\"Theoretical physics is the effort to create mathematical models that describe phenomena in nature and to make predictions with these models that can be tested through experiment and observation. The standard model (SM) of particle physics and Einstein\'s theory of general...
\"Theoretical physics is the effort to create mathematical models that describe phenomena in nature and to make predictions with these models that can be tested through experiment and observation. The standard model (SM) of particle physics and Einstein\'s theory of general relativity (GR) are the two main pillars of modern day theoretical physics that provide us with a magnificent framework to understand much of what we see in the universe, from particle collisions to the expansion of the cosmos.
And yet, there are gaps in this exquisite picture and indications that something is not quite right or, at least, incomplete in our understanding of the world of physics. Galactic rotation curves, the accelerated expansion of the universe and precision measurements of the cosmic microwave background cannot be explained in terms of the visible matter. Either we accept the existence of an unknown form of \"\"dark matter\"\" and \"\"dark energy\"\", whose form we can not satisfactorily explain within the standard model of particle physics, or we are prepared to modify the laws of gravity beyond Einstein\'s relativity. These questions are deeply related to the nature of gravity and the quest for answers forms the core of our RISE project.
More specifically, the goals of our project can be summarized as follows. (1) What can we learn about the enigmatic dark matter from observing black holes? (2) Are black holes really the specific class of objects described by general relativity or is there yet another twist to them? (3) Can we directly observe the spacetime distortion created by black holes in the form of the shadows they cast? (4) How can we test whether Einstein\'s theory is also correct in the regime of extremely strong gravity? Do we need to generalize the theory? (5) Does our world have more than four dimensions which would explain the weakness of gravity?
From a practically minded viewpoint, one might wonder, of course, why we should pursue questions like this when immediate technical benefit is not obvious. History, however, thunders a warning against such a viewpoint: Fundamental research may at times be glacially slow in providing practical benefits, but in the end it always does and does so with the overwhelming power of a glacier. Quantum mechanics, for instance, forms the foundation for all modern electronics. Number theory, pursued as early as about 3000 years ago in antique Greece, became the foundation of modern day encryption in the 20th century. General relativity itself found its way into the multi-billion Euro business of global positioning. Furthermore, the fascination with astrophysics and the fundamental building blocks of our world has always attracted the next generation of researchers. Carrying across this fascination forms a second major goal of our project, besides the immediate research.\"
\"Before we go into more details on how we explore \"\"beyond SM+GR\"\" physics in our project, it is important to realize that such a situation is not new; we have been in it twice in the 19th century when astronomers observed anomalies in the orbits of Uranus and Mercury. The former found an explanation in the form of \"\"dark matter\"\": a new planet, Neptune, was found based on theoretical predictions derived from Uranus\' anomalies. Similarly, a planet \"\"Vulcan\"\" was conjectured to explain Mercury\'s orbital peculiarities, but Vulcan was never found. Instead, a new theory of gravity, namely Einstein\'s general relativity, provided the answer. Bearing in mind this lesson of history, we explore both possibilities, dark matter and modified gravity.
Dark matter: The particles of nature can be categorized into two families called bosons and fermions. Fermions include the electron and proton and make up most of the matter we experience in our daily lives, while bosons include the photon and mediate forces in physics. The currently most promising dark matter candidates are boson fields and as such do not obey the Pauli exclusion principle. In this project, we have identified a wide range of signatures through which dark matter candidates may be found or ruled out through electromagnetic and gravitational observations.
* Contrary to previous belief, boson fields accumulating around stars, do not trigger collape to a black hole, but settle down into breathing configurations.
* Binary systems composed of compact, self gravitating boson fields, so-called boson stars, emmit characteristic gravitational wave signals distinguishing them from black hole or neutron star binaries.
* Black holes act as gravitational lenses, creating a characteristic, self-similar lensed image of objects behind them. Image and shadow depend on the presence or absence of boson fields around the hole as well as the underlying theory of gravity.
* The presence of a boson field around astrophysical X-ray sources (black holes accreting ordinary matter) leads to a shift in the quasi-peridic oscillations of the X-ray signal which can be detected with future missions such as LOFT.
Modified gravity: Numerous modifications to Einstein\'s relativity have been suggested in past decades. Here, we study a wide range of theories with the goal of finding ways to observationally test them versus Einstein\'s theory.
* The quasi-periodic oscillations of X-ray sources also allow us to test for modified theories of gravity. We have studied how future observations will allow us to test so-called quadratic gravity theories in this way.
* The remnant black hole resulting from the merger of two compact objects is known to settle down through a ring-down with characteristic frequencies depending on the theory of gravity. We have calculated that the EU space mission LISA will be able to test the true nature of black holes even at early times of the universe.
* We have found a long-lived (years or centuries) gravitational wave pattern arising in massive scalar-tensory theory of gravity. By directing gravitational wave searches ar historic supernovae such as Keppler 1604, we can test these theories.
* Extra spatial dimensions may reveal themselves through black hole formation in particle collisions at energies well above the TeV. In such collisions, energy is lost through gravitational wave emission. We have calculated this loss in up to 10 spacetime dimensions for head-on collisions.
\"All the work described above, as well as in more detail in the technical report, represents extension beyond the state of knowledge available at the start of this project. Highlights include the following.
* We have performed the first fully nonlinear evolutions of superradiant instabilities.
* We have identified the endpoints of these evolutions: A black hole surrounded by a synchronized field.
* We assessed the possibility of doing \"\"gravitational spectroscopy\"\", i.e., to measure of multiple quasinormal mode frequencies from the remnant of a black hole mergers, using present and future gravitational-wave detectors.
* Our extraction method in higher dimensions is the first fully consistent method that accounts for the entire amount of gravitational radiation.
* We have demonstrated that rapidly rotating black holes in six spacetime dimensions lead to the formation of naked singularities -- pathological points in the spacetime not hidden inside an event horizon.
In future work, we will extend these studies to wider classes of binary systems containing black holes, neutron stars and boson stars with or without boson fields.\"