The Physics of the Far Future

www.phenomenica.com (I took the image from this website)

In this post I worry about the very far future - thousands of  billions of years from now when Earth will be gone and the universe will be bigger and much emptier than it is today.  It is believed that eventually all the matter and radiation in the universe will be absorbed by the cosmological horizon, which grows in response.  Nothing will be left other than slowly evaporating supermassive black holes. Black holes are thought to be the densest and most lasting objects in the universe.

In http://arxiv.org/abs/1201.1298 (some more papers will follow), we study the thermodynamics of our local universe in this future. The local group is expected to collapse to a supermassive black hole that will slowly evaporate in an universe dominated by dark energy for which the simplest model is a cosmological constant. Empty space with a cosmological constant is knows as deSitter space.

We look at the dynamics between the extremely cold cosmological horizon and the hotter black hole horizon. As the black hole evaporates, heat will flow from the warmer black hole to the colder cosmological horizon producing entropy. If you miraculously add a black hole to an empty deSitter universe, you find that the presence of the black hole initially depresses the total entropy, which increases increases back to the entropy of empty deSitter as the black hole evaporates. 

What is the end state of the universe? If the cosmological constant is a true constant, then the universe will reach its final thermodynamics equilibrium state in empty deSitter, i.e., empty space that expands forever. When quantum effects are included, deSitter may be unstable and decay to flat Minkowski space. Alternatively,  if a slow rolling scalar field mimics the cosmological constant, this scalar field could eventually reach the bottom of its potential and then the universe would stop expanding becoming flat.

What is the entropy of flat space? Flat space would be indistinguishable from a space with a very small cosmological constant. The entropy of deSitter depends on the inverse of the cosmological constant and so as the cosmological constant gets smaller, the entropy of the universe increases. With this assumption, flat space would have a infinitely large entropy.

What about the Weyl curvature hypothesis? Perhaps you have all heard about it and wonder if it can be violated or perhaps you will hear about it now for the first time. Roger Penrose states that the difference in entropy between the initial and final state of the universe is related to the growth of the Weyl curvature. The Weyl curvature is small at the beginning of the universe, but grows with the production of singularities. However,  empty deSitter space has zero Weyl curvature.  We modify the conjecture by stating that the entropy does not come directly from the Weyl tensor, but from a coarse-graining over the states of the Weyl tensor. The cosmological constant limits the wavelength of the gravitational wave modes. When a black hole evaporates, the cosmological horizon grows allowing more gravitational wave modes. This increases the number of available microstates in the Weyl tensor and hence the entropy of the space. The cosmological constant is both an energy and an entropy scale. It plays a very important role in black hole thermodynamics that still has to be understood.

The Right Pitch to Shatter a Neutron Star

Our paper on crust shattering of neutron stars was spotlighted by PRL and given a synopsis by a science writer! It was later picked up in the news! This is the New Scientist article. Another article about it is in ArsTechnica and the paper is even referred to on wikipedia when precursors to short Gamma Ray Bursts (sGRBs) are mentioned. This work resulted from a collaboration with David Tsang (Caltech), Jocelyn Read (University of Mississippi), Tanja Hinderer (Caltech), and Tony Piro (Caltech), which was lead by Dave and Jocelyn.

The paper is about a potential explanation for precursors of short Gamma Ray Bursts (sGRBs). GRBs are some of the most luminous events in the universe outshining any other gamma ray source in the sky*. Their high luminosity coupled with their short emission timescales implies an enormous amount of energy must released from a small volume of space ( 100km). They typically have isotropic equivalent luminosities of 10¹⁷ x the luminosity of the sun over a duration of less than 2 seconds. These highly luminous bursts are seen by the NASA's Swift and Fermi telescopes.

A leading model for sGRBs is the neutron star- neutron star merger. As the two neutron stars in the binary get closer together, the tidal frequency increases. The neutron star crust is believed to be very stiff and can have a resonant frequency just like glass.  When the tidal frequency matches the resonant frequency of the crust, the crust shatters just like a wine glass shatters when an opera singer hits the right note and excites high energy emission, which can explain the flares seen just prior to sGRBs.

From David Tsang, Caltech

Here is Dave's fancier summary: "Can neutron stars, dead stars composed of exotic material trillions of times more dense than a normal star, shatter like an ordinary wine glass? Our new research shows that indeed they can. As a neutron star spirals in towards another neutron star or black hole due to emission of gravitational waves, tidal forces act on the star with increasing frequency. When this frequency matches the resonance frequency of the neutron star crust -- just like an opera singer hitting the right note for a wine glass -- the crust shatters. The shattering crust may excite high-energy emission, explaining gamma-ray flares seen just prior to short gamma-ray bursts. Just as the note at which a wineglass shatters tells you about the composition and shape of that wineglass, studying the timing of these flares could allow physicists to learn about the properties of dense matter in neutron star crusts, material that cannot be probed by ordinary terrestrial experiments."

An opera singer and a broken glass can be seen below:

Disclaimer: Unfortunately, I do not know who are the authors of either the opera singer or the broken glass photo.







*Gamma rays are light of very high frequency of over 10¹⁹ Hz (more than 1 000 000 times the frequency of visible light) and wavelengths of less than 10 pm (a tenth of the diameter of an atom). Light of very high frequency also has very high energy.

Welcome 2012! Happy new year everyone!

Since I am most thankful for the happy children in my house, I am writing this post about them.

Edward and his legos

Edward will be 1 year and 5 months old next week. He admires his cousin David with his whole heart and imitates him as much as he can. This year was the first Christmas when Edward was old enough to run and play. He can put together legos now and his favorite toys are cars, which he calls "masina".  Some other words he says are: mama (with different intonations), apa (water), bomboana (candy; maybe not so good for his diet), cheese, papu (shoes), DeDe or David (depending on his mood), tata or daddy, pita (bread), Titzi (either the guest cat to be explained later or my breast; he is still nursing at night), knock-knock (which he can accompany by knocking), poc, buff, mu-mu (most animals including sheep), ham-ham (usually dogs), up, brate (arms in Romanian when he wants to be picked up).

David in the livingroom-to-kitchen window

 David at 4 years and 10 months has a rich imagination and likes to exaggerate. He could not give a paper plane to Edward the other day because it was really a rocket that would explode if not handled properly and, of course, he is the only one who has the expertise to use this rocket. So, sometimes discipline becomes harder to enforce, and I have never been too good at enforcing discipline in the first place. He also thinks that he became the richest David in the whole world when my brother brought him a suitcase of books and that almost every cake that my mom makes is the best cake ever. The latter is a reasonably good habit to cultivate. In 20 years from now his girlfriend or wife will enjoy this type of compliments.  And David's opinion is that fireworks should be called atomic bombs because it's just a more suitable word that would be easier to say for Edward.  I did explain to him how dangerous an atomic bomb is, but he does not understand bad things well yet. In the end, I guess that all words are a just a name for things that could change and do change some times in different languages/cultures and as adults we tend to forget that.

The Guest Cat

Who was the guest cat? We found a cat a few days before Christmas.  She followed the children and my mother home and entered the house on her own. She clearly loved children and various kinds of meat including fish. Edward would sometimes pull her tail, and she never even once hissed and did not run away from him. I put flyers at the bus station and, eventually, her rightful owner showed up to claim her on the 31st of December. We found out that she had been a barn cat belonging to the brother of her current owner only 5 weeks ago and that she was let into the house when she followed the children of the guy in. We received champagne, candy and martipan in return for the cat, but we still miss her sometimes.