The "physical process" version of the first law and the generalized second law for charged and rotating black holes

We investigate both the ``physical process'' version of the first law and the second law of black hole thermodynamics for charged and rotating black holes. We begin by deriving general formulas for the first order variation in ADM mass and angular momentum for linear perturbations off a stationary, electrovac background in terms of the perturbed non-electromagnetic stress-energy, $\delta T_{ab}$, and the perturbed charge current density, $\delta j^a$. Using these formulas, we prove the "physical process version" of the first law for charged, stationary black holes. We then investigate the generalized second law of thermodynamics (GSL) for charged, stationary black holes for processes in which a box containing charged matter is lowered toward the black hole and then released (at which point the box and its contents fall into the black hole and/or thermalize with the ``thermal atmosphere'' surrounding the black hole). Assuming that the thermal atmosphere admits a local, thermodynamic description with respect to observers following orbits of the horizon Killing field, and assuming that the combined black hole/thermal atmosphere system is in a state of maximum entropy at fixed mass, angular momentum, and charge, we show that the total generalized entropy cannot decrease during the lowering process or in the ``release process''. Consequently, the GSL always holds in such processes. No entropy bounds on matter are assumed to hold in any of our arguments.Comment: 35 pages; 1 eps figur

On the massive wave equation on slowly rotating Kerr-AdS spacetimes

The massive wave equation $\Box_g \psi - \alpha\frac{\Lambda}{3} \psi = 0$ is studied on a fixed Kerr-anti de Sitter background $(\mathcal{M},g_{M,a,\Lambda})$. We first prove that in the Schwarzschild case (a=0), $\psi$ remains uniformly bounded on the black hole exterior provided that $\alpha < {9/4}$, i.e. the Breitenlohner-Freedman bound holds. Our proof is based on vectorfield multipliers and commutators: The usual energy current arising from the timelike Killing vector field $T$ (which fails to be non-negative pointwise) is shown to be non-negative with the help of a Hardy inequality after integration over a spacelike slice. In addition to $T$, we construct a vectorfield whose energy identity captures the redshift producing good estimates close to the horizon. The argument is finally generalized to slowly rotating Kerr-AdS backgrounds. This is achieved by replacing the Killing vectorfield $T=\partial_t$ with $K=\partial_t + \lambda \partial_\phi$ for an appropriate $\lambda \sim a$, which is also Killing and--in contrast to the asymptotically flat case--everywhere causal on the black hole exterior. The separability properties of the wave equation on Kerr-AdS are not used. As a consequence, the theorem also applies to spacetimes sufficiently close to the Kerr-AdS spacetime, as long as they admit a causal Killing field $K$ which is null on the horizon.Comment: 1 figure; typos corrected, references added, introduction revised; to appear in CM

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

Deflection and Rotation of CMEs from Active Region 11158

Between the 13 and 16 of February 2011 a series of coronal mass ejections (CMEs) erupted from multiple polarity inversion lines within active region 11158. For seven of these CMEs we use the Graduated Cylindrical Shell (GCS) flux rope model to determine the CME trajectory using both Solar Terrestrial Relations Observatory (STEREO) extreme ultraviolet (EUV) and coronagraph images. We then use the Forecasting a CME's Altered Trajectory (ForeCAT) model for nonradial CME dynamics driven by magnetic forces, to simulate the deflection and rotation of the seven CMEs. We find good agreement between the ForeCAT results and the reconstructed CME positions and orientations. The CME deflections range in magnitude between 10 degrees and 30 degrees. All CMEs deflect to the north but we find variations in the direction of the longitudinal deflection. The rotations range between 5\mydeg and 50\mydeg with both clockwise and counterclockwise rotations occurring. Three of the CMEs begin with initial positions within 2 degrees of one another. These three CMEs all deflect primarily northward, with some minor eastward deflection, and rotate counterclockwise. Their final positions and orientations, however, respectively differ by 20 degrees and 30 degrees. This variation in deflection and rotation results from differences in the CME expansion and radial propagation close to the Sun, as well as the CME mass. Ultimately, only one of these seven CMEs yielded discernible in situ signatures near Earth, despite the active region facing near Earth throughout the eruptions. We suggest that the differences in the deflection and rotation of the CMEs can explain whether each CME impacted or missed the Earth.Comment: 18 pages, 6 figures, accepted in Solar Physic

On the Particle Definition in the presence of Black Holes

A canonical particle definition via the diagonalisation of the Hamiltonian for a quantum field theory in specific curved space-times is presented. Within the provided approach radial ingoing or outgoing Minkowski particles do not exist. An application of this formalism to the Rindler metric recovers the well-known Unruh effect. For the situation of a black hole the Hamiltonian splits up into two independent parts accounting for the interior and the exterior domain, respectively. It turns out that a reasonable particle definition may be accomplished for the outside region only. The Hamiltonian of the field inside the black hole is unbounded from above and below and hence possesses no ground state. The corresponding equation of motion displays a linear global instability. Possible consequences of this instability are discussed and its relations to the sonic analogues of black holes are addressed. PACS-numbers: 04.70.Dy, 04.62.+v, 10.10.Ef, 03.65.Db.Comment: 44 pages, LaTeX, no figures, accepted for publication in Phys. Rev.

Applications of a New Proposal for Solving the "Problem of Time" to Some Simple Quantum Cosmological Models

We apply a recent proposal for defining states and observables in quantum gravity to simple models. First, we consider a Klein-Gordon particle in an ex- ternal potential in Minkowski space and compare our proposal to the theory ob- tained by deparametrizing with respect to a time slicing prior to quantiza- tion. We show explicitly that the dynamics of the deparametrization approach depends on the time slicing. Our proposal yields a dynamics independent of the choice of time slicing at intermediate times but after the potential is turned off, the dynamics does not return to the free particle dynamics. Next we apply our proposal to the closed Robertson-Walker quantum cosmology with a massless scalar field with the size of the universe as our time variable, so the only dynamical variable is the scalar field. We show that the resulting theory has the semi-classical behavior up to the classical turning point from expansion to contraction, i.e., given a classical solution which expands for much longer than the Planck time, there is a quantum state whose dynamical evolution closely approximates this classical solution during the expansion. However, when the "time" gets larger than the classical maximum, the scalar field be- comes "frozen" at its value at the maximum expansion. We also obtain similar results in the Taub model. In an Appendix we derive the form of the Wheeler- DeWitt equation for the Bianchi models by performing a proper quantum reduc- tion of the momentum constraints; this equation differs from the usual one ob- tained by solving the momentum constraints classically, prior to quantization.Comment: 30 pages, LaTeX 3 figures (postscript file or hard copy) available upon request, BUTP-94/1

Assessment of atmospheric aerosols from two reanalysis products over Australia

Assessments of atmospheric aerosols from reanalysis are important for understanding uncertainty in model simulations, and ultimately predictions, such as for solar power or air quality forecasts and assessments. This study intercompares total aerosol optical depth (AOD) and dust AOD (DAOD) from two global reanalyses datasets, the European Centre for Medium-Range Weather Forecasts (ECMWF) Monitoring Atmospheric Composition and Climate (MACC) and the NASA Modern-Era Retrospective Analysis for Research-2 (MERRA-2). These are evaluated against AeroSpan (Aerosol characterisation via Sun photometry: Australian Network) ground observations which forms part of the Aerosol Robotic Network (AERONET) over the Australian continent for the 2002–2012 period. During dust storms, AeroSpan/AERONET AOD measurements were missing due to cloud screening. To overcome validation limitations in sun photometry for dust events, a nephelometer's scattering coefficient is qualitatively compared against reanalysis of DAOD at a key dust storm activation site, Tinga Tingana in South Australia (~200 km east of Lake Eyre). A specific extreme event that occurred in 2009 originating from the Lake Eyre basin, a major dust source covering one-sixth of Australia, was studied. The results show that MERRA-2 reanalysis overestimates monthly total AOD twice as much compared to AeroSpan/AERONET ground observations but seems better correlated against AeroSpan/AERONET than ECMWF/MACC. Mean data of MERRA-2 time series over 10 years provide lower DAOD values and lower dust aerosol estimates than ECMWF/MACC reanalysis (over the Lake Eyre basin with spatial averaging). Specifically at Tinga Tingana, the correlation from MERRA-2 (0.45 correlation) and ECMWF/MACC (0.43 correlation) against AeroSpan/AERONET's AOD were similar. Between MERRA-2 and ECMWF/MACC decade long daily gridded DAOD, the correlation coefficient was high at 0.73, again indicating similarity between the datasets. MERRA-2 total AOD correlation is significantly higher (by 0.26) against AeroSpan/AERONET than ECMWF/MACC. MERRA-2 also provides higher AOD values in extreme cases which may correspond to dust storms. During dust storms, a hybrid strategy using nephelometers and hourly reanalysis from MERRA-2 is able to identify dust storms better than AeroSpan/AERONET. Overall, this work can enable and inform better aerosol data assimilation into forecast models such as for solar energy, agriculture or air quality over Australia

Black Hole Evaporation in the Presence of a Short Distance Cutoff

A derivation of the Hawking effect is given which avoids reference to field modes above some cutoff frequency $\omega_c\gg M^{-1}$ in the free-fall frame of the black hole. To avoid reference to arbitrarily high frequencies, it is necessary to impose a boundary condition on the quantum field in a timelike region near the horizon, rather than on a (spacelike) Cauchy surface either outside the horizon or at early times before the horizon forms. Due to the nature of the horizon as an infinite redshift surface, the correct boundary condition at late times outside the horizon cannot be deduced, within the confines of a theory that applies only below the cutoff, from initial conditions prior to the formation of the hole. A boundary condition is formulated which leads to the Hawking effect in a cutoff theory. It is argued that it is possible the boundary condition is {\it not} satisfied, so that the spectrum of black hole radiation may be significantly different from that predicted by Hawking, even without the back-reaction near the horizon becoming of order unity relative to the curvature.Comment: 35 pages, plain LaTeX, UMDGR93-32, NSF-ITP-93-2

The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes

Quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis. We discuss a condition on the wave front set for the corresponding n-point distributions, called ``microlocal spectrum condition'' ($\mu$SC). On Minkowski space, this condition is satisfied as a consequence of the usual spectrum condition. Based on Radzikowski's determination of the wave front set of the two-point function of a free scalar field, satisfying the Hadamard condition in the Kay and Wald sense, we construct in the second part of this paper all Wick polynomials including the energy-momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition.Comment: 21 pages, AMS-LaTeX, 2 figures appended as Postscript file

Geological relationships and laser ablation ICP-MS U-Pb geochronology of the Saint George Batholith, southwestern New Brunswick, Canada: implications for its tectonomagmatic evolution

  The Late Silurian to Late Devonian Saint George Batholith in southwestern New Brunswick is a large composite intrusion (2000 km2) emplaced into the continental margin of the peri-Gondwanan microcontinent of Ganderia. The batholith includes: (1) Bocabec Gabbro; (2) equigranular Utopia and Wellington Lake biotite granites; (3) Welsford, Jake Lee Mountain, and Parks Brook peralkaline granites; (4) two-mica John Lee Brook Granite; (6) Jimmy Hill and Magaguadavic megacrystic granites; and (6) rapakivi Mount Douglas Granite. New LA ICP-MS in situ analyses of six samples from the Saint George Batholith are as follows: (1) U-Pb monazite crystallization age of 425.5 ± 2.1 Ma for the Utopia Granite in the western part of the batholith (2) U-Pb zircon crystallization ages of 420.4 ± 2.4 Ma and 420.0 ± 3.5 Ma for two samples of the Utopia Granite from the central part of the batholith; (3) U-Pb zircon crystallization age of 418.0 ± 2.3 Ma for the Jake Lee Mountain Granite; (4) U-Pb zircon crystallization age of 415.5 ± 2.1 Ma for the Wellington Lake Granite; and (5) U-Pb monazite crystallization age of 413.3 ± 2.1 Ma for the John Lee Brook Granite. The new geochronological together with new and existing geochemical data suggest that the protracted magmatic evolution of the Late Silurian to Early Devonian plutonic rocks is related to the transition of the Silurian Kingston arc-Mascarene backarc system from an extensional to compressional tectonic environment during collision of the Avalonian microcontinent with Laurentia followed by slab break-off.