic fields, showing that no information is lost in collapse to a black hole. On the other hand, recent developments in noncommutative geometry have shown that, in general relativity, the effects of non-commutativity can be taken into account by keeping the standard form of the Einstein tensor on the left-hand side of the field equations and introducing a modified energy-momentum tensor as a source on the right-hand side. Relying on the recently obtained non-commutativity effect on a static, spherically symmetric metric, we have considered from a new perspective the quantum amplitudes in black hole evaporation. The general relativity analysis of spin-2 amplitudes has been shown to be modified by a multiplicative factor F depending on a constant non-commutativity parameter and on the upper limit R of the radial coordinate. Limiting forms of F have been derived which are compatible with the adiabatic approximation.Comment: 8 pages, Latex file with IOP macros, prepared for the QFEXT07 Conference, Leipzig, September 200

The Human Cytomegalovirus Fc Receptor gp68 Binds the Fc CH2-CH3 Interface of Immunoglobulin G

Recognition of immunoglobulin G (IgG) by surface receptors for the Fc domain of immunoglobulin G (Fc{gamma}), Fc{gamma}Rs, can trigger both humoral and cellular immune responses. Two human cytomegalovirus (HCMV)-encoded type I transmembrane receptors with Fc{gamma}-binding properties (vFc{gamma}Rs), gp34 and gp68, have been identified on the surface of HCMV-infected cells and are assumed to confer protection against IgG-mediated immunity. Here we show that Fc{gamma} recognition by both vFc{gamma}Rs occurs independently of N-linked glycosylation of Fc{gamma}, in contrast with the properties of host Fc{gamma}Rs. To gain further insight into the interaction with Fc{gamma}, truncation mutants of the vFc{gamma}R gp68 ectodomain were probed for Fc{gamma} binding, resulting in localization of the Fc{gamma} binding site on gp68 to residues 71 to 289, a region including an immunoglobulin-like domain. Gel filtration and biosensor binding experiments revealed that, unlike host Fc{gamma}Rs but similar to the herpes simplex virus type 1 (HSV-1) Fc receptor gE-gI, gp68 binds to the CH2-CH3 interdomain interface of the Fc{gamma} dimer with a nanomolar affinity and a 2:1 stoichiometry. Unlike gE-gI, which binds Fc{gamma} at the slightly basic pH of the extracellular milieu but not at the acidic pH of endosomes, the gp68/Fc{gamma} complex is stable at pH values from 5.6 to pH 8.1. These data indicate that the mechanistic details of Fc binding by HCMV gp68 differ from those of host Fc{gamma}Rs and from that of HSV-1 gE-gI, suggesting distinct functional and recognition properties

Gravitational amplitudes in black-hole evaporation: the effect of non-commutative geometry

Recent work in the literature has studied the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat space-time and weak radiation at a very late time. The relevant quantum amplitudes have been evaluated for bosonic and fermionic fields, showing that no information is lost in collapse to a black hole. On the other hand, recent developments in noncommutative geometry have shown that, in general relativity, the effects of noncommutativity can be taken into account by keeping the standard form of the Einstein tensor on the left-hand side of the field equations and introducing a modified energy-momentum tensor as a source on the right-hand side. The present paper, relying on the recently obtained noncommutativity effect on a static, spherically symmetric metric, considers from a new perspective the quantum amplitudes in black hole evaporation. The general relativity analysis of spin-2 amplitudes is shown to be modified by a multiplicative factor F depending on a constant non-commutativity parameter and on the upper limit R of the radial coordinate. Limiting forms of F are derived which are compatible with the adiabatic approximation here exploited. Approximate formulae for the particle emission rate are also obtained within this framework.Comment: 14 pages, 2 figures, Latex macros. In the final version, section 5 has been amended, the presentation has been improved, and References 21-24 have been added. Last misprints amended in Section 5 and Ref. 2