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

Symmetries, Horizons, and Black Hole Entropy

Black holes behave as thermodynamic systems, and a central task of any quantum theory of gravity is to explain these thermal properties. A statistical mechanical description of black hole entropy once seemed remote, but today we suffer an embarrassment of riches: despite counting very different states, many inequivalent approaches to quantum gravity obtain identical results. Such ``universality'' may reflect an underlying two-dimensional conformal symmetry near the horizon, which can be powerful enough to control the thermal characteristics independent of other details of the theory. This picture suggests an elegant description of the relevant degrees of freedom as Goldstone-boson-like excitations arising from symmetry breaking by the conformal anomaly.Comment: 6 pages; first prize essay, 2007 Gravity Research Foundation essay contes

Effects of Meson Mass Reduction on the Properties of Neutron Star Matter

We investigate the effects of meson-mass reduction on the properties of the neutron star matter. We adopt the Brown-Rho scaling law to take into account density dependence of meson masses in the quantum hadrodynamics, quark-meson coupling and modified quark-meson coupling models. It is found that the equation of state becomes stiff when the mass of meson is reduced in dense medium. We discuss its implication on the properties of the neutron star.Comment: 3 pages, 2 figures and 10 references. Use espcrc1.sty. Appeared in the proceedings of the 7th international symposium on Nuclei in the Cosmos, Fuji-Yoshida, Japan, July 8-12, 200

The Impact of New EUV Diagnostics on CME-Related Kinematics

We present the application of novel diagnostics to the spectroscopic observation of a Coronal Mass Ejection (CME) on disk by the Extreme Ultraviolet Imaging Spectrometer (EIS) on the Hinode spacecraft. We apply a recently developed line profile asymmetry analysis to the spectroscopic observation of NOAA AR 10930 on 14-15 December 2006 to three raster observations before and during the eruption of a 1000km/s CME. We see the impact that the observer's line-of-sight and magnetic field geometry have on the diagnostics used. Further, and more importantly, we identify the on-disk signature of a high-speed outflow behind the CME in the dimming region arising as a result of the eruption. Supported by recent coronal observations of the STEREO spacecraft, we speculate about the momentum flux resulting from this outflow as a secondary momentum source to the CME. The results presented highlight the importance of spectroscopic measurements in relation to CME kinematics, and the need for full-disk synoptic spectroscopic observations of the coronal and chromospheric plasmas to capture the signature of such explosive energy release as a way of providing better constraints of CME propagation times to L1, or any other point of interest in the heliosphere.Comment: Accepted to appear in Solar Physics Topical Issue titled "Remote Sensing of the Inner Heliosphere". Manuscript has 14 pages, 5 color figures. Movies supporting the figures can be found in http://download.hao.ucar.edu/pub/mscott/papers/Weathe

Duality of Quasilocal Gravitational Energy and Charges with Non-orthogonal Boundaries

We study the duality of quasilocal energy and charges with non-orthogonal boundaries in the (2+1)-dimensional low-energy string theory. Quasilocal quantities shown in the previous work and some new variables arisen from considering the non-orthogonal boundaries as well are presented, and the boost relations between those quantities are discussed. Moreover, we show that the dual properties of quasilocal variables such as quasilocal energy density, momentum densities, surface stress densities, dilaton pressure densities, and Neuve-Schwarz(NS) charge density, are still valid in the moving observer's frame.Comment: 19pages, 1figure, RevTe

Thermodynamics of a Kerr Newman de Sitter Black Hole

We compute the conserved quantities of the four-dimensional Kerr-Newman-dS (KNdS) black hole through the use of the counterterm renormalization method, and obtain a generalized Smarr formula for the mass as a function of the entropy, the angular momentum and the electric charge. The first law of thermodynamics associated to the cosmological horizon of KNdS is also investigated. Using the minimal number of intrinsic boundary counterterms, we consider the quasilocal thermodynamics of asymptotic de Sitter Reissner-Nordstrom black hole, and find that the temperature is equal to the product of the surface gravity (divided by $2\pi$) and the Tolman redshift factor. We also perform a quasilocal stability analysis by computing the determinant of Hessian matrix of the energy with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles and obtain a complete set of phase diagrams. We then turn to the quasilocal thermodynamics of four-dimensional Kerr-Newman-de Sitter black hole for virtually all possible values of the mass, the rotation and the charge parameters that leave the quasilocal boundary inside the cosmological event horizon, and perform a quasilocal stability analysis of KNdS black hole.Comment: REVTEX4, 12 pages, 12 figures, references added and some points in Sec II have been clarified, version to appear in Can. J. Phy

Sexual offenders’ parental and adult attachments and preferences for therapists’ interpersonal qualities

This study explored sex offenders' parental and adult attachment difficulties and assessed the extent to which these were associated with preferences for therapists' interpersonal qualities. One-hundred and twelve adult male child sexual offenders were invited to provide self-report data on their attachment histories, adult attachments and preferences for therapists' interpersonal qualities. A weak relationship between childhood and adulthood secure attachment was found, suggesting that attachment at the time of offending may be more relevant than childhood attachment to the aetiology of sexual offending. Participants valued a range of therapists' qualities previously identified as important for positive treatment change. Therapist trust and genuineness were perceived as particularly important by those with attachment difficulties, demonstrating the need for these qualities in offender programmes where attachment difficulties would be expected. There were some differences in the preferences for therapists' qualities between participants with different adult attachment types, highlighting the importance of responsivity factors in treatment. © 2015 Taylor & Franci

Entropy of Lovelock Black Holes

A general formula for the entropy of stationary black holes in Lovelock gravity theories is obtained by integrating the first law of black hole mechanics, which is derived by Hamiltonian methods. The entropy is not simply one quarter of the surface area of the horizon, but also includes a sum of intrinsic curvature invariants integrated over a cross section of the horizon.Comment: 15 pages, plain Latex, NSF-ITP-93-4

TASI Lectures on the Cosmological Constant

The energy density of the vacuum, Lambda, is at least 60 orders of magnitude smaller than several known contributions to it. Approaches to this problem are tightly constrained by data ranging from elementary observations to precision experiments. Absent overwhelming evidence to the contrary, dark energy can only be interpreted as vacuum energy, so the venerable assumption that Lambda=0 conflicts with observation. The possibility remains that Lambda is fundamentally variable, though constant over large spacetime regions. This can explain the observed value, but only in a theory satisfying a number of restrictive kinematic and dynamical conditions. String theory offers a concrete realization through its landscape of metastable vacua.Comment: 39 pages, 3 figure

Averaged Energy Conditions and Quantum Inequalities

Connections are uncovered between the averaged weak (AWEC) and averaged null (ANEC) energy conditions, and quantum inequality restrictions on negative energy for free massless scalar fields. In a two-dimensional compactified Minkowski universe, we derive a covariant quantum inequality-type bound on the difference of the expectation values of the energy density in an arbitrary quantum state and in the Casimir vacuum state. From this bound, it is shown that the difference of expectation values also obeys AWEC and ANEC-type integral conditions. In contrast, it is well-known that the stress tensor in the Casimir vacuum state alone satisfies neither quantum inequalities nor averaged energy conditions. Such difference inequalities represent limits on the degree of energy condition violation that is allowed over and above any violation due to negative energy densities in a background vacuum state. In our simple two-dimensional model, they provide physically interesting examples of new constraints on negative energy which hold even when the usual AWEC, ANEC, and quantum inequality restrictions fail. In the limit when the size of the space is allowed to go to infinity, we derive quantum inequalities for timelike and null geodesics which, in appropriate limits, reduce to AWEC and ANEC in ordinary two-dimensional Minkowski spacetime. We also derive a quantum inequality bound on the energy density seen by an inertial observer in four-dimensional Minkowski spacetime. The bound implies that any inertial observer in flat spacetime cannot see an arbitrarily large negative energy density which lasts for an arbitrarily long period of time.Comment: 20pp, plain LATEX, TUTP-94-1