The Geometry inside a Black Hole

black hole

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What is a Black Hole?

Black holes are some of the strangest, densest and fascinating objects of the Universe that we know. They have attracted a lot of attention in the last century; both from the science fraternity and from the general public as well. But what is a black hole?

A black hole is a supermassive star that has collapsed into itself due to its high gravitational pull. The gravitational pull of the black hole is tremendous: so strong that nothing can escape from its vicinity, not even light.

 

Life and Death of Stars

Stars exist as a stable system because of an equilibrium between the pressure generated due to nuclear fusion and the gravitational pull it exerts on itself. As the star burns more and more fuel, the Hydrogen fuses into Helium, Helium to Lithium and so on until they form iron.

what holds star together

With Iron, it is somewhat difficult to achieve the fusion reaction because of the high coulombic repulsion between two Iron nuclei. It can absorb a neutron or an alpha particle to turn into heavier elements like Nickel but this process is overall endothermic: meaning we need to provide energy for the reaction to occur. Due to this reason, as stars burn more and more, a lump (more like a sphere) of iron keeps accumulating in its core.

This iron does not provide energy and hence does not contribute to the outwards pressure that would normally balance out the gravity. After a limit, the fusion pressure is not enough to balance the gravitational pull and it starts to shrink. The star literally collapses upon itself. This, in turn, increases the density even further, which increases the gravitational pull. At this moment where everything is being pulled towards itself with immense pressure and speed, iron nuclei can fuse together to form even heavier elements, like lead. This is how super heavy elements like Uranium or Thorium were formed in the early Universe.

 

Supernova and A Black Hole

The rapid collapse of a star causes a shockwave that ends up in a gigantic explosion, known as a Supernova. A Supernova is a massive, massive explosion and is really bright. They are so bright that they can even be seen in the sky during the day. The leftover material that is not blown away from the explosion is somewhat colder but incredibly dense. There is a cloud of hot gases around this core, known as a Nebula.

galaxy

The geometry of a Black Hole

This core, if left behind by a super massive star, one with a mass nearly ten times that of our sun is so dense that even after ejecting so much mass it cannot counter the gravitational pull and hence collapses into a singularity. A singularity is a point mass and hence has an infinite mass density.

life of blackhole

A black hole is thus born, and it has a singularity at its center. The gravitational pull around the black hole is strong enough to suck in any or all light that passes near it. A black hole is so massive that it warps and curves the space around itself. Let us understand it with an analogy.

According to the General Theory of Relativity, Spacetime can be imagined as a fabric that stretches across the entire universe. Let us imagine that the bed sheet spread over your bed is this same fabric. If we place an object, such as your hand on it, it sinks inwards. The heavier the object, the deeper it sinks. If we place an object, such as a marble near the depression caused, the object would roll into the cavity formed. This is a visualization of the force of gravity coming into play.

In case of a black hole, this sinking down of the fabric is so intense that it can be imagined as a tear in the fabric, or as shown in the figure below:

black hole

Since this ‘well’ created by a black hole is so deep, and the walls are so steep it is impossible to escape the pull of its gravity.

 

Issues with the Point Singularity

All the stars in the Universe rotate about their axis. This is true for all the stars and is accepted as a general fact. The matter falling into a star gives it some angular momentum as well and in absence of friction or dissipative forces, there is no torque to counter this spinning. When the stars collapse, the angular momentum being conserved causes the core to spin even faster as it goes smaller and smaller.

Since a point mass cannot have a spin, it cannot have any angular momentum about its axis. So in order to conserve the angular momentum it has, the core collapses into a ring instead of a single point and this is called a Singularity. It is a ring with zero thickness but a non zero radius. Since the distribution of the mass is not spherical, there is an equatorial bulge as shown in the image:

black hole horizon

This bulge is called the Ergosphere and it’s an interesting region in many different ways. The singularity is rotating and hence it leads to some interesting consequences. The ring, as it rotates, drags the nearby spacetime with it and forces it to rotate with it.

Let us see another analogy to visualize what is happening. Place your hand on the bedsheet, and apply very slight pressure. The sheet would slightly move but it won’t be dragged along. However, if we increase the pressure then the sheet would twist and curl around our hand as it rotates. A very similar thing happens with the space around a spinning black hole; space is dragged along and hence anything that is in that region starts to encircle the black hole despite being at rest in its own reference frame.

We can also see that the area immediately around our hand is warped more than an area at a distance. Similarly, the area at a certain distance from this singularity is warped but only slightly. This area is the Ergosphere. This region is slightly broken in terms of physical laws but not completely. And these incompletely broken laws are what we also find fascinating. Beyond the Ergosphere is the Event Horizon and that is the boundary: the point of no return.

 

Point versus Ring Singularity

As we work out the Physics of the singularities, we find out that the formation of a Point Singularity requires very extreme conditions which often lead to quantum effects coming into play and causing hindrance in the formation of a singularity. If Quantum Gravitational effects do not kick in, there are no hindrances in the formation of a point singularity as such. According to certain predictions of the General Relativity, the inner horizon of the ring singularity might not be stable due to something known as blueshift. This has also been hinted at by certain observations, but as mentioned previously we cannot conserve Angular Momentum solely with a  point singularity.

While a lot of research has been done, a lot of resources being poured into the studies and a lot of things have been learned; the collapse of Stars into Black Holes and the geometry of the resultant celestial body remains a hotbed of active research in the science fraternity today.

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