Black hole is that region of space-time that has the audacity to hold even the irrevocably almighty light captive in an enigmatic dungeon. When one ponders about the black holes, it is normal to imagine oneself as Captain Kirk meandering through infinite galaxies or as Mather McConaughey plummeting in and out of a fourth-dimensional void inside the black hole. Unfortunately, for those who are interested in the tons of mysteries underlying the shroud of black hole, the properties we currently observe inundates these fantasies. The no-hair conjecture is a hypothesis that predicts that a stable black hole will have only three observable properties: mass, charge and angular momentum.
On the basis of the no-hair conjecture, black holes have been classified into three name-heavy categories: black holes that are static and have mass but lack charge and angular momentum are known as the Schwarzschild black holes; those that are charged and stationary are referred to Reissner-Nordström black holes and the uncharged rotating black holes have been coined the name of Kerr black holes.
The charge and angular momentum of a black hole are uniquely dependent on its mass by a formula:
Where Q represents the total electric charge, J stands for the total angular momentum and M is the black hole’s mass. Black holes with the least mass obeying this inequality are known as extremals.
This inequality is essential in determining the nature of a black hole, however solutions exist that do not follow this inequality. What is the problem with such black holes? Such black holes possess a naked singularity, which means that they lack an event horizon. On the other hand, independent calculations rule out such a possibility, since naked singularities are unphysical, and it is very unlikely that realistic matter would collapse to give a naked singularity.
Let’s now discuss the alluring features of a black hole. Firstly, the most common term when we come across an article on black holes is the term ‘event horizon’ – it is an inevitable boundary through which nothing can escape. Why can nothing escape the tyranny of an event horizon? We all know that mass deforms space-time such that paths taken by particles bend towards the mass. Since the event horizon bends the space-time curvature to a great extent, the path of the particle bends heavily inwards and there are no paths leading away. Furthermore, an event horizon is shaped according to the nature of a black hole: for a static black hole, it is almost spherical and for a rotating black hole, it is oblate. Unfortunately, Einstein’s principle of equivalence makes it is impossible (even for Tom Cruise and the directors of the Mission Impossible franchise) to determine the location of event horizon.
An event horizon is always interesting to study for its unique feature of gravitational time dilation. Essentially, an object falling towards the black hole will take infinite time to slow down and will appear redder due to gravitational redshift, until the object eventually fades away.
Another term often associated with black holes is ‘gravitational singularity’. At the singularity, the space-time curvature becomes infinite. For a static black hole, the singularity is a single point whereas for a rotating black hole, it forms a ring that lies in the plane of rotation. These singularities have theoretically zero volume but house the entire mass of a black hole. Thus, a singularity will have an infinite density! A tantalizing phenomenon noticeable at a singularity is the “noodle effect”. At the singularity, the object falling in would be crushed to infinite density and its mass is added to the total mass of black holes (obviously we have no way of tasting these noodles!).
The term singularity is enough to make many grab their head and try to soothe their tottering brains. Could we avoid it? It turns out that we can! We now know that since a Schwarzschild black hole is a static black hole, its singularity is a single point and any object crossing its event horizon will head for the singularity. Contrastingly, in a Reissner-Nordström or Kerr black hole, when we extend the solutions, we come out with a possibility of using the black hole as a wormhole (cheer up sci-fi enthusiasts!) and avoiding the idea of a singularity.
The words ‘singularity’ and ‘event horizon’ are terms you’ll often come across on almost every black hole article, but now let’s uncover the seldom-uttered terms relating to black holes. A proton sphere is a spherical boundary with zero thickness where protons are trapped by the centripetal force, hence the protons move at tangents to that sphere but the centripetal force acting towards the center keeps them moving in circles. The light that reaches us from a black hole is from the special region sandwiched between the proton sphere and the event horizon.
Is there anywhere else light can escape from in a black hole? An ergosphere is a region outside the event horizon of rotating black holes where objects cannot remain stationary. Why does an ergosphere only appear in a rotating black hole? While the black hole rotates it will drag the space-time surrounding it and this region is the ergosphere. Any object in the ergosphere will tend to move in the direction of black hole’s rotation in an effect known as frame-dragging. For a rotating black hole, the effect of frame-dragging is so strong that an object in the ergosphere would have to move faster than light in the opposite direction to remain still.
Objects and radiation normally flee the ergosphere through a process known as Penrose process, which can be used to extract energy from black holes. Hence, anything that comes out of the ergosphere is dialed up with a ginormous supplement of energy, which exceeds the energy it entered the ergosphere with. Remember that since energy cannot be created, the additional energy an object coming out of the ergosphere receives is by slowing down the black hole and taking its rotational energy.
Apart from the cruel ergosphere that enervates a black hole of its rotational energy, an object can move stably around the black holes. The smallest circular orbit in which an object can move stably and non-chaotically around the black hole is known as the Innermost Stable Circular Object (ISCO). The ISCO’s location depends on the spin of the black hole.
This bring us to the end of the article, where we’ve discussed a litany of features these gorgeous warehouses of wonder possess. Summarizing these features, we could conclude that a black hole isn’t as monotonous as it seems and the possibility of marveling on them is not shattered yet. To know more about black holes, look out for the upcoming articles. So, keep reading!!! And continue to speculate, innovate till you constipate!