## Final Report Summary - NRHEP (Numerical Relativity and High Energy Physics)

In his 1923 book “The Mathematical theory of Relativity”, Arthur Eddington wrote: “The problem of two bodies on Einstein’s theory remains an outstanding challenge to mathematicians like the problem of three bodies in Newton’s theory.”

Eddington's statement was visionary. It took over 80 years to obtain first solution of the two bodies problem in General Relativity - i.e. two bodies orbiting one another - could be completely solved. In 2005, after a struggle of four decades, it was possible to solve all stages of the simplest two bodies problem in General Relativity: two black holes orbiting one another, releasing energy into gravitational waves and finally coallescing. In solving this problem, a powerful computational infrustructure and numerical codes were developed. It was soon realised these tools could be used to tackle other strong gravity systems, namely those motivated by High Energy Physics. Exploring numerical relativity techniques, both within the traditional astrophysics arena but also in new settings, was the main motivation of this IRSES "Numerical Relativity and High Energy Physics (NRHEP)" network.

The network explored scientific synergies between the partners, including different technical expertises and backgrounds, and built up on already existing collaborations to create new, stronger and more inclusive ones, reaching the wider scientific community. During the network's lifetime, five main (global) meetings were organized which included scientists outside the network and originated review papers or books of proceedings to reach a wider audience. We point out four examples - three of which are truly community efforts - that will form, we believe, a long lived legacy of the network: 1) the "NRHEP:road map for the future" paper (Class.Quant.Grav. 29 (2012) 244001), grown from the effort to create this network, edited by the coordinators of the four European nodes and counting with contributions of 28 other world leading scientists in this field; 2) the write up of the "NRHEP spring school", organized within the network, which gave birth to the special volume (Int.J.Mod.Phys. A28 (2013) 22-23) where 8 young promising scientists wrote up lectures on different aspects of this scientific area; 3) the "Testing General Relativity with Present and Future Astrophysical Observations" paper (Class.Quant.Grav. 32 (2015) 243001), a reference review in this scientific area that emerged from another global meeting of the network and that includes the contributions of 53 world leading scientists in this field, including the node coordinators of this network; and 4) the "Exploring New Physics Frontiers Through Numerical Relativity" review paper, authored by the coordinators of the four European nodes, that appeared in the prestigious, invitation only, Living Reviews in Relativity journal (Living Rev. Relativity 18 (2015) 1) which summarizes the state of the art in precisely the network's topic. As a final memory, we are preparing a special volume of the International Journal of Modern Physics D, that will appear in 2016, with a review paper on the recent developments on NRHEP and in particular the contributions of this network, co-authored by the coordinators of the 6 European nodes and with 29 other contributed papers from scientists that participated in the last global meeting of the network that took place in September-October 2015.

Concerning the scientific work itself, the network produced over one hundred scientific papers published in top international journals with refereeing, including eleven papers published in the prestigious Physical Review Letters. We highlight the following scientific results: we have

- produced some of the best phenomenological values in D dimensions for the energy radiated - into gravitational radiation - in the collision of two point like particles at the speed of light, of relevance for TeV gravity scenarios, being tested at the LHC (Phys.Rev.Lett. 108 (2012) 181102);

- used an instability mechanism of astrophysical black holes to set bounds on the photon mass competitive with particle physics bounds (Phys.Rev.Lett. 109 (2012) 131102);

- provided some of the most compelling evidence for the idea that "matter does not matter" in very high energy collisions (Phys.Rev.Lett. 111 (2013) 041101);

- solved a long standing problem of computing perturbations of the Kerr-Newman black hole (Phys.Rev.Lett. 110 (2013) 241103);

- uncovered two mechanisms that can make Kerr black holes unstable in a class of alternative theories of gravity (Phys.Rev.Lett. 111 (2013) 111101);

- found a new type of rotating black holes, with potential astrophysical relevance, that circumvented long standing "no-hair" theorems and an established belief that GR with simple, physical, matter sources only admitted Kerr-like black holes as solutions (Phys.Rev.Lett. 112 (2014) 221101). These new black holes, moreover can have very different phenomenological properties, as shown, for instance, for their shadows (Phys.Rev.Lett. 115 (2015) 21, 211102);

- showed that particle collisions in the vicinity of rapidly rotating black holes can produce high-energy ejecta and hints at the tantalizing possibility that the collisional Penrose process may power gamma rays and ultra-high-energy cosmic rays (Phys.Rev.Lett. 114 (2015) 25, 251103);

- provided further insight into the evolution of black hole spins in black hole binary inspirals and discuss potential gravitational wave signatures (Phys.Rev.Lett. 114 (2015) 8, 081103; Phys.Rev.Lett. 115 (2015) 141102);

- showed that dark matter can pile up in stars and lead to much more stable configurations than previously thought (Phys.Rev.Lett. 115 (2015) 11, 111301).

These and other results caught the attention of the international community which led to various distinctions, such as: two papers got honorable mentions in the 2014 and 2015 Gravity Research Foundation essay competition; four papers chosen as IOPSelects or in CQG+; one paper in the CQG highlights 2012-13 and one (PRL) paper got chosen for Physics Synopsis.

Finally, one of the achievements of this network was the training and involvment of young scientists that were given the opportunity to know other institutions and interact with senior scientists from all over the world. Five satelite meetings of this network, four of which organized in Brazil and one in Portugal played a key role in promoting this interaction as well as one school organized in Lisbon in 2013.

Eddington's statement was visionary. It took over 80 years to obtain first solution of the two bodies problem in General Relativity - i.e. two bodies orbiting one another - could be completely solved. In 2005, after a struggle of four decades, it was possible to solve all stages of the simplest two bodies problem in General Relativity: two black holes orbiting one another, releasing energy into gravitational waves and finally coallescing. In solving this problem, a powerful computational infrustructure and numerical codes were developed. It was soon realised these tools could be used to tackle other strong gravity systems, namely those motivated by High Energy Physics. Exploring numerical relativity techniques, both within the traditional astrophysics arena but also in new settings, was the main motivation of this IRSES "Numerical Relativity and High Energy Physics (NRHEP)" network.

The network explored scientific synergies between the partners, including different technical expertises and backgrounds, and built up on already existing collaborations to create new, stronger and more inclusive ones, reaching the wider scientific community. During the network's lifetime, five main (global) meetings were organized which included scientists outside the network and originated review papers or books of proceedings to reach a wider audience. We point out four examples - three of which are truly community efforts - that will form, we believe, a long lived legacy of the network: 1) the "NRHEP:road map for the future" paper (Class.Quant.Grav. 29 (2012) 244001), grown from the effort to create this network, edited by the coordinators of the four European nodes and counting with contributions of 28 other world leading scientists in this field; 2) the write up of the "NRHEP spring school", organized within the network, which gave birth to the special volume (Int.J.Mod.Phys. A28 (2013) 22-23) where 8 young promising scientists wrote up lectures on different aspects of this scientific area; 3) the "Testing General Relativity with Present and Future Astrophysical Observations" paper (Class.Quant.Grav. 32 (2015) 243001), a reference review in this scientific area that emerged from another global meeting of the network and that includes the contributions of 53 world leading scientists in this field, including the node coordinators of this network; and 4) the "Exploring New Physics Frontiers Through Numerical Relativity" review paper, authored by the coordinators of the four European nodes, that appeared in the prestigious, invitation only, Living Reviews in Relativity journal (Living Rev. Relativity 18 (2015) 1) which summarizes the state of the art in precisely the network's topic. As a final memory, we are preparing a special volume of the International Journal of Modern Physics D, that will appear in 2016, with a review paper on the recent developments on NRHEP and in particular the contributions of this network, co-authored by the coordinators of the 6 European nodes and with 29 other contributed papers from scientists that participated in the last global meeting of the network that took place in September-October 2015.

Concerning the scientific work itself, the network produced over one hundred scientific papers published in top international journals with refereeing, including eleven papers published in the prestigious Physical Review Letters. We highlight the following scientific results: we have

- produced some of the best phenomenological values in D dimensions for the energy radiated - into gravitational radiation - in the collision of two point like particles at the speed of light, of relevance for TeV gravity scenarios, being tested at the LHC (Phys.Rev.Lett. 108 (2012) 181102);

- used an instability mechanism of astrophysical black holes to set bounds on the photon mass competitive with particle physics bounds (Phys.Rev.Lett. 109 (2012) 131102);

- provided some of the most compelling evidence for the idea that "matter does not matter" in very high energy collisions (Phys.Rev.Lett. 111 (2013) 041101);

- solved a long standing problem of computing perturbations of the Kerr-Newman black hole (Phys.Rev.Lett. 110 (2013) 241103);

- uncovered two mechanisms that can make Kerr black holes unstable in a class of alternative theories of gravity (Phys.Rev.Lett. 111 (2013) 111101);

- found a new type of rotating black holes, with potential astrophysical relevance, that circumvented long standing "no-hair" theorems and an established belief that GR with simple, physical, matter sources only admitted Kerr-like black holes as solutions (Phys.Rev.Lett. 112 (2014) 221101). These new black holes, moreover can have very different phenomenological properties, as shown, for instance, for their shadows (Phys.Rev.Lett. 115 (2015) 21, 211102);

- showed that particle collisions in the vicinity of rapidly rotating black holes can produce high-energy ejecta and hints at the tantalizing possibility that the collisional Penrose process may power gamma rays and ultra-high-energy cosmic rays (Phys.Rev.Lett. 114 (2015) 25, 251103);

- provided further insight into the evolution of black hole spins in black hole binary inspirals and discuss potential gravitational wave signatures (Phys.Rev.Lett. 114 (2015) 8, 081103; Phys.Rev.Lett. 115 (2015) 141102);

- showed that dark matter can pile up in stars and lead to much more stable configurations than previously thought (Phys.Rev.Lett. 115 (2015) 11, 111301).

These and other results caught the attention of the international community which led to various distinctions, such as: two papers got honorable mentions in the 2014 and 2015 Gravity Research Foundation essay competition; four papers chosen as IOPSelects or in CQG+; one paper in the CQG highlights 2012-13 and one (PRL) paper got chosen for Physics Synopsis.

Finally, one of the achievements of this network was the training and involvment of young scientists that were given the opportunity to know other institutions and interact with senior scientists from all over the world. Five satelite meetings of this network, four of which organized in Brazil and one in Portugal played a key role in promoting this interaction as well as one school organized in Lisbon in 2013.