by Sebastian Völkel and Kostas Kokkotas
Could you distinguish the sound of a wormhole from an ultra compact star or black hole?
Such an exotic, though quite fundamental question, could be asked to any physicist after the groundbreaking and Nobel Prize winning discoveries of gravitational waves from merging black holes and neutron stars. Gravitational waves provide mankind with a novel sense, the ability to hear the universe. This analogy, between sound waves and gravitational waves, will bring to the minds of many physicists Mark Kac’s famous question: “Can One hear the Shape of a Drum?” , and not just to the drummers amongst us. The possibility of this analogy is one of the ways in which gravitational waves are very distinct from the usual tool of astronomy, light.
To answer the question for our exotic instruments, we will rephrase it in a more technical form. In the simplest version one can describe linear perturbations of spherically symmetric and non-rotating models of wormholes and ultra compact stars. It is well known that the perturbation equations for these cases can simplify to the study of the one-dimensional wave equation with an effective potential. The solutions, which are usually given as a set of modes, represent the characteristic sound of the object. The so-called quasi-normal mode (QNM) spectrum is the starting point for our discussion.
FIG. 1. Sebastian Völkel (right) is a PhD student in the Theoretical Astrophysics group of Professor Kostas Kokkotas at the University of Tübingen, located in the south of Germany. Among his research interests is the study of compact objects along with the associated gravitational wave emissions. More information about his research can be found here.
Professor Kostas Kokkotas (left) is leading the group of Theoretical Astrophysics at the University of Tübingen. The focus of his research is on the dynamics of compact objects (neutron stars & black-holes) as sources of gravitational waves in general relativity and in alternative theories of gravity. More information about the group can be found here.
Photo by Severin Frank.
According to Einstein’s theory of general relativity (GR), black holes are ferocious beasts able to swallow and destroy everything within their reach. Their strong gravitational pull deforms the space-time causal structure in such a way that nothing can get out of them once their event horizon is crossed. The fate of those incautious observers curious enough to cross this border is to suffer a painful spaghettification process due to the strong tidal forces before being destroyed at the center of the black hole.
For a theoretical physicist, the suffering of observers is admissible (one might even consider it part of an experimentalist’s job) but their total destruction is not. The destruction of observers (and light signals) is determined by the fact that the affine parameter of their word-line (its geodesic) stops at the center of the black hole. Their clocks no longer tick and, therefore, there is no way for them to exchange or acquire new information. This implies the breakdown of the predictability of the laws of physics because physical measurements are no longer possible at that point. For this reason, when a space-time has incomplete geodesics — word-lines whose affine parameter does not cover the whole real line — we say that it is singular.
In order to overcome the conceptual problems raised by singularities, a careful analysis of what causes the destruction of observers is necessary. Our intuition may get satisfied by blaming the enormous tidal forces near the center, but the problem is much subtler. This is precisely what we explore in our paper. Continue reading
Sebastian Fischetti (left) is a graduate student of Professor Don Marolf (middle) at UCSB. Aron Wall (right) is a member of the School of Natural Sciences at the Institute for Advanced Study.
One of the most useful features of gauge/gravity duality is that it converts difficult problems in certain types of gauge theories into (relatively) simple geometric problems in gravity in one higher dimension. For example, the Hubeny-Rangamani-Takayagani (HRT) conjecture says that Continue reading