Numerical investigation of black hole interiors

Gravitational perturbations which are present in any realistic stellar collapse to a black hole, die off in the exterior of the hole, but experience an infinite blueshift in the interior. This is believed to lead to a slowly contracting lightlike scalar curvature singularity, characterized by a divergence of the hole's (quasi-local) mass function along the inner horizon. The region near the inner horizon is described to great accuracy by a plane wave spacetime. While Einstein's equations for this metric are still too complicated to be solved in closed form it is relatively simple to integrate them numerically. We find for generic regular initial data the predicted mass inflation type null singularity, rather than a spacelike singularity. It thus seems that mass inflation indeed represents a generic self-consistent picture of the black hole interior.Comment: 6 pages LaTeX, 3 eps figure

The late-time singularity inside non-spherical black holes

It was long believed that the singularity inside a realistic, rotating black hole must be spacelike. However, studies of the internal geometry of black holes indicate a more complicated structure is typical. While it seems likely that an observer falling into a black hole with the collapsing star encounters a crushing spacelike singularity, an observer falling in at late times generally reaches a null singularity which is vastly different in character to the standard Belinsky, Khalatnikov and Lifschitz (BKL) spacelike singularity. In the spirit of the classic work of BKL we present an asymptotic analysis of the null singularity inside a realistic black hole. Motivated by current understanding of spherical models, we argue that the Einstein equations reduce to a simple form in the neighborhood of the null singularity. The main results arising from this approach are demonstrated using an almost plane symmetric model. The analysis shows that the null singularity results from the blueshift of the late-time gravitational wave tail; the amplitude of these gravitational waves is taken to decay as an inverse power of advanced time as suggested by perturbation theory. The divergence of the Weyl curvature at the null singularity is dominated by the propagating modes of the gravitational field. The null singularity is weak in the sense that tidal distortion remains bounded along timelike geodesics crossing the Cauchy horizon. These results are in agreement with previous analyses of black hole interiors. We briefly discuss some outstanding problems which must be resolved before the picture of the generic black hole interior is complete.Comment: 16 pages, RevTeX, 3 figures included using psfi

Size Gap for Zero Temperature Black Holes in Semiclassical Gravity

We show that a gap exists in the allowed sizes of all zero temperature static spherically symmetric black holes in semiclassical gravity when only conformally invariant fields are present. The result holds for both charged and uncharged black holes. By size we mean the proper area of the event horizon. The range of sizes that do not occur depends on the numbers and types of quantized fields that are present. We also derive some general properties that both zero and nonzero temperature black holes have in all classical and semiclassical metric theories of gravity.Comment: 4 pages, ReVTeX, no figure

Census of the Local Universe (CLU) Narrow-Band Survey I: Galaxy Catalogs from Preliminary Fields

We present the Census of the Local Universe (CLU) narrow-band survey to search for emission-line (\ha) galaxies. CLU-\ha~has imaged $\approx$3$\pi$ of the sky (26,470~deg$^2$) with 4 narrow-band filters that probe a distance out to 200~Mpc. We have obtained spectroscopic follow-up for galaxy candidates in 14 preliminary fields (101.6~deg$^2$) to characterize the limits and completeness of the survey. In these preliminary fields, CLU can identify emission lines down to an \ha~flux limit of $10^{-14}$~$\rm{erg~s^{-1}~cm^{-2}}$ at 90\% completeness, and recovers 83\% (67\%) of the \ha~flux from catalogued galaxies in our search volume at the $\Sigma$=2.5 ($\Sigma$=5) color excess levels. The contamination from galaxies with no emission lines is 61\% (12\%) for $\Sigma$=2.5 ($\Sigma$=5). Also, in the regions of overlap between our preliminary fields and previous emission-line surveys, we recover the majority of the galaxies found in previous surveys and identify an additional $\approx$300 galaxies. In total, we find 90 galaxies with no previous distance information, several of which are interesting objects: 7 blue compact dwarfs, 1 green pea, and a Seyfert galaxy; we also identified a known planetary nebula. These objects show that the CLU-\ha~survey can be a discovery machine for objects in our own Galaxy and extreme galaxies out to intermediate redshifts. However, the majority of the CLU-\ha~galaxies identified in this work show properties consistent with normal star-forming galaxies. CLU-\ha~galaxies with new redshifts will be added to existing galaxy catalogs to focus the search for the electromagnetic counterpart to gravitational wave events.Comment: 28 pages, 22 figures, 4 tables (Accepted to ApJ

Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium

We investigate the decay of a scalar field outside a Schwarzschild anti de Sitter black hole. This is determined by computing the complex frequencies associated with quasinormal modes. There are qualitative differences from the asymptotically flat case, even in the limit of small black holes. In particular, for a given angular dependence, the decay is always exponential - there are no power law tails at late times. In terms of the AdS/CFT correspondence, a large black hole corresponds to an approximately thermal state in the field theory, and the decay of the scalar field corresponds to the decay of a perturbation of this state. Thus one obtains the timescale for the approach to thermal equilibrium. We compute these timescales for the strongly coupled field theories in three, four, and six dimensions which are dual to string theory in asymptotically AdS spacetimes.Comment: 25 pages, 9 figures extended discussion of horizon boundary conditions, added note on higher l mode

Quasi-normal modes of Schwarzschild-de Sitter black holes

The low-laying frequencies of characteristic quasi-normal modes (QNM) of Schwarzschild-de Sitter (SdS) black holes have been calculated for fields of different spin using the 6th-order WKB approximation and the approximation by the P\"{o}shl-Teller potential. The well-known asymptotic formula for large $l$ is generalized here on a case of the Schwarzchild-de Sitter black hole. In the limit of the near extreme $\Lambda$ term the results given by both methods are in a very good agreement, and in this limit fields of different spin decay with the same rate.Comment: 9 pages, 1 ancillary Mathematica(R) noteboo

Spatial Imaging and Screening for Regime Shifts

Screening is a strategy for detecting undesirable change prior to manifestation of symptoms or adverse effects. Although the well-recognized utility of screening makes it commonplace in medicine, it has yet to be implemented in ecosystem management. Ecosystem management is in an era of diagnosis and treatment of undesirable change, and as a result, remains more reactive than proactive and unable to effectively deal with today’s plethora of non-stationary conditions. In this paper, we introduce spatial imaging-based screening to ecology. We link advancements in spatial resilience theory, data, and technological and computational capabilities and power to detect regime shifts (i.e., vegetation state transitions) that are known to be detrimental to human well-being and ecosystem service delivery. With a state-of-the-art landcover dataset and freely available, cloud-based, geospatial computing platform, we screen for spatial signals of the three most iconic vegetation transitions studied in western USA rangelands: (1) erosion and desertification; (2) woody encroachment; and (3) annual exotic grass invasion. For a series of locations that differ in ecological complexity and geographic extent, we answer the following questions: (1) Which regime shift is expected or of greatest concern? (2) Can we detect a signal associated with the expected regime shift? (3) If detected, is the signal transient or persistent over time? (4) If detected and persistent, is the transition signal stationary or non-stationary over time? (5) What other signals do we detect? Our approach reveals a powerful and flexible methodology, whereby professionals can use spatial imaging to verify the occurrence of alternative vegetation regimes, image the spatial boundaries separating regimes, track the magnitude and direction of regime shift signals, differentiate persistent and stationary transition signals that warrant continued screening from more concerning persistent and non-stationary transition signals, and leverage disciplinary strength and resources for more targeted diagnostic testing (e.g., inventory and monitoring) and treatment (e.g., management) of regime shifts. While the rapid screening approach used here can continue to be implemented and refined for rangelands, it has broader implications and can be adapted to other ecological systems to revolutionize the information space needed to better manage critical transitions in nature

Beyond Inventories: Emergence of a New Era in Rangeland Monitoring

In the absence of technology-driven monitoring platforms, US rangeland policies, management practices, and outcome assessments have been primarily informed by the extrapolation of local information from national-scale rangeland inventories. A persistent monitoring gap between plot-level inventories and the scale at which rangeland assessments are conducted has required decision makers to fill data gaps with statistical extrapolations or assumptions of homogeneity and equilibrium. This gap is now being bridged with spatially comprehensive, annual, rangeland monitoring data across all western US rangelands to as- sess vegetation conditions at a resolution appropriate to inform cross-scale assessments and decisions. In this paper, 20-yr trends in plant functional type cover are presented, confirming two widespread national rangeland resource concerns: widespread increases in annual grass cover and tree cover. Rangeland vegetation monitoring is now available to inform national to regional policies and provide essential data at the scales at which decisions are made and implemented

Gravitational collapse of massless scalar field and radiation fluid

Several classes of conformally-flat and spherically symmetric exact solutions to the Einstein field equations coupled with either a massless scalar field or a radiation fluid are given, and their main properties are studied. It is found that some represent the formation of black holes due to the gravitational collapse of the matter fields. When the spacetimes have continuous self-similarity (CSS), the masses of black holes take a scaling form $M_{BH} \propto (P - P^{*})^{\gamma}$, where $\gamma = 0.5$ for massless scalar field and $\gamma = 1$ for radiation fluid. The reasons for the difference between the values of $\gamma$ obtained here and those obtained previously are discussed. When the spacetimes have neither CSS nor DSS (Discrete self-similarity), the masses of black holes always turn on with finite non-zero values.Comment: Two figures have been removed, and the text has been re-written. To appear in Phys. Rev.