Black hole evaporation and stress tensor correlations

General Relativity is one of the greatest scientific achievementes of the 20th century along with quantum theory. These two theories are extremely beautiful and they are well verified by experiments, but they are apparently incompatible. Hints towards understanding these problems can be derived studying Black Holes, some the most puzzling solutions of General Relativity. The main topic of this Master Thesis is the study of Black Holes, in particular the Physics of Hawking Radiation. After a short review of General Relativity, I study in detail the Schwarzschild solution with particular emphasis on the coordinates systems used and the mathematical proof of the classical laws of Black Hole "Thermodynamics". Then I introduce the theory of Quantum Fields in Curved Spacetime, from Bogolubov transformations to the Schwinger-De Witt expansion, useful for the renormalization of the stress energy tensor. After that I introduce a 2D model of gravitational collapse to study the Hawking radiation phenomenon. Particular emphasis is given to the analysis of the quantum states, from correlations to the physical implication of this quantum effect (e.g. Information Paradox, Black Hole Thermodynamics). Then I introduce the renormalized stress energy tensor. Using the Schwinger-De Witt expansion I renormalize this object and I compute it analytically in the various quantum states of interest. Moreover, I study the correlations between these objects. They are interesting because they are linked to the Hawking radiation experimental search in acoustic Black Hole models. In particular I find that there is a characteristic peak in correlations between points inside and outside the Black Hole region, which correpsonds to entangled excitations inside and outside the Black Hole. These peaks hopefully will be measurable soon in supersonic BEC.

Duality of coordinates and matter fields in curved spacetime

We show that there exists a duality between the local coordinates and the solutions of the Klein-Gerdon equation in curved spacetime in the same sense as in the Minkowski spacetime. However, the duality in curved spacetime does not have the same generality as in flat spacetime and it holds only if the system satisfies certain constraints. We derive these constraints and the basic equations of duality and discuss the implications in the quantum theory. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Quantum versus classical instability of scalar fields in curved backgrounds

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Uniqueness of black holes with bubbles in minimal supergravity

We generalize uniqueness theorems for non-extremal black holes with three mutually independent Killing vector fields in five-dimensional minimal supergravity in order to account for the existence of non-trivial two-cycles in the domain of outer communication. The black hole space-times we consider may contain multiple disconnected horizons and be asymptotically flat or asymptotically Kaluza–Klein. We show that in order to uniquely specify the black hole space-time, besides providing its domain structure and a set of asymptotic and local charges, it is necessary to measure the magnetic fluxes that support the two-cycles as well as fluxes in the two semi-infinite rotation planes of the domain diagram.

Ion trap simulations of quantum fields in an expanding universe

We propose an experiment in which the phonon excitation of ion(s) in a trap, with a trap frequency exponentially modulated at rate kappa, exhibits a thermal spectrum with an Unruh temperature given by k(B)T=h kappa. We discuss the similarities of this experiment to the response of detectors in a de Sitter universe and the usual Unruh effect for uniformly accelerated detectors. We demonstrate a new Unruh effect for detectors that respond to antinormally ordered moments using the ion's first blue sideband transition.

Do static sources respond to massive scalar particles from the Hawking radiation as uniformly accelerated ones do in the inertial vacuum?

We examine the recently found equivalence for the response of a static scalar source interacting with a massless Klein-Gordon field when the source is (i) static in Schwarzschild spacetime, in the Unruh vacuum associated with the Hawking radiation, and (ii) uniformly accelerated in Minkowski spacetime, in the inertial vacuum, provided that the source's proper acceleration is the same in both cases. It is shown that this equivalence is broken when the massless Klein-Gordon field is replaced by a massive one.

ANOMALIES IN CURVED SPACETIME AT FINITE TEMPERATURE

We discuss the problem of the breakdown of conformal and gauge symmetries at finite temperature in curved-spacetime background, when the changes in the background are gradual, in order to have a well-defined quantum field theory at finite temperature. We obtain the expressions for Seeley's coefficients and the heat-kernel expansion in this regime. As applications, we consider the self-interacting lambdaphi4 and chiral Schwinger models in curved backgrounds at finite temperature.

Instability of nonminimally coupled scalar fields in the spacetime of slowly rotating compact objects

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Search for narrow resonances and quantum black holes in inclusive and b-tagged dijet mass spectra from pp collisions at root s=7 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Black holes in the early universe, in compact binaries, and as energy sources inside solar-type stars

This thesis consists of three separate studies of roles that black holes might play in our universe.

In the first part we formulate a statistical method for inferring the cosmological parameters of our universe from LIGO/VIRGO measurements of the gravitational waves produced by coalescing black-hole/neutron-star binaries. This method is based on the cosmological distance-redshift relation, with "luminosity distances" determined directly, and redshifts indirectly, from the gravitational waveforms. Using the current estimates of binary coalescence rates and projected "advanced" LIGO noise spectra, we conclude that by our method the Hubble constant should be measurable to within an error of a few percent. The errors for the mean density of the universe and the cosmological constant will depend strongly on the size of the universe, varying from about 10% for a "small" universe up to and beyond 100% for a "large" universe. We further study the effects of random gravitational lensing and find that it may strongly impair the determination of the cosmological constant.

In the second part of this thesis we disprove a conjecture that black holes cannot form in an early, inflationary era of our universe, because of a quantum-field-theory induced instability of the black-hole horizon. This instability was supposed to arise from the difference in temperatures of any black-hole horizon and the inflationary cosmological horizon; it was thought that this temperature difference would make every quantum state that is regular at the cosmological horizon be singular at the black-hole horizon. We disprove this conjecture by explicitly constructing a quantum vacuum state that is everywhere regular for a massless scalar field. We further show that this quantum state has all the nice thermal properties that one has come to expect of "good" vacuum states, both at the black-hole horizon and at the cosmological horizon.

In the third part of the thesis we study the evolution and implications of a hypothetical primordial black hole that might have found its way into the center of the Sun or any other solar-type star. As a foundation for our analysis, we generalize the mixing-length theory of convection to an optically thick, spherically symmetric accretion flow (and find in passing that the radial stretching of the inflowing fluid elements leads to a modification of the standard Schwarzschild criterion for convection). When the accretion is that of solar matter onto the primordial hole, the rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport of this heat, extracts angular momentum from the inflowing gas, thereby buffering the torus into a lower luminosity than one might have expected. As a result, the solar surface will not be influenced noticeably by the torus's luminosity until at most three days before the Sun is finally devoured by the black hole. As a simple consequence, accretion onto a black hole inside the Sun cannot be an answer to the solar neutrino puzzle.

THERMAL RADIATION FROM A FLUCTUATING EVENT HORIZON

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Strong gravity, black holes, and hadrons

Analogies between the properties of black holes (in the framework of strong gravity) and those of elementary particles are discussed especially in connection with recent works on black holes with gauge charges and blackhole thermodynamics.

Thermal correlation functions of twisted quantum fields

We derive the thermal correlators for twisted quantum fields on noncommutative spacetime. We show that the thermal expectation value of the number operator is same as in commutative spacetime, but that higher correlators are sensitive to the noncommutativity parameters phi(mu nu).

Light-cone fluctuations and the renormalized stress tensor of a massless scalar field

We investigate the effects of light-cone fluctuations over the renormalized vacuum expectation value of the stress-energy tensor of a real massless minimally coupled scalar field defined in a (d+1)-dimensional flat space-time with topology R×Td. For modeling the influence of light-cone fluctuations over the quantum field, we consider a random Klein-Gordon equation. We study the case of centered Gaussian processes. After taking into account all the realizations of the random processes, we present the correction caused by random fluctuations. The averaged renormalized vacuum expectation value of the stress-energy associated with the scalar field is presented. © 2013 World Scientific Publishing Company.

Evolution of primordial black holes in a radiation and phantom energy environment

In this work we extend previous work on the evolution of a primordial black hole (PBH) to address the presence of a dark energy component with a super-negative equation of state as a background, investigating the competition between the radiation accretion, the Hawking evaporation and the phantom accretion, the latter two causing a decrease on black hole mass. It is found that there is an instant during the matter-dominated era after which the radiation accretion becomes negligible compared to the phantom accretion. The Hawking evaporation may become important again depending on a mass threshold. The evaporation of PBHs is quite modified at late times by these effects, but only if the generalized second law of thermodynamics is violated.