Alumnus Update: Sagar Lokhande
Sagar Lokhande is a 2015 scholar who pursued a Phd in Theoretical High Energy Physics / String Theory at the University of Amsterdam. He currently holds a temporary research position in University of Illinois, USA.
This week he discusses aspects of black holes, the supermassive stars with intriguing physics.
Black Holes
Since times unknown, mankind has been fascinated by space and celestial objects that call it home. Stars, planets, comets, asteroids. Modern astronomy has led to tremendous progress in our knowledge of these far-yet-visible objects. In this article, I will discuss about one such astronomical object. It is called a black hole and it has fascinated astronomers, physicists, mathematicians and the general population alike for more than a century now.
Our story begins with stars. These are massive balls of gas that are held together by the force of gravity. They are found everywhere in the universe, and it is estimated that there are more than a trillion trillions of them in the universe. The Sun is the prototypical example, with a mass equalling 3.3 million Earths. As Newton first discussed in the 17th century, the force of gravity between two objects is proportional to the masses of the two objects. This simple mathematical fact, however, raises the question of whether or not a star can remain stable. After all, it would surely be bad for us if our Sun was to explode or implode! The problem of stability concerns with very massive stars. If enough gas accumulates so as to create very strong gravitational force, does the star remain a ball of gas? Various physicists studied this question in the earlier half of 20th century. In particular, Subramanian Chandrasekhar proposed [1] that when stars become roughly twice the mass of the Sun, they collapse (or implode) under their own weight and lead to a new type of object, the black hole. A black hole is also defined as a region in space where the force of gravity is so strong that nothing, not even light, can escape the region. It is believed that there are supermassive black holes in the center of many galaxies, including our own Milky Way. In 2016, LIGO collaboration discovered signals coming from the merger of two black holes [2], thus providing the first observational proof that black holes exist. In 2019, EHT collaboration captured the first-ever image of a black hole from a nearby galaxy [3], shown in the image above.
For a precise understanding of black holes, one needs to use Einstein’s theory of gravity [4], also known as general relativity. This theory asserts that:
1. Space and time form a continuum, known as spacetime, providing a stage for the drama of physics to take place.
2. Spacetime can fluctuate. The fluctuations are caused by matter or energy.
As per general relativity, the force of gravity is a result of curvature of spacetime. These statements were succinctly packaged in Einstein’s equations
Rμν − 21Rgμν + Λgμν = 8πGN Tμν , (1) 1
where all the symbols have a precise meaning but we will not discuss it here. Famous American physicist John Wheeler [5] interpreted these equations as Spacetime tells matter how to move, matter tells spacetime how to curve.
Mathematically, Einstein’s equations (1) are a set differential equations, a more complicated application of differential calculus that is taught to young students worldwide. How do these equations connect to astrophysical objects? One finds solutions to these equations, and different solutions then describe different astrophysical objects. Many types of astrophysical objects have been studied in this way. A black hole is the one of interest to us, as it is one of the most enigmatic celestial object. When super massive stars collapse under their own weight, they lead to the creation of black holes. Depending on how massive the star was, the black hole comes with a special radius surrounding it, called Schwarzschild radius. No object, not even light, can escape the pull of the black hole once it is inside this radius.
This was the conventional wisdom accepted by physics community, until Stephen Hawking came along. In 1975, Hawking showed that black holes emit radiation [6], just like a heated piece of coal in a laboratory would. This was contrary to the consensus that nothing escapes a black hole. Further, the radiation escaping the black hole is similar to the radiation escaping from the so-called black body, a cylindrical object with a hole that is used in physics laboratories frequently. Albeit, the radiation coming from the black holes is much much fainter, making it hard to detect. To show this similarity mathematically, Stephen Hawking modeled the radiation using particles. Then he showed that if a faw-away detector measures the radiation particles, then the probability that they have energy ω is the same as if those particles were emitted by the black body
N(ω) ∼ 1 (2) eω/Rs −1
where Rs is the Schwarzschild radius of the black hole. These particles together constituted energy that was radiated away from the black hole, eventually resulting in a decrease in the mass of the black hole. This process is called Hawking evaporation. Even though it has sound theoretical basis, it has not been observed experimentally until to- day. Nevertheless, it raises some very important questions. Astrophysical black holes are formed from gases and these ingredients have certain information about them, for example their type, fraction, etc. However, thermal radiation has no information about the source where it comes from! This means that if the entire black hole evaporates away in thermal radiation, all that information about the ingredients that existed at the beginning will get lost by the time the black hole evaporates. This is a problem, since information about objects cannot just vanish away. Then, how does one reconcile this fact with the thermal radiation emitted by black holes? Are black holes special in that they do not obey the normal laws of physics? Or are the laws of physics incomplete? This is the famous Black Hole Information Problem [7, 8]. A lot of research has been done on this problem since it concerns the fundamental laws of our universe, but the problem has not been fully solved yet. There is hope that solving the Information Problem will open new avenues in physics. So, stay tuned.
Image: Black hole at the center of galaxy M87. Credit: EHT Collaboration.
References
[1] S. Chandrasekhar, The Maximum Mass of Ideal White Dwarfs, The Astrophysical Journal 74 (1931) 81.
[2] LIGO Scientific, Virgo collaboration, B. P. Abbott et al., Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116 (2016) 061102 [1602.03837].
[3] Event Horizon Telescope collaboration, K. Akiyama et al., First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, Astrophys. J. 875 (2019) L1 [1906.11238].
[4] A. Einstein, Die Grundlage der allgemeinen Relativit ̈atstheorie, Annalen der Physik 354 (1916) 769.
[5] J. A. Wheeler and K. Ford, Geons, black holes and quantum foam: a life in physics, 2000.
[6] S. W. Hawking, Particle creation by black holes, Communications in Mathematical Physics 43 (1975) 199.
[7] S. D. Mathur, The Information paradox: A Pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [0909.1038].
[8] J. Polchinski, The Black Hole Information Problem, in New Frontiers in Fields and Strings (TASI 2015), pp. 353–397, 2017, 1609.04036, DOI.
