Paulo Custodio

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 the 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 Ω 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 du...

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 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.

The formation of Primordial Black Holes is a robust prediction of several gravitational theories. Whereas the creation of PBHs was very active in the remote past, such process seem to be very negligible at the present epoch. In this work, we estimate the effects from the radiation surrounding PBHs due to the absorption term in the equations that describe how their masses depend on time. The Hawking radiation contributes with mass loss and the absorption term contributes with gain, but a interesting competition between these terms is analysed. These effects are included in the equations describing PBHs and its mass density as the universe evolves in time and the model is able to describes the evolution of the numerical density of PBHs and the mass evolution and comparisons with cosmological constraints set upper limits in their abundances. We evaluate the effect of this accretion onto PBHs and we get some corrections for the initial masses that indicates some deviations from de- faul...

Em escalas proximas à escala de Planck todas as teorias perturbativas de cordas produzem essenciamente a mesma relação de conmutação entre as coordenadas e impulsos (a chamada "álgebra deformada"), permitindo assim estudar a física resultante independentemente dos detalhes da teoria de cordas que seja considerada correta. Este resultado completamente geral, que inclui as interações gravitacionais junto com o resto dos campos pode ser considerada uma versão generalizada (GUP) do Princípio de Incerteza de Heisenberg. Aplicamos neste trabalho essas relações de conmutação para dois sistemas físicos bem definidos: buracos negros de massas próximas à massa de Planck, e flutuações quânticas em pequenas escalas antes do universo sofrer inflação. Obtemos dois resultados concretos dos efeitos do GUP : o primeiro é que o GUP impede a evaporação completa de buracos negros microscópicos na extensão do formalismo semiclássico, deixando assim remanescentes de pequena massa que já foram postulados como candidatos a matéria escura. O segundo resultado é o 'smoothing' das flutuações primordiais em pequenas escalas que levariam à produção de buracos negros primordiais após a inflação, impedindo assim a produção abundante destes últimos e predizendo abundancias atuais bem menores do que os limites disponíveis. Concluimos que, analogamente a utilização do Princípio de Incerteza de Heisenberg para estudar e determinar propriedades fundamentais das interações sem gravitação, o GUP e uma ferramenta poderosa para estudar uma ampla variedade de sistemas trans-Planckianos e predizer seu comportamento dispensando cálculos mais detalhados proprios da teoria quântica da gravitação.

We evaluate in the proper and cosmological frames the effects of nonzero velocities on the mass gain or loss of primordial black holes. An upper limit of twice the initial Lorentz factor is derived from the mass gain of the black holes, a value that may be enough to preclude their evaporation. Next, we analyze accelerated black holes and find that the Unruh effect can delay the onset of the evaporation regime. Finally, we reassess the equilibrium between black holes and the relic thermal radiation. S0556-28219900718-3

In this work we revisit the growth of small primordial black holes (PBHs) immersed in a quintessential field and/or radiation to the su-permassive 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 Ω 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.

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 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.

The formation of Primordial Black Holes is a robust prediction of several gravitational theories. Whereas the creation of PBHs was very active in the remote past, such process seem to be very negligible at the present epoch. In this work, we estimate the effects from the radiation surrounding PBHs due to the absorption term in the equations that describe how their masses depend on time. The Hawking radiation contributes with mass loss and the absorption term contributes with gain, but a interesting competition between these terms is analysed. These effects are included in the equations describing PBHs and its mass density as the universe evolves in time and the model is able to describes the evolution of the numerical density of PBHs and the mass evolution and comparisons with cosmological constraints set upper limits in their abundances. Moreover, we evaluate the fraction of PBHs (in terms of the critical density) formed from the high-energy collision of particles before Inflation, when the temperatures were close to Planck values. We consider that the Universe has dimension D, and we evaluate the e-folds number in order get a universe free from such Primordial Black Holes. Finally, the Holographic constraint is used to estimate upper bounds to temperature and mass of PBHs with monochromatic spectrum.

The formation of Primordial Black Holes is a robust prediction of several gravitational theories. Whereas the creation of PBHs was very active in the remote past, such process seem to be very negligible at the present epoch. In this work, we estimate the effects from the radiation surrounding PBHs due to the absorption term in the equations that describe how their masses depend on time. The Hawking radiation contributes with mass loss and the absorption term contributes with gain, but a interesting competition between these terms is analysed. These effects are included in the equations describing PBHs and its mass density as the universe evolves in time and the model is able to describes the evolution of the numerical density of PBHs and the mass evolution and comparisons with cosmological constraints set upper limits in their abundances. Moreover, we evaluate the fraction of PBHs (in terms of the critical density) formed from the high-energy collision of particles before Inflation, when the temperatures were close to Planck values. We consider that the Universe has dimension D, and we evaluate the e-folds number in order get a universe free from such Primordial Black Holes. Finally, the Holographic constraint is used to estimate upper bounds to temperature and mass of PBHs with monochromatic spectrum.

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 the 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 Ω 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 Appendix.

Nesta primeira seção apresento um resumo sobre Mecânica Relativística e uma rápida revisão sobre Operadores Diferenciais. Esta é a apresentação de um curso mais extenso sobre Buracos Negros, a ser apresentado em seções diversas, esta é a primeira delas.

The formation of Primordial Black Holes is a robust prediction of several gravitational theories. Whereas the creation of PBHs was very active in the remote past, such process seem to be very negligible at the present epoch. In this work, we estimate the fraction of PBHs (in terms of the critical density) formed from the high-energy collision of particles before Inflation, when the temperatures were close to Planck values. We consider that the Universe has dimension D, and we evaluate the e-folds number in order get a universe free from such Primordial Black Holes. Finally, the Holographic constraint is used to estimate upper bounds to temperature and mass of PBHs with monochromatic spectrum.

The formation of Primordial Black Holes is a robust prediction of several gravitational theories. Whereas the creation of PBHs was very active in the remote past, such process seem to be very negligible at the present epoch. In this work, we estimate the effects from the radiation surrounding PBHs due to the absorption term in the equations that describe how their masses depend on time. The Hawking radiation contributes with mass loss and the absorption term contributes with gain, but a interesting competition between these terms is analysed. These effects are included in the equations describing PBHs and its mass density as the universe evolves in time and the model is able to describes the evolution of the numerical density of PBHs and the mass evolution and comparisons with cosmological constraints set upper limits in their abundances. We evaluate the effect of this accretion onto PBHs and we get some corrections for the initial masses that indicates some deviations from default values for the time scale for evaporation. The scale time of the PBHs in the early universe is modified due to the energy accretion and we can estimate how these contributions may alter the standard model of PBHs.

The formation of Primordial Black Holes is a robust prediction of several gravitational theories. Whereas the creation of PBHs was very active in the remote past, such process seem to be very negligible at the present epoch. In this work, we estimate the effects from the radiation surrounding PBHs due to the absorption term in the equations that describe how their masses depend on time. The Hawking radiation contributes with mass loss and the absorption term contributes with gain, but a interesting competition between these terms is analysed. These effects are included in the equations describing PBHs and its mass density as the universe evolves in time and the model is able to describes the evolution of the numerical density of PBHs and the mass evolution and comparisons with cosmological constraints set upper limits in their abundances. We evaluate the effect of this accretion onto PBHs and we get some corrections for the initial masses that indicates some deviations from default values for the time scale for evaporation. The scale time of the PBHs in the early universe is modified due to the energy accretion and we can estimate how these contributions may alter the standard model of PBHs.