Let’s look at black holes. Black holes are thought to be these powerful, mass-sucking entities deep in space but in reality, they are more than that. Black holes feature the concept of gravity – something that is still not very well understood – at work. The gravitational force in black holes is immense, but what does this really mean? To be more precise, gravity is extremely strong inside the interior of a black hole, which is past the event horizon (or the surface). The effects of gravity of black holes are only apparent within a close distance(a few Schwarzschild radii). From a large distance, gravity is no different from that of normal objects, as it will behave according to the inverse square law(the greater the distance between any two objects, the weaker the gravitational attraction). The inverse square law is an important law in all of physics and it states that any physical quantity(light, radiation, forces) will be inversely proportional to the square of the distance1. However, the event horizon is still not the most intriguing part of a black hole, so what is the most elusive part of it?
If we dive deeper into a black hole, we will see the very centre of it. This is called the singularity, where the spacetime curvature(think of gravity warping and distorting the fabric of spacetime) becomes infinite. Since density tends to infinity, and density = mass/volume, the mass of a black hole is exceedingly large, whilst the volume is really tiny. But what is the mass and volume in this case? To understand that, we must look at the formation of black holes. Black holes form when extremely massive stars run out of helium fuel and collapse in upon itself, resulting in lots of mass being compressed into a very tiny volume. You can think of something the size of planet Earth being packed into something tiny like your school bag- this point is called the singularity or the centre of a black hole. Black hole formation is quite an interesting topic: the recent Nobel Prize in 20202 was given to a robust mathematical prediction of black holes in general relativity(the field equations), which is quite a feat. Physics and mathematics ‘break down’ at the singularity, and it is a region in spacetime that doesn’t make sense, so understanding it would be extremely vital to science. Additionally, the term singularity also applies to mathematics – you come across singularities when dividing by zero3! This, in a way, has some connections with the mathematics of black holes.
Let’s return to the ‘point of no return’, otherwise known as the event horizon. Once you reach the event horizon, don’t even think of turning back: you can’t. To understand this, we must look at escape velocities. To give you an idea, the escape velocity for Earth4 is 11.2km/sec. Escape velocity is the minimum velocity an object must travel in order to escape the gravitational force of a body, for instance, a planet. What about the escape velocity of a black hole? The equations are not complicated to calculate at all, and after doing some algebra, you can get c to be your answer(use the Schwarzschild radius). Therefore, we can say that to escape the black hole at the event horizon, the minimum velocity must be the speed of light, which effectively means that nothing can escape, not even light.
You may have heard of white holes, which are purely hypothetical and extremely unstable objects in space. They are based on mathematical predictions in the study of general relativity and can be thought of as opposites of a black hole. There are no direct observations of it yet, but the main idea of a white hole is that light and energy can escape from it, whilst nothing can go in. Some physicists, such as Stephen Hawking, believe that supermassive black holes also form supermassive white holes. The word supermassive just means a collision of two black holes(or white holes) which creates an even bigger black/white hole. This process takes quite some time, usually hundreds of millions of years, and once it happens, it makes a ‘chirp’ sound which produces gravitational waves that are analogous to the ripples in spacetime. The first detection of gravitational waves won the 2017 Physics Nobel Prize which was a wonderful advancement in science, and now in late 2021, an astronomical record of gravitational waves have been detected5.
Mathematical Interlude(if you want to know more):
The Newtonian law of gravitation is F = GMmr2, where F is the gravitational force of attraction in Newtons, G is Newton’s constant, M and m are two different masses of two objects and r is the distance of separation between the two objects. However, this law only applies to classical physics, where speeds are very slow compared to the speed of light c. Hence, this law does not work near relativistic speeds(speeds near the speed of light), which is called a cutoff, as this equation ignores speeds near c. In order to include relativity in this equation, some factor/correction term must be added to preserve the laws of special relativity, namely that nothing can exceed the speed of light.
This addition is called the Lorentz factor6 and is denoted by the symbol gamma , which is given by the equation 1/(1-v2c2), so the velocity v cannot be greater than c, or else the result will be an imaginary/complex. This factor can be placed in Einstein’s famous mass-energy equation to form E=mc2(E=mc2 is for objects at rest), or Newton’s second law F = ma. Hence, the relativistic version of Newton’s law of gravitation can be written as F = GMmr2.
References:
- Inverse Square Law. (2021). Gsu.edu. http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/isq.html#isqg
- The Nobel Prize in Physics 2020. (2020). NobelPrize.org. https://www.nobelprize.org/prizes/physics/2020/press-release/
- The Schwarzschild Metric. (2012). Ucsd.edu. https://hepweb.ucsd.edu/ph110b/110b_notes/node75.html
- Escape velocity. (2015). National Aeronautics and Space Administration Wiki. https://nasa.fandom.com/wiki/Escape_velocity#:~:text=On%20the%20surface%20of%20the,less%20than%207.1%20km%2Fs.
- staff, S. X. (2021, November 8). Scientists detect a “tsunami” of gravitational waves. Phys.org; Phys.org. https://phys.org/news/2021-11-scientists-tsunami-gravitational.html
- Fernflores, F. (2019). The Equivalence of Mass and Energy (Stanford Encyclopedia of Philosophy). Stanford.edu. https://plato.stanford.edu/entries/equivME/
