Nonlinear and out-of equilibrium Holography and Black Holes

This proposal is divided in 2 research topics. Topic I develops in-depth a project proposed in my original ER grant. The fact that there are now 3-dimensional numerical schemes (required to achieve the aims in the gravitational sector) justifies that I request the computer & human resources to enhance/develop this program (w.r.t. the original ER proposal that aimed the scalar sector). Topic II is not a project of my original ER grant. However, it extends the original holographic studies in a direction whose timeliness, scientific relevance and expected impact is justified.

I. Black holes with a single isometry. Superradiant physics and its endpoint


Superradiance is the process whereby a wave is amplified when it scatters a black hole (BH) and, in an anti-de Sitter (AdS) background, it leads to an instability. The time evolution, endpoint and novel phases associated with this phenomenon are largely unknown. This project aims to:
1) Construct nonlinearly charged hairy BH and solitonic solutions that are associated with the zero-mode of the scalar superradiant instability in the charged Reissner-Nordström-AdS BH. Consequently, complete the phase diagram of static solutions of the d=4 Einstein-AdS theory.
2) Find the time evolution & endpoint of scalar superradiance.
3) Construct nonlinearly the single isometry BHs that, in a phase diagram, bifurcate from the Kerr-AdS BH family at the onset curve of the rotating gravitational superradiant instability (we have perturbative evidence for the existence of these BHs). Such BHs will challenge the current BH paradigm: they will prove that, against current assumptions, the Kerr-AdS BH is not the only stationary BH of Einstein-AdS theory.
4) Find the time evolution & endpoint of rotating gravitational superradiance. This is one the most important open questions of gravitational physics.
5) In the context of the gauge/gravity duality, find the dual interpretation of the superradiant instability. Find also the dual interpretation of the novel hairy and single Killing field phases.

II. Holographic heavy ion collisions. Out-of-equilibrium holography


In the context of holographic gauge/gravity dualities, Einstein's equation encodes hydrodynamic near-equilibrium physics but also the far-from-equilibrium dynamics. Consequently, it can be used to model the far-from-equilibrium dynamics of heavy ion collisions that form the strongly coupled quark gluon plasma (sQGP) at LHC-CERN. The broad objective is to develop the available holographic studies on this subject to compute the dynamics of models that mimic more accurately the experiments at CERN, namely:
1) Collide 2 gravitational shock waves (SWs) with non-vanishing impact parameter. This will model holographically the peripheral collisions and elliptic flow observed at RHIC and LHC. That is, when the collision is not head-on, the two disks intercept in an elliptic-shapped area. A plasma formed with this shape in vacuum will necessarily expand at different rates along the 2 axis of the ellipse.
2) Study non-head-on collisions with different initial radial profiles for the SWs and find how they affect the thermalization properties and the sQGP profile.
3) Collide two SWs with asymmetric properties (to model the collision of two beams of different ions that will be studied at RHIC). This will allow to identify the intrinsic sQGP properties that are independent of the initial conditions and how the system reacts to different initial anisotropies.
4) RHIC/LHC experiments reveal the presence of interesting phenomena in the sGQP like jet quenching, conical SW flow and turbulence (sQGP has low viscosity). Search for signatures of these in the above holographic simulations.

A byproduct aim of this proposal is to communicate with other scientific communities where numerical schemes are more mature in order develop and optimise numerical methods required to solve non-linear and out-of-equilibrium holographic and BH problems

- Training of highly skilled people that has potential for economic & societal impact:

I have been collaborating (with a total of 8 publications) and guiding the career development of 6 PhD students, namely:
M. Stein (PhD @ Cambridge w/ M. Perry),
R. Monteiro (PhD @ Cambridge w/ S. Hawking; now at Oxford),
J. Santos (PhD @ Cambridge w/ M. Perry; now at Stanford & Cambridge),
A. Macarrone (PhD @ Barcelona w/ R. Emparan; now editor of a scientific dissemination magazine),
J. Hovbedo (PhD @ PI w/ R. Myers; now researcher in a biotechnology company)
N. Santos (PhD @ IST, Lisbon w/ J. Lemos; now works in a financial company).

I request funds to hire a PhD & a young post-doc. Given my proven successful experience training students, and the nature of my proposed scientific projects, it is natural to expect that they will significantly contribute to the training of highly skilled researchers. Young researchers with these skills are currently in high demand in science. But even if these researchers decide to leave the academy, all official reports indicate that such skills are highly rated by the technological, management and financial markets. Evidence of this can also be found in the above list of PhD students. There is thus overwhelming evidence that the outcome of my proposal has great potential for high economic and societal impact in the mid term.

- Communications & Engagement. Outreach. Improving teaching & learning

Following my past experience and involvement on events targeting the dissemination of science to society, I plan to participate actively in a series of activities intended to raise awareness of and enthusiasm about science. As a concrete example that proves my commitment to these outreach activities, I mention that as this proposal is being written, COST, HoloGrav and Gatis - European funded scientific networks that involve several Universities (including Southampton) - organized their Summer School for PhD students/post-docs (12-18 July 2014):
http://faraday.fc.up.pt/cfp-pages/School/program.html

This School included a Public Outreach lecture for a general audience that I have been invited to present. I discussed black holes, holography, hydrodynamics and turbulence that are all related by the holographic correspondence. This attracted the attention of a very generalised audience that included several engineers (especially mechanical engineers) and even an economist & a psychologist, as I found out from the interactions I had with the audience during the discussion section and coffee break.

Southampton recently created a new center - the Southampton Theory Astronomy Gravity (STAG) center - which will promote research in the areas of Physics, Astronomy & Mathematics. One of its missions is to divulge science to the wider public and it will promote a series of regular "Public Lectures", some by distinguished scientists. I will participate actively on the organisation of these events and I will give some lectures. Indicative of the impact of this initiative, next October the Physics Nobel Laureate Gerard 't Hooft will give a Public lecture in Southampton:
http://www.southampton.ac.uk/stag/outreach/index.page?

- Exploitation & Application

One of my scientific projects is to holographically simulate the heavy ion collisions at the Large hadron Collider at CERN. The expectation is that these studies might provide a theoretical framework to help understanding the outcome of CERN experiments. This would contribute significantly to justify the large investment done on the LHC construction. Evidence for the importance and timeliness of this programme is given by the fact that CERN is organizing a workshop on Numerical Holography and holographic collisions ( https://indico.cern.ch/event/309107/ ) next December to boost the commitment and collaborations of the community to this endeavour. This proposal is an opportunity for the UK to be at the frontline of this international programme.