## Final Report Summary - QM-SING (Quantum Resolution of Gravitational Singularities)

String theory is a promising theory of elementary particles and fundamental interactions, unifying all known forces in a theory of “quantum gravity”. However, it is notoriously hard to extract testable predictions from it. Black holes are ubiquitous in string theory and therefore the study of black holes offers a shortcut towards successfully testing the validity of string theory. This projects pursued a theoretical test of string theory, through the study of black holes.

The classical theory of General Relativity (GR) describes the effects of gravity as effects on space and time. GR predicts black hole solutions, the very dense end states of gravitational collapse, whose existence has been confirmed by experiment. In GR, black holes are solutions with enigmatic properties, such as a singularity in the fabric of space and time. When coupling them to quantum mechanics, the physics of the subatomic world, there appear even more questions: the information paradox and black hole entropy.

In this project, we addressed these issues by studying black hole microstates. Black hole microstate geometries are smooth solutions of string theory that do not have a singularity, could explain black hole entropy and can help evade the information paradox. For supersymmetric black holes, which are extremely unrealistic, there has been quite some success in constructing these microstates, but not nearly enough to solve all black hole problems. We set out three objectives as a first step in the theoretical black hole test of string theory as a theory of quantum gravity:

(1) To construct new supersymmetric black hole microstates (which can be viewed as toy models), (2) To construct new non-supersymmetric black holes (which are more like realistic black holes),

(3) To initiate the impact on cosmological singularities through a training in cosmology.

To reach the first two objectives, the MC fellow worked with PhD students in Amsterdam and researchers abroad. Together they constructed new supersymmetric and non-supersymmetric solutions of the equations of supergravity, the limit in which string theory becomes a theory of gravity with particle excitations. To find the non-supersymmetric solutions, the fellow had to learn new mathematical techniques involving group theory. He also found how collapsing matter can form singularity-free microstate geometries rather than turning into a black hole, through a process known as quantum mechanical tunneling.

Before starting the third objective, the MC fellow received intensive training with world-leading cosmologists in Stanford University, to see how to apply black hole methods to the cosmological evolution of the entire universe. Our universe is currently expanding in an accelerating way. Understanding this acceleration is still not fully understood in string theory. The fellow took on the responsibility of supervising a PhD student in Amsterdam, and together with colleagues in Leuven University, Belgium, has worked out the consistency of the building blocks (called “anti-D3 branes”) that underlie accelerating cosmological solutions within string theory. With colleagues in Stanford and Oxford he has also constructed a new way of finding solutions of accelerating universes in string theory.

The main result with lasting impact is the link between the two sides of the grant (aims (1) and (2) no black holes as opposed to aim (3) relating to cosmology). Based on some of the fellow's earlier work, with the completion of the grant the fellow understood the mechanism that underlies microstate geometries and saw how that enters in the cosmological setting through a “Smarr relation”, a mathematical expression for the energy contained in spacetime. This allowed us to shed a new light on a very important ongoing debate on the consistency of using “anti-D3 branes” for cosmological spacetimes in string theory. The fellow worked with string theorists involved in two sides of the debate during the research project, and it seems that the debate is near consensus.

A corollary impact factor is an additional training in science communication. To learn more aboutdissemination to the general public, the MC researcher also entered FameLab, one of the world's largest competitions for science communication. In FameLab, researchers have to pitch their research in three minutes. Bert Vercnocke won the Dutch national finals and obtained a considerable amount of training in this field, assisted in several additional public events. These experiences will help him to be a great science communicator. Some of the research of ths Marie Curie project explained in three minutes is available at https://youtu.be/E1Id_yRPS2g.

The classical theory of General Relativity (GR) describes the effects of gravity as effects on space and time. GR predicts black hole solutions, the very dense end states of gravitational collapse, whose existence has been confirmed by experiment. In GR, black holes are solutions with enigmatic properties, such as a singularity in the fabric of space and time. When coupling them to quantum mechanics, the physics of the subatomic world, there appear even more questions: the information paradox and black hole entropy.

In this project, we addressed these issues by studying black hole microstates. Black hole microstate geometries are smooth solutions of string theory that do not have a singularity, could explain black hole entropy and can help evade the information paradox. For supersymmetric black holes, which are extremely unrealistic, there has been quite some success in constructing these microstates, but not nearly enough to solve all black hole problems. We set out three objectives as a first step in the theoretical black hole test of string theory as a theory of quantum gravity:

(1) To construct new supersymmetric black hole microstates (which can be viewed as toy models), (2) To construct new non-supersymmetric black holes (which are more like realistic black holes),

(3) To initiate the impact on cosmological singularities through a training in cosmology.

To reach the first two objectives, the MC fellow worked with PhD students in Amsterdam and researchers abroad. Together they constructed new supersymmetric and non-supersymmetric solutions of the equations of supergravity, the limit in which string theory becomes a theory of gravity with particle excitations. To find the non-supersymmetric solutions, the fellow had to learn new mathematical techniques involving group theory. He also found how collapsing matter can form singularity-free microstate geometries rather than turning into a black hole, through a process known as quantum mechanical tunneling.

Before starting the third objective, the MC fellow received intensive training with world-leading cosmologists in Stanford University, to see how to apply black hole methods to the cosmological evolution of the entire universe. Our universe is currently expanding in an accelerating way. Understanding this acceleration is still not fully understood in string theory. The fellow took on the responsibility of supervising a PhD student in Amsterdam, and together with colleagues in Leuven University, Belgium, has worked out the consistency of the building blocks (called “anti-D3 branes”) that underlie accelerating cosmological solutions within string theory. With colleagues in Stanford and Oxford he has also constructed a new way of finding solutions of accelerating universes in string theory.

The main result with lasting impact is the link between the two sides of the grant (aims (1) and (2) no black holes as opposed to aim (3) relating to cosmology). Based on some of the fellow's earlier work, with the completion of the grant the fellow understood the mechanism that underlies microstate geometries and saw how that enters in the cosmological setting through a “Smarr relation”, a mathematical expression for the energy contained in spacetime. This allowed us to shed a new light on a very important ongoing debate on the consistency of using “anti-D3 branes” for cosmological spacetimes in string theory. The fellow worked with string theorists involved in two sides of the debate during the research project, and it seems that the debate is near consensus.

A corollary impact factor is an additional training in science communication. To learn more aboutdissemination to the general public, the MC researcher also entered FameLab, one of the world's largest competitions for science communication. In FameLab, researchers have to pitch their research in three minutes. Bert Vercnocke won the Dutch national finals and obtained a considerable amount of training in this field, assisted in several additional public events. These experiences will help him to be a great science communicator. Some of the research of ths Marie Curie project explained in three minutes is available at https://youtu.be/E1Id_yRPS2g.