1) Quantum fields in curved space and black hole evaporation

2) Acoustic black holes

3) Black holes and cosmology in braneworlds

1) One of the most atonishing results of last century

theoretical physics is with no doubts the prediction

made by Hawking that black holes are not completely

black but radiate thermally. This surprising result has

been derived by Hawking using the framework of quantum

field theory in curved spacetimes, where matter fields

are quantized with the use of standard quantum field

theory methods whereas gravity is treated classically

according to Einstein General Relativity theory.

A detailed and pedagogical presentation of the Hawking effect

and its physical implications, as well as a discussion on backreaction

effects in black hole spacetimes has been presented in the

book "Modeling black hole evaporation", published by Imperial College

Press/World Scientific in January 2005.

We have determined the leading order quantum correction

to the Schwarzschild metric and to the Newtonian potential via a

numerical calculation of the stress energy tensor for conformal fields

in a zero temperature (Boulware) vacuum state. The results are in

agreement with those obtained in the weak-field approximation using

Feynman diagrams.

Finally, we have shown that the regularity conditions for the stress tensor

in the extreme Reissner-Nordstrom black hole are fulfilled irrespective

of the type of collapse and of the model used.

2) In 1981 a remarkable paper by Unruh showed that a quantum

emission similar to the one predicted by Hawking for black

holes is expected in a seemingly completely different

context, namely fluids undergoing hypersonic motion. This

far reaching result opened a continuously developing field

of research (the so called black hole analogue models) in

condensed matter physics where, unlike gravity, the hope to

perform experimental tests on these theoretical predictions

does not seem so remote.

In this context we have studied for the first time, using

theoretical methods borrowed from quantum field theory in

curved spacetimes, the backreaction this emitted radiation

has on the fluid. In particular we have shown that the quantum

effects slow down the fluid and that, in analogy with the evaporation

of charged black holes, the temperature of the emitted phonons

decreases.

3) A new scenario where one can in principle attack the

backreaction problem in black hole spacetimes concerns the use

of the Randall-Sundrum (RS) braneworlds, where our

universe is seen as a hypersurface (the brane) immersed in

five dimensional anti-de Sitter spacetime (the bulk),

and of Maldacena's AdS/CFT correspondence. In this context

we have verified that the classical bulk computation concerning

the correction to the newtonian potential on the brane is in agreement

with the semiclassical one described above (see point 1).

Aside from this, we have also studied brane cosmological solutions

resulting from anisotropic bulk configurations.

Research Program:

For the future we intend to perform the following investigations:

- Search for analytical approximations of the stress energy tensor

in Boulware state in Schwarzschild spacetime to match the results

found numerically.

- Numerical study of vacuum polarization in static black holes;

- Numerical and analytical studies of analog models of black holes,

in particular those constructed from Bose-Einstein condensates;

- Numerical and analytical studies of classical bulk solutions in RS

models corresponding to time dependent (gravitational collapse)

configurations in the brane and connection to black hole evaporation.