# Black hole physics and holography

Lead Research Organisation:
University of Southampton

Department Name: Sch of Mathematical Sciences

### Abstract

Paul Rodgers will develop research in the area of black hole physics and holographic correspondences.

There are two main lines of research:

1) Scalar fields in a charged or rotating Anti-de Sitter black hole background are afflicted by two kinds of instabilities, namely the superradiant and near-horizon scalar condensation instabilities. As a result, there are novel black hole solutions with scalar hair in these theories that have been found in the last years. It is well known that fermions cannot be superradiantly scattered in similar black hole backgrounds. This is closely connected and justified by the so-called Klein paradox. However, the very same argument that suggests the existence of the near-horizon instability for scalar fields also hold for fermions. This raises the possibility that fermions in AdS black holes can lead to an instability and, consequently, to novel black holes with fermion hair. Can this happen in charged and/or rotating backgrounds? These are some of the problem that will be addressed during this Ph.D.

2) Recent studies indicate that, at least in some de Sitter backgrounds, the strong cosmic censorship conjecture can be violated. More concretely, in four spacetime dimensions it can be violated in static de Sitter backgrounds but not in rotating black holes. How universal are these results, that is to say, what are the key ingredients that a background needs to have to preserve or violate this conjecture. For example, does the presence of rotation always preserve the conjecture? Is this a property of the Einstein theory exclusively in 4 dimensions or is it an intrinsic feature of the theory that holds in any dimension. During this PhD these questions will also be addressed.

To achieve these aims two main methods will be used: a) holographic dualities (aka gravity/gauge theory correspondences), and b) when necessary, numerical schemes to solve the coupled systems of Einstein's differential equations.

There are two main lines of research:

1) Scalar fields in a charged or rotating Anti-de Sitter black hole background are afflicted by two kinds of instabilities, namely the superradiant and near-horizon scalar condensation instabilities. As a result, there are novel black hole solutions with scalar hair in these theories that have been found in the last years. It is well known that fermions cannot be superradiantly scattered in similar black hole backgrounds. This is closely connected and justified by the so-called Klein paradox. However, the very same argument that suggests the existence of the near-horizon instability for scalar fields also hold for fermions. This raises the possibility that fermions in AdS black holes can lead to an instability and, consequently, to novel black holes with fermion hair. Can this happen in charged and/or rotating backgrounds? These are some of the problem that will be addressed during this Ph.D.

2) Recent studies indicate that, at least in some de Sitter backgrounds, the strong cosmic censorship conjecture can be violated. More concretely, in four spacetime dimensions it can be violated in static de Sitter backgrounds but not in rotating black holes. How universal are these results, that is to say, what are the key ingredients that a background needs to have to preserve or violate this conjecture. For example, does the presence of rotation always preserve the conjecture? Is this a property of the Einstein theory exclusively in 4 dimensions or is it an intrinsic feature of the theory that holds in any dimension. During this PhD these questions will also be addressed.

To achieve these aims two main methods will be used: a) holographic dualities (aka gravity/gauge theory correspondences), and b) when necessary, numerical schemes to solve the coupled systems of Einstein's differential equations.

## People |
## ORCID iD |

Oscar Joao Campos Dias (Primary Supervisor) | |

Paul Rodgers (Student) |

### Studentship Projects

Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|

EP/N509747/1 | 01/10/2016 | 30/09/2021 | |||

1949009 | Studentship | EP/N509747/1 | 28/09/2017 | 31/03/2021 | Paul Rodgers |

Description | So far I have published the following: https://arxiv.org/abs/1910.04181. There will be 2 more (at least) publications before receiving my PhD. All of my work concerns black hole instabilities and associated consequences. There is a famous theorem in General Relativity which roughly says that any fundamental fields (particles) near a black hole will decay around the black hole horizon and fall inside (to be turned into radiation). The black hole therefore should remain unaffected overall (the mathematical solution remains the same). However it is now known that in certain conditions, some fields (particles) can escape and extract energy from the black hole. If more energy is extracted from the black hole than enters it the black hole becomes unstable (i.e the mathematical solution breaks down and it evolves towards a new configuration). An everyday analogy would be the following: When heat is applied to ice, it becomes unstable and turns into water (and then steam if even more heat is applied). I am interested in looking at how and why black holes become unstable and what do these new states look like mathematically and physically. My PhD will discuss some of these issues in detail. |

Exploitation Route | All of my projects importantly answer the question which we set out to answer. However each result I have is very much a starting point for many different types of studies which fall in and out of my area of expertise. Natural and interesting questions arise from my results which other researchers may want to study in more detail. |

Sectors | Other |

URL | https://arxiv.org/abs/1910.04181 |