In the business of writing my master thesis about the possible treatment of naked singularities with canonical quantization I encountered a lot of papers of Pankaj S. Joshi, who is a theoretical physics at the Tata Institute of Fundamental Research in Mumbai, India. He is an expert in the field of general relativity and cosmology with a big interest in the fascinating topic of dynamical collapse scenarios.
Since I started my master thesis only some month ago and I am completely new in this field I looked around for some references that treat gravitational collapses and their outcomes, i.e. black holes and naked singularities, at a very broad sense. In January of this year Prof. Joshi published his book 'the story of collapsing stars' via the Oxford University Press. In order to get more knowledge about my kind of research I decided to read his book and now, finally, I finished an want to give a little review.
Before betting into detail I want to sum up my impression about the book: Overall his book quite nice to read and most notably very comprehensible. For everyone who is interested in topic concerning the formation of stars I would really recommend this book to read.
The first chapter of the book has the title 'our universe' and concerns the role of gravity in the evolution of our universe. In particular this is were the reader meets the word 'singularity' for the first time. In the following three chapters we makes these concepts more concrete and talks also about problems that arise from these concepts. Most importantly he points at the problem of the so-called cosmic censorship conjecture(CCC) which states that every gravitational collapse of reasonable initial conditions should result in a black hole, i.e. a singularity that is covered by an event horizon that forbids and interaction the to far away part of the universe. In other words, this conjecture would rule out the existence of so-called naked singularities. The mathematical problems of defining such a theorem or conjecture are pointed out and explained. The conclusion was made that only the study of different types of collapsing scenarios can give us a hint whether the CCC is right has to be thrown away.
He also explains that a star under reasonable initial conditions will more likely end up as a naked singularity instead of a black hole. After this statement has been made he explains various other types and models of gravitational collapses and points out that naked singularities are as common as black holes. This makes it, of course, difficult to write down an explicit form of the CCC.
In the last parts of his book he explains how naked singularities affect the structure of spacetime and discusses some phenomena that might be observed to distinguish between a naked singularity and a black hole.
Today I was invited to give a tiny talk about my current research in my master’s thesis. In 15 minutes I had the opportunity to explain to the audience the concepts a black holes, naked singularities and to tell them something about my ultimate goal of quantizing solutions of Einstein’s field equations that have naked singularities as solutions.
In the first part I talked a little bit about the so-called Schwarzschild solution. There I have shown in a hand-waving way that there are two types of singularities. The first type is a real singularity and the other type was a so-called event horizon which is a surface in spacetime that has the property, that if you pass it, you are doomed to fall into the black hole and there is no way to escape this fate. Summarized, there is no way to escape from a singularity since there is an event horizon surrounding it, i.e. no communication to the outside is possible.
A naked singularity is now the case where a real singularity is not hidden behind an event horizon. In several calculations people have shown that this are ‘real’ solutions for some choices of initial data. In particular in the case of the so-called LTB-model it is possible to write down analytical solutions that have a naked singularity in the center. This is the sage of my current work.
Also I have shown that the existence of naked singularities violates the notion of causality, i.e. there are closed curves in spacetime itself. For example I could travel through a naked singularity back in time to kill my father. In order to avoid these weird phenomena Roger Penrosé imposed in 1969 the so-called cosmic censorship hypotheses, which tells that under certain initial conditions a formation of a naked singularity is not possible. But since naked singularities predict somehow predict the breakdown of general relativity itself one tries to solve this:
One idea is, that naked singularities or singularities at all are only one artifact of general relativity which result from the fact of neglecting quantum mechanical effects. Therefor in the last part of my master thesis I will try to ally to procedure of canonical quantization to a solution of Einstein’s field equations that admit a naked singularity. If everything works properly I will study the properties of my solution. I am really looking forward to this because the result is completely unknown and even wage predictions are not possible at all.
You can find the slides to my talk here.
At the last Wednesday, the 24.09, I have a talk at my old high school with the title:
Black Holes and Information.
I tried to explain to people of normal high school level to explain by a lot of analogies like fishes in a pool with a drain hole are "analog" to a black hole and several others, how the idea of holography came up during the last decades and how we can understand this.
This talk was very close to the one Leonard Susskind gave some years are and I have chosen his way, expect of the String Theory part, because it summarizes the whole concept of holographic gravity in a very basic way that is even for pupils easy to understand.
This kind of talk is the second on I gave (the first one was exactly one year ago in the same school and had something to do with Quantum Information Theory) and I will definitely continue to give more talks like this on a public level because I think it is very import that we should not sit in our universities and wait for students to come to us. Rather we should try to go to them and fascinate them we the things we accomplished.
Here you can find the slides to the talk (German):
And here is also a report of my talk from the high school:
The concept of time is the most important one to find a unification of quantum mechanics and gravity.
On the first glance these two seem to be incompatible because they take care of time in two complete different ways.
Quantum mechanics needs absolute time to be consistent and Einstein's general relativity tells us on the other hand, that time is a
relativistic phenomena depending on velocities and the matter surrounding us, i.e. depend on the fact, where we are.
The first approach, by Wheeler and DeWitt, were able to combine these two and created the Wheeler-DeWitt-equation to honor them for their work.
But this equation opened a complete new problem, because it predicts on the first glance, that there is absolute NO time in our universe, that is that our universe
should appear static, what is in complete contradiction to our everyday experience.
In the year 1983 Don Page and William Wooters had an interesting solution to this problem:
They showed that an observer inside of the universe can use the entangled particles to build a clock, and on the other hand, that an external observer of the
universe is not able to measure time with these two particles.
This might seem confusing and extremely philosophic but in the year 2013 E. Moreva, G. Brida, M. Garmegna, V. Giovannetti, L. Maccone and M. Genovese
made an experiment to show that these theoretic ideal really describes the properties of time in our universe.
(For more details I refer to their publication: )
This new feature has to be extend further and to be integrated in the most recent theories of quantum gravity.
I'm curious to see what comes out of it.