Thermodynamics of black holes in finite boxes

We analyze the thermodynamical behavior of black holes in closed finite boxes. First the black hole mass evolution is analyzed in an initially empty box. Using the conservation of the energy and the Hawking evaporation flux, we deduce a minimal volume above which one black hole can loss all of its mass to the box, a result which agrees with the previous analysis made by Page. We then obtain analogous results using a box initially containing radiation, allowed to be absorbed by the black hole. The equilibrium times and masses are evaluated and their behavior discussed to highlight some interesting features arising. These results are generalized to $N$ black holes + thermal radiation. Using physically simple arguments, we prove that these black holes achieve the same equilibrium masses (even that the initial masses were different). The entropy of the system is used to obtain the dependence of the equilibrium mass on the box volume, number of black holes and the initial radiation. The equilibrium mass is shown to be proportional to a {\it positive} power law of the effective volume (contrary to naive expectations), a result explained in terms of the detailed features of the system. The effect of the reflection of the radiation on the box walls which comes back into the black hole is explicitly considered. All these results (some of them counter-intuitive) may be useful to formulate alternative problems in thermodynamic courses for graduate and advanced undergraduate students. A handful of them are suggested in the Appendix.Comment: RevTex file, 2 .ps figures. Submitted to AmJPhy

Cosmological quintessence accretion onto primordial black holes : conditions for their growth to the supermassive scale

In this work we revisit the growth of small primordial black holes (PBHs) immersed in a quintessential field and/or radiation to the supermassive black hole (SMBHs) scale. We show the difficulties of scenarios in which such huge growth is possible. For that purpose we evaluated analytical solutions of the differential equations (describing mass evolution) and point out the strong fine tuning for that conclusions. The timescale for growth in a model with a constant quintessence flux is calculated and we show that it is much bigger than the Hubble time.The fractional gain of the mass is further evaluated in other forms, including quintessence and/or radiation. We calculate the cosmological density $\Omega$ due to quintessence necessary to grow BHs to the supermassive range and show it to be much bigger than one. We also describe the set of complete equations analyzing the evolution of the BH+quintessence universe, showing some interesting effects such the quenching of the BH mass growth due to the evolution of the background energy. Additional constraints obtained by using the Holographic Bound are also described. The general equilibrium conditions for evaporating/accreting black holes evolving in a quintessence/radiation universe are discussed in the Appendix.Comment: 21 pp., 2 Figures, To appear in IJMP

Holographic Principle bounds on Primordial Black Hole abundances

The generalized Second Law of thermodynamics and the Holographic Principle are combined to obtain the maximum mass of black holes formed inside a static spherical box of size $R$ filled with radiation at initial temperature $T_{i}$. The final temperature after the formation of black holes is evaluated, and we show that a critical threshold exists for the radiation to be fully consumed by the process. We next argue that if some form of Holographic Principle holds, upper bounds to the mass density of PBHs formed in the early universe may be obtained. The limits are worked out for inflationary and non-inflationary cosmological models. This method is independent of the known limits based on the background fluxes (from cosmic rays, radiation and other forms of energy) and applies to potentially important epochs of PBH formation, resulting in quite strong constraints to $\Omega_{pbh}$.Comment: Latex file, 2 .ps figures. To appear in Classical and Quantum Gravit

Bounds on the cosmological abundance of primordial black holes from diffuse sky brightness: single mass spectra

We constrain the mass abundance of unclustered primordial black holes (PBHs), formed with a simple mass distribution and subject to the Hawking evaporation and particle absorption from the environment. Since the radiative flux is proportional to the numerical density, an upper bound is obtained by comparing the calculated and observed diffuse background values, (similarly to the Olbers paradox in which point sources are considered) for finite bandwidths. For a significative range of formation redshifts the bounds are better than several values obtained by other arguments $\Omega_{pbh} \leq 10^{-10}$; and they apply to PBHs which are evaporating today.Comment: 20 pages, 5 figures, to appear in PR

Caracterização de acessos de Paspalum notatum Fluegge por meio da análise de componentes principais.

A espécie Paspalum notatum e altamente cosmopoljta, tendo sido encontrados diversos ecótipos adaptados a regiões específicas. 0 objetivo é a identificação dos descritores morfológicos vegetativos e reprodutivos principais na caracterização de oito acessos de P.notatum e um acesso de Paspalum sp. coletados em deferentes regiões brasileiras. 0 trabalho foi desenvolvido na Embrapa Pecuária Sudeste localizada em São Carlos-SP, onde se encontra o Banco Ativo de Germoplasma do gênero Paspalum. Na coleta de dados foi utilizada uma lista de 1068 descritores morfológicos vegetativos e reprodutivos. Realizou-se a análise de componentes principais que, além da dispersão gráfica da divergência entre genótipo, possibilita a identificação dos caracteres majs representativos para explicar a variância total. Na análise foi utilizado o programa SAS/STAT 6.03. Previamente os descritores foram divididos em grupos de relação. A primeira seleção eliminou descritores cujas características não apresentavam variação entre os acessos, diminuindo-os para 272. A segunda seleção analisou a correlação entre os 272 descritores, dentro de cada grupo. Utilizaram-se as componentes com acúmulo de variância a 80%. Nos componentes foram selecionados os descritores de major valor absoluto, resultando em 81 descritores principais. Os caracteres descontínuos que se destacaram foram os de comprimento e largura do requis e lamina floral. Do grupo Planta/Inflorescência/Ráquis os principais foram a pilosidade do Ráquis e a forma da Inflorescência. Os da Lamina foliar foram 05 de pilosidade. Descritores de destaque do grupo Lígula e Bainha foram à pilosidade da lígula e da bainha e os do grupo Espigueta/Pedúnculo foram de pilosidade do Pedúnculo. 0 grupo Flor/ Antêcio pode ser caracterizado pelo tamanho do Lema Fértil e Lema Estéril em relação a Gluma e translucidez do Lema Estéril. Por fim, os descritores principais da Gluma são a forma, cor e translucidez da Prjmeira Gluma. A metodologia utilizada foi eficiente na detecção da presença de variabilidade intraespecífica de Paspalum notatum

Caracterização morfológica do acesso BRA-008311 de Paspalum chacoense Parodi.

A espécie Paspalum notatum e altamente cosmopolita, tendo sido encontrados diversos ecótipos adaptados a regiões especificas. O objetivo e a identificação dos descritores morfológicos vegetativos e reprodutivos principais na caracterização de oito acessos de P.notatum e um acesso de Paspalum sp. coletados em diferentes regiões brasileiras. O trabalho foi desenvolvido na Embrapa Pecuárja Sudeste localizada em São Carlos-SP, onde se encontra o Banco Ativo de Germoplasma do gênero Paspalum. Na coleta de dados foi utilizada uma lista de 1068 descritores morfológicos vegetativos e reprodutivos. Realizou-se a análise de componentes principais que, além da dispersão gráfica da divergência entre genótipo, possibilita a identificação dos caracteres mais representativos para explicar a variância total. Na análise foi utilizado o programa SAS/STAT 6.03. Previamente os descritores foram divididos em grupos de relação. A primeira seleção eliminou descritor cujas características não apresentavam variação entre 05 acessos, diminuindo-os para 272. A segunda seleção analisou a correlação entre os 272 descritores, dentro de cada grupo. Utilizaram-se as Componentes com acúmulo de variância a 80%. Nos Componente foram Selecionados os descritores de major valor absoluto, resultando em 81 descritores principais. Os caracteres descontínuos que se destacaram foram os de comprimento e largura do ráquis e lâmina foliar foram . Do grupo Planta/lnflorescencia/Raquis os principais foram a pilosidade do Raquis e a forma da Inflorescência. Os da Lamina foliar foram os de pilosidade. Descritores de destaque do grupo lígula e Bainhas foram a pilosidade da lígula e da bajnha e os do grupo Espigueta/Pedunculo foram de pilo5jdade do Pedúnculo. O grupo Flor/ Antécio pode ser caracterizado pelo tamanho do Lema Fértil e Lema Estéril em relação á Gluma e translucidez do Lema Estéril. Por fim, os descritore5 principais da Gluma são a forma, cor e translucidez da Primeira Gluma. A metodologia utilizada foi eficiente na detecção da presença de variabilidade intraespecífica de Paspalum notatum

Evolution of a Primordial Black Hole Population

We reconsider in this work the effects of an energy absorption term in the evolution of primordial black holes (hereafter PBHs) in the several epochs of the Universe. A critical mass is introduced as a boundary between the accreting and evaporating regimes of the PBHs. We show that the growth of PBHs is negligible in the Radiation-dominated Era due to scarcity of energy density supply from the expanding background, in agreement with a previous analysis by Carr and Hawking, but that nevertheless the absorption term is large enough for black holes above the critical mass to preclude their evaporation until the universe has cooled sufficiently. The effects of PBH motion are also discussed: the Doppler effect may give rise to energy accretion in black-holes with large peculiar motions relative to background. We discuss how cosmological constraints are modified by the introduction of the critical mass since that PBHs above it do not disturb the CMBR. We show that there is a large range of admissible masses for PBHs above the critical mass but well below the cosmological horizon. Finally we outline a minimal kinetic formalism, solved in some limiting cases, to deal with more complicated cases of PBH populationsComment: RevTex file, 8 pp., 3 .ps figures available upon request from [email protected]

A common deep source for upper-mantle upwellings below the Ibero-western Maghreb region from teleseismic P-wave travel-time tomography

Upper-mantle upwellings are often invoked as the cause of Cenozoic volcanism in the Ibero-western Maghreb region. However, their nature, geometry and origin are unclear. This study takes advantage of dense seismic networks, which cover an area extending from the Pyrenees in the north to the Canaries in the south, to provide a new high-resolution P-wave velocity model of the upper-mantle and topmost lower-mantle structure. Our images show three subvertical upper-mantle upwellings below the Canaries, the Atlas Ranges and the Gibraltar Arc, which appear to be rooted beneath the upper-mantle transition zone (MTZ). Two other mantle upwellings beneath the eastern Rif and eastern Betics surround the Gibraltar subduction zone. We propose a new geodynamic model in which narrow upper-mantle upwellings below the Canaries, the Atlas Ranges and the Gibraltar Arc rise from a laterally-propagating layer of material below the MTZ, which in turn is fed by a common deep source below the Canaries. In the Gibraltar region, the deeply rooted upwelling interacts with the Gibraltar slab. Quasi-toroidal flow driven by slab rollback induces the hot mantle material to flow around the slab, creating the two low-velocity anomalies below the eastern Betics and eastern Rif. Our results suggest that the Central Atlantic plume is a likely source of hot mantle material for upper-mantle upwellings in the Ibero-western Maghreb region