Nonlinear and out-of-equilibrium Holography and Black Holes
Lead Research Organisation:
University of Southampton
Department Name: Sch of Mathematical Sciences
Abstract
Black hole (BH) thermodynamics and Hawking quantum radiation suggest the existence of a statistical or microscopic description of BHs behind the scenes. This description necessarily requires quantum gravity. BHs have an entropy (a quantity that measures the disorder of the system) proportional not to its volume (as usual in other systems) but instead to its horizon's area. This suggests that the quantum information of the BH is distributed over a surface rather than on a volume. This motivates the holographic principle according to which quantum gravity in a given volume should have a dual equivalent description in terms of a quantum field theory (QFT) on its boundary surface.
The gravity/gauge theory or holographic dualities (correspondences or maps) are a concrete realization of this holographic principle. Take (quantum) gravity on an anti-de Sitter (AdS) universe. An AdS background has a gravitational barrier that reflects back any object: effectively, gravity is confined inside a box. The idea behind the holographic principle is that the information inside the "AdS box", where we have typically a BH, is projected (as a hologram) into the boundary wall. There, the same information is encoded in a QFT (ie, gauge theory). So we can write the same information in two different scientific languages (the gravitational and the QFT). It is fundamental to develop the dictionary between these two languages to understand phenomena in one theory that involves hard computations by reformulating it on the dual language where computations can be easier. This proposal will develop this dictionary to understand properties of BHs and QFTs (of the kind that describe the strong nuclear interactions being studied at the Large Hadron Collider - LHC - at CERN).
As can be inferred from the description above, BHs play an essential role in these holographic correspondences. On the gravity side of the duality, BHs are the most extreme gravitational objects. On the other hand, because they have Hawking temperature, on the QFT side they are the heating source that excites the system up to the point where energetic phenomena appears. In particular, BHs do exhibit other phenomena related to the emission of radiation (and that is actually typically entangled with Hawking radiation). This is known as superradiance. This is a process whereby a electromagnetic or gravitational wave scatters a BH and gets amplified because it extracts energy and spin from the BH. In addition, if the BH is confined inside the AdS box, the previously amplified radiation will be reflected back to the BH where it gets further amplified. These multiple amplifications/reflections lead to an instability. Remarkably, we still do not know much about how such a BH with radiation orbiting around it will evolve in time and what is the endpoint of this unstable system. This proposal proposes to fill this gap in our knowledge and aims to find the answer to these open questions.
LHC at CERN is colliding two beams of heavy ion collisions and observing the byproducts of this violent crash. Within the holographic correspondence, this process maps to the collision of two gravitational shock waves (ie two disks or beams of gravitational energy) that is described by Einstein's equations. This proposal will thus use Einstein's equations to simulate these collisions using the aforementioned dual scientific language. In particular, these gravitational numerical simulations will allow to follow the time evolution of the system after the collision and study how the system evolves towards its final state where it equilibrates and cools down. This might be particularly useful to help interpret what is happening at LHC because the standard technical tools that the QFT scientists at LHC have (and that are extremely successful in other contexts where the quantum system is at equilibrium) are not applicable in such violent out-of-equilibrium stages that occur during and after a collision.
The gravity/gauge theory or holographic dualities (correspondences or maps) are a concrete realization of this holographic principle. Take (quantum) gravity on an anti-de Sitter (AdS) universe. An AdS background has a gravitational barrier that reflects back any object: effectively, gravity is confined inside a box. The idea behind the holographic principle is that the information inside the "AdS box", where we have typically a BH, is projected (as a hologram) into the boundary wall. There, the same information is encoded in a QFT (ie, gauge theory). So we can write the same information in two different scientific languages (the gravitational and the QFT). It is fundamental to develop the dictionary between these two languages to understand phenomena in one theory that involves hard computations by reformulating it on the dual language where computations can be easier. This proposal will develop this dictionary to understand properties of BHs and QFTs (of the kind that describe the strong nuclear interactions being studied at the Large Hadron Collider - LHC - at CERN).
As can be inferred from the description above, BHs play an essential role in these holographic correspondences. On the gravity side of the duality, BHs are the most extreme gravitational objects. On the other hand, because they have Hawking temperature, on the QFT side they are the heating source that excites the system up to the point where energetic phenomena appears. In particular, BHs do exhibit other phenomena related to the emission of radiation (and that is actually typically entangled with Hawking radiation). This is known as superradiance. This is a process whereby a electromagnetic or gravitational wave scatters a BH and gets amplified because it extracts energy and spin from the BH. In addition, if the BH is confined inside the AdS box, the previously amplified radiation will be reflected back to the BH where it gets further amplified. These multiple amplifications/reflections lead to an instability. Remarkably, we still do not know much about how such a BH with radiation orbiting around it will evolve in time and what is the endpoint of this unstable system. This proposal proposes to fill this gap in our knowledge and aims to find the answer to these open questions.
LHC at CERN is colliding two beams of heavy ion collisions and observing the byproducts of this violent crash. Within the holographic correspondence, this process maps to the collision of two gravitational shock waves (ie two disks or beams of gravitational energy) that is described by Einstein's equations. This proposal will thus use Einstein's equations to simulate these collisions using the aforementioned dual scientific language. In particular, these gravitational numerical simulations will allow to follow the time evolution of the system after the collision and study how the system evolves towards its final state where it equilibrates and cools down. This might be particularly useful to help interpret what is happening at LHC because the standard technical tools that the QFT scientists at LHC have (and that are extremely successful in other contexts where the quantum system is at equilibrium) are not applicable in such violent out-of-equilibrium stages that occur during and after a collision.
Planned Impact
- 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.
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.
Organisations
People |
ORCID iD |
| Oscar Joao Campos Dias (Principal Investigator) |
Publications
Bea Y
(2021)
Crossing a large-N phase transition at finite volume
Bea Y
(2021)
Crossing a large-N phase transition at finite volume
in Journal of High Energy Physics
Bena I
(2019)
Holographic dual of hot Polchinski-Strassler quark-gluon plasma
in Journal of High Energy Physics
Betzios P
(2019)
Euclidean wormholes and holography
in Journal of High Energy Physics
Betzios P
(2018)
Antipodal correlation on the meron wormhole and a bang-crunch universe
in Physical Review D
Cardoso V
(2018)
Constraining the mass of dark photons and axion-like particles through black-hole superradiance
in Journal of Cosmology and Astroparticle Physics
Cayuso R
(2020)
Massive vector fields in Kerr-Newman and Kerr-Sen black hole spacetimes
in Journal of High Energy Physics
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| ST/M004147/1 | 01/04/2015 | 30/09/2018 | |||
| 1657264 | Studentship | ST/M004147/1 | 01/10/2015 | 30/09/2018 | Ramon Masachs Gonzalez |
| Description | It was widely accepted that if a gravitational system is linearly stable, it ought to be also non-linearly stable. My recent papers (the last one this year) on the nonlinear instability of the Anti-de Sitter space (AdS; the simplest solution of Einstein's gravity with negative curvature that is linearly stable) proved this expectation wrong. Remarkably, this nonlinear instability further shows that turbulence occurs in a gravitational system. The older two papers of this series were selected by the Editors of Classical and Quantum Gravity to be among the journal's Highlights. One of the most prominent open questions in Einstein's General Relativity is to find the properties, endpoint and novel BH solutions of the superradiant instability. (Superradiance is wave analogue of the Penrose process whereby energy and angular momentum is extracted from a black hole). We have found novel black hole solutions with a single isometry that are associated with the onset of the superradiant instability. Their existence was surprising since it was widely believed that they were ruled-out by the famous Hawking's rigidity theorem 1). However, we have shown that an assumption of this theorem can be evaded. We also have shown that 'No hair' theorems 2) formulated for asymptotically flat cannot be extended to anti-de Sitter (AdS) backgrounds. In addition, we gave overwhelming evidence to conjecture that Cosmic censorship is violated in the evolution of these systems. With Ramon Masachs (a PhD student funded by this grant), we have three publications were we describe the superradiant instability and associated black holes of charged systems. Recently, we have also studied how the superradiant instability can help us putting astrophysical bounds on the mass of certain fields that might exist in our Universe. In the context of the gauge/gravity correspondence, in a paper published in Physical Review Letters, we have numerically constructed asymptotically global AdS5 × S5 black holes that are localised on the S5. These are solutions to type IIB supergravity with S8 horizon topology that dominate the theory in the microcanonical ensemble at small energies. At higher energies, there is a first-order phase transition to AdS5-Schwarzschild×S5. By the AdS/CFT correspondence, this transition is dual to spontaneously breaking the SO(6) R-symmetry of N = 4 super Yang-Mills down to SO(5). We pinpointed the location of this phase transition and computed the expectation value of the resulting scalar operators in the low energy phase Still in the context of the gauge/gravity correspondence, at low energies or temperatures, maximally supersymmetric Yang-Mills theory on R(t) × S1 with large N gauge group SU(N) and strong t'Hooft coupling is conjectured to be dual to the low energy dynamics of a collection of D0-branes on a circle. We constructed thermal states in the gravitational side of the correspondence where we find a first-order phase transition between states that are uniform on the S1 and states that are localised on it. When compared with lattice computations that are now available, these critical values provide the first instance where a first-order phase transition is tested on both sides of gauge/gravity duality. In the last years we also have pathbreaking contributions in the fields of differential equations and numerical solvers of Einstein's PDEs. Indeed, we have been involved in a long-term program to understand reformulations of Einstein's equation as a manifestly elliptic system of PDEs (for symmetric ansätz) and developing numerical schemes to solve the (non-)linear systems of coupled PDEs of Einstein's gravity. Accordingly, we were invited to write a Topical Review for Classical and Quantum Gravity entitled `Numerical Methods for Finding Stationary Gravitational Solutions' with the state-of-the-art technical tools. As an illustrative sharp example, to construct the BHs with a single isometry aforementioned we had to solve a coupled system of ten (10) non-linear 2nd order PDEs that depend on three (3) variables. |
| Exploitation Route | My research is on theoretical physics and mainly on black holes. Therefore it does not have an immediate direct impact on technological and economical applications. However, our findings include novel research directions that can be used by other researchers and the development of analytical and numerical tools that will be used by the scientific community. For example we recently published an invited Topical Review with state-of-the-art numerical techniques to solve Einstein's equations. I expect this review to be a reference for the scientific community. |
| Sectors | Education,Other |
| Description | Outreach activity: Royal Society Summer Exhibit in London 3-9 July 2017 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Public/other audiences |
| Results and Impact | The Gravitational group of Mathematical School of university of Southampton is part of a consortium that provides a gravitational-wave exhibit during the Royal Society Summer Exhibit in London 3-9 July, 2017. This takes place at the Royal Society and attracts many thousand visitors. |
| Year(s) Of Engagement Activity | 2017 |
| Description | Science Day, Outreach activity, University of Southampton, 18 March 2017 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Public/other audiences |
| Results and Impact | "Black holes - Einstein's enigma", Science Day, Outreach activity (posters and personal interaction/discussions), University of Southampton, 18 March 2017 |
| Year(s) Of Engagement Activity | 2017 |
| Description | Winchester Science Festival |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Public/other audiences |
| Results and Impact | "Winchester Science Festival", 12-13 May 2018, Winchester Science Centre, Winchester, UK. Member of the team responsible for the organization and presentation of one of the 10 invited hands-on exhibitions: "Playing with Maths". Target Public: general young public (mainly kids with their parents). |
| Year(s) Of Engagement Activity | 2018 |