Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy

We consider a general, classical theory of gravity with arbitrary matter fields in $n$ dimensions, arising from a diffeomorphism invariant Lagrangian, \bL. We first show that \bL always can be written in a ``manifestly covariant" form. We then show that the symplectic potential current $(n-1)$-form, $\th$, and the symplectic current $(n-1)$-form, \om, for the theory always can be globally defined in a covariant manner. Associated with any infinitesimal diffeomorphism is a Noether current $(n-1)$-form, \bJ, and corresponding Noether charge $(n-2)$-form, \bQ. We derive a general ``decomposition formula" for \bQ. Using this formula for the Noether charge, we prove that the first law of black hole mechanics holds for arbitrary perturbations of a stationary black hole. (For higher derivative theories, previous arguments had established this law only for stationary perturbations.) Finally, we propose a local, geometrical prescription for the entropy, $S_{dyn}$, of a dynamical black hole. This prescription agrees with the Noether charge formula for stationary black holes and their perturbations, and is independent of all ambiguities associated with the choices of \bL, $\th$, and \bQ. However, the issue of whether this dynamical entropy in general obeys a ``second law" of black hole mechanics remains open. In an appendix, we apply some of our results to theories with a nondynamical metric and also briefly develop the theory of stress-energy pseudotensors.Comment: 30 pages, LaTe

Transverse electrokinetic and microfluidic effects in micro-patterned channels: lubrication analysis for slab geometries

Off-diagonal (transverse) effects in micro-patterned geometries are predicted and analyzed within the general frame of linear response theory, relating applied presure gradient and electric field to flow and electric current. These effects could contribute to the design of pumps, mixers or flow detectors. Shape and charge density modulations are proposed as a means to obtain sizeable transverse effects, as demonstrated by focusing on simple geometries and using the lubrication approximation.Comment: 9 pages, 7 figure

The renormalization of the effective Lagrangian with spontaneous symmetry breaking: the SU(2) case

We study the renormalization of the nonlinear effective SU(2) Lagrangian up to $O(p^4)$ with spontaneous symmetry breaking. The Stueckelberg transformation, the background field gauge, the Schwinger proper time and heat kernel method, and the covariant short distance expansion technology, guarantee the gauge covariance and incooperate the Ward indentities in our calculations. The renormalization group equations of the effective couplings are derived and analyzed. We find that the difference between the results gotten from the direct method and the renormalization group equation method can be quite large when the Higgs scalar is far below its decoupling limit.Comment: ReVTeX, 12 figures, 22 pages, some bugs are kicked off from programs, numerical analysis is renew

Black Hole Entropy is Noether Charge

We consider a general, classical theory of gravity in $n$ dimensions, arising from a diffeomorphism invariant Lagrangian. In any such theory, to each vector field, $\xi^a$, on spacetime one can associate a local symmetry and, hence, a Noether current $(n-1)$-form, ${\bf j}$, and (for solutions to the field equations) a Noether charge $(n-2)$-form, ${\bf Q}$. Assuming only that the theory admits stationary black hole solutions with a bifurcate Killing horizon, and that the canonical mass and angular momentum of solutions are well defined at infinity, we show that the first law of black hole mechanics always holds for perturbations to nearby stationary black hole solutions. The quantity playing the role of black hole entropy in this formula is simply $2 \pi$ times the integral over $\Sigma$ of the Noether charge $(n-2)$-form associated with the horizon Killing field, normalized so as to have unit surface gravity. Furthermore, we show that this black hole entropy always is given by a local geometrical expression on the horizon of the black hole. We thereby obtain a natural candidate for the entropy of a dynamical black hole in a general theory of gravity. Our results show that the validity of the ``second law" of black hole mechanics in dynamical evolution from an initially stationary black hole to a final stationary state is equivalent to the positivity of a total Noether flux, and thus may be intimately related to the positive energy properties of the theory. The relationship between the derivation of our formula for black hole entropy and the derivation via ``Euclidean methods" also is explained.Comment: 16 pages, EFI 93-4

(Anti-)self-dual homogeneous vacuum gluon field as an origin of confinement and SUL(NF)×SUR(NF)SU_L(N_F)\times SU_R(N_F) symmetry breaking in QCD

It is shown that an (anti-)self-dual homogeneous vacuum gluon field appears in a natural way within the problem of calculation of the QCD partition function in the form of Euclidean functional integral with periodic boundary conditions. There is no violation of cluster property within this formulation, nor are parity, color and rotational symmetries broken explicitly. The massless limit of the product of the quark masses and condensates, $m_f \langle \bar\psi_f \psi_f \rangle$, is calculated to all loop orders. This quantity does not vanish and is proportional to the gluon condensate appearing due to the nonzero strength of the vacuum gluon field. We conclude that the gluon condensate can be considered as an order parameter both for confinement and chiral symmetry breaking.Comment: 16 pages, LaTe

Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric States Versus De Sitter Invariant Vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar field is revisited. Formally, it is possible to construct a de Sitter invariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observer's space-time path grows linearly with the observer's proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy momentum tensor, both in the O(4) invariant states introduced by Allen and Follaci, and in the de Sitter invariant vacuum. We find that the vacuum energy density in the O(4) invariant case is larger than in the de Sitter invariant case.Comment: TUTP-92-1, to appear in Phys. Rev.

General relativity as an effective field theory: The leading quantum corrections

I describe the treatment of gravity as a quantum effective field theory. This allows a natural separation of the (known) low energy quantum effects from the (unknown) high energy contributions. Within this framework, gravity is a well behaved quantum field theory at ordinary energies. In studying the class of quantum corrections at low energy, the dominant effects at large distance can be isolated, as these are due to the propagation of the massless particles (including gravitons) of the theory and are manifested in the nonlocal/nonanalytic contributions to vertex functions and propagators. These leading quantum corrections are parameter-free and represent necessary consequences of quantum gravity. The methodology is illustrated by a calculation of the leading quantum corrections to the gravitational interaction of two heavy masses.Comment: 34 pages, Latex, UMHEP-40

The primary structure of three hemoglobin chains from the indigo snake (Drymarchon corais erebennus, Serpentes): First evidence for αD chains and two β chain types in snakes

The hemoglobin of the indigo snake (Drymarchon corais erebennus, Colubrinae) consists of two components, HbA and HbD, in the ratio of 1:1. They differ in both their alpha and beta chains. The amino acid sequences of both alpha chains (alpha(A) and alpha(D)) and one beta chain (betaI) were determined. The presence of an alpha(D)chain in a snake hemoglobin is described for the first time. A comparison of all snake beta chain sequences revealed the existence of two paralogous beta chain types in snakes as well, which are designated as betaI and betaII type. For the discussion of the physiological properties of Drymarchon hemoglobin, the sequences were compared with those of the human alpha and beta chains and those of the closely related water snake Liophis miliaris where functional data are available. Among the heme contacts, the substitution alpha(D)58(E7)His-->Gln is unusual but most likely without any effect. The residues responsible for the main part of the Bohr effect are the same as in mammalian hemoglobins. In each of the three globin chains only two residues at positions involved in the alpha1/beta2 interface contacts, most important for the stability and the properties of the hemoglobin molecule, are substituted with regard to human hemoglobin. On the contrary, nine, eleven, and six alpha1/beta1 contact residues are replaced in the alpha(A), alpha(D), betaI chains, respectively

Thermal partition function of photons and gravitons in a Rindler wedge

The thermal partition function of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local $\zeta$-function regularization approach. The correct Planckian leading order temperature dependence $T^4$ is obtained in both cases. For the photons, the existence of a surface term giving a negative contribution to the entropy is confirmed, as earlier obtained by Kabat, but this term is shown to be gauge dependent in the four-dimensional case and, therefore is discarded. It is argued that similar terms could appear dealing with any integer spin $s\geq 1$ in the massless case and in more general manifolds. Our conjecture is checked in the case of a graviton in the harmonic gauge, where different surface terms also appear, and physically consistent results arise dropping these terms. The results are discussed in relation to the quantum corrections to the black hole entropy.Comment: 29 pages, RevTeX, no figures. Minor errors corrected and a few comments changed since first submission. To be published on Phys.Rev.

Split-off dimer defects on the Si(001)2x1 surface

Dimer vacancy (DV) defect complexes in the Si(001)2x1 surface were investigated using high-resolution scanning tunneling microscopy and first principles calculations. We find that under low bias filled-state tunneling conditions, isolated 'split-off' dimers in these defect complexes are imaged as pairs of protrusions while the surrounding Si surface dimers appear as the usual 'bean-shaped' protrusions. We attribute this to the formation of pi-bonds between the two atoms of the split-off dimer and second layer atoms, and present charge density plots to support this assignment. We observe a local brightness enhancement due to strain for different DV complexes and provide the first experimental confirmation of an earlier prediction that the 1+2-DV induces less surface strain than other DV complexes. Finally, we present a previously unreported triangular shaped split-off dimer defect complex that exists at SB-type step edges, and propose a structure for this defect involving a bound Si monomer.Comment: 8 pages, 7 figures, submitted to Phys. Rev.