The effects of black holes on visible objects and elementary particles

Abstract:

In the following paper I will attempt to predict the newtonian forces that are applied on any state of matter when it gains access to the event horizon. Also, I will study the notable changes in an objects center of mass, distortion of mass and final mass. I believe that the factors above should always be referred to when attempting to recreate or predict the unknown occurrences in the event horizon. I will too take these elements in consideration when manufacturing an equation to represent matters reaction when interfering with the event horizon. In order to make the effects easier to predict, we will attempt to test my equation on visible items that surround us, due to the fact that measuring changes in the quantum structure of atoms entering the event horizon will be extremely hard and will not provide us with sufficient data.

Keywords: Black holes, matter, center of mass, loss of mass, event horizon

Note:

In this paper, you will come by the term “singularity” quite often. It is important to note that this refers to the point in which a particle is unable to split and divide due to the force of gravity. For example, when I say an object has reached singularity, I therefore mean that it is now infinitely dense, unable to collapse into a smaller elementary state.

Introduction:

Black holes have surprised, interested and puzzled us ever since they were discovered. In this paper, we will attempt to answer some challenging questions about them.

Immediately upon entering the event horizon membrane, which is represented by the formulae Rgb = 2GMb/c2 , where G acts as the Newtonian Gravitational constant and C is the speed of light [1]. Multiple forces attempt to manipulate the objects structure. Once a physical state of matter enters the event horizon, it is unable to escape. It is a well known fact that black holes have an enormous gravitational force [3], therefore, each millimeter or almost certainly an even smaller unit of measurement can affect the shape and structure of any physical object, despite its scale or shape. To make it easier for me to narrate the shift in an objects structure, I will use an everyday pencil as my object of choice.

Once our object of choice somehow enters the event horizon, depending on it’s orientation, the point closest to the black holes core will get extend first, now, let’s assume that the pencil is highly elastic. Initially, the pencil will extend until its introductory center of mass, subsequently, the center of mass will rise higher up the object and the process will continue until the pencil reaches a point in which it has to split. Since this is simply an introduction, more detail will be provided later on in this paper.

The fragment of the pencil that managed to enter the event horizon first, will be going at much faster speeds than the rest of our preferred object, therefore, according to Albert Einstein’s special theory of relativity, the pencil should experience time in a much slower sense, and from it’s perspective it is highly likely that it will take it hours to condense into a singularity. That is mainly what we will discuss in this paper, we will observe these effects and attempt to manufacture an equation. With no further due, let’s explore the calculations that will help us predict the deformation of an object.

1. Changes in an objects center of mass

When entering the event horizon, an objects center of mass rises upwards due to the spaggetification effect from the black hole Our physical object will deform and will form an accretion disk. According to Albert Einsteins [5] theory of special relativity, from the objects perspective it would take hours for the object to collapse into a singularity, thus, by the time the entire object enters the event horizon, it will be unevenly stretched, therefore, causing the objects center of mass to rise towards the point further away from the black hole . Below is an equation describing the change in an objects center of mass:

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In the above equation, delta stands for change, M represents mass and the miniature circle represents the center of mass. For the equation to be right, we must consider the following factor: ½ of the objects mass enters the black hole to form an accretion disk. When this happens, we are able to mentally divide the object in to four equal parts, and when ½ of the object enters the event horizon, the objects center of mass is estimated to rise up by 25%

Also, the object will follow the below mass conservation equation as it becomes part of or creates an accretion disk [1, 2]:

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“ where, x, u, ρ, P and λ(x) are the radial distance, radial velocity, density, isotropic pressure and specific angular momentum of the flow” [source 1]

The above equation will potentially help a researcher verify his predictable observations.

2. Depletion/loss of Mass

In this paragraph we research the depletion or loss of mass once an object enters the event horizon. As I previously stated the event horizon is the point in which an object that occupies space initiates its collapse into a singularity, here we will calculate the measurable effects of the spagettification effect, and come up with a reasonable equation that will help predict these events. I will also create a timeline to visually characterize the proceedings.

As the tip of a pencil enters the event horizon, its nose is immediately stretched around the black hole, and as ½ of the pencils original mass flows into the black hole, we calculate that the objects center of mass increases by 25% towards the part that is yet to fully enter. Eventually, the objects center of mass will experience intense amounts of pressure and will split into two equal parts. This process will continue until the object achieves a singularity. Thankfully, the process can be easily calculated using the below equation:

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Unfortunately, it is a well known fact that by squatting a number, you will never be able to reach a singularity (which is represented by 1). This can be achieved by a mass less particle, or in our case an object such as a photon. A photon contains no mass, and thus it represents a singularity or a 1 in simple mathematical digits. Since it is unable to divide any further, it has reached singularity.

Thankfully, Albert Einstein has come up with a revolutionary equation that allows mass to be converted into energy and vise versa. The famous E=mc2 equation [source 5] will allow us to find out how the objects mass will be turned into energy and thus radiation.

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Above, “M” represents the requirement for mass (m) to be transformed into energy (e). Then we see that the requirement is mass multiplied by the speed of light squared.

In order for an object or particle to be converted into energy, it needs to concentrate enough momentum. This is easily done by the particles acceleration caused by the black holes gravitational pull. This can be described by Einstein’s original relativity equation displayed below [5]:

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Now, you may work backwards to calculate the point in which a particle will achieve singularity and convert itself to radiation/energy form.

3. Momentum

The momentum of an object that enters the event horizon is expected to rise. Depending on how stable the element is, we should expect its momentum to rise as it approaches the black holes singularity [3,10, 7]. This happens because of the increase in the gravitational force that acts upon our theoretical element. For example, the speed of a block of wood would be much faster at the core of the black hole than in its outer rims, assuming it is powerful enough to withstand the immense pressure. This can also be seen in space near the Earth. A satellite orbiting at 300KM would orbit much faster than a satellite at 900KM. Since the satellite is closer to the Earth [8], the gravitational attraction between it and our planet is much stronger, hence, forcing it to fall down to the Earth. But since the satellite is in orbit, it generates angular momentum, which allows the satellite to swing up to its apoapsis before re entering the atmosphere, which thus continues the cycle.

To calculate this, we can use one of the equations provided in Newtons’ paper, the universal law of gravitation. The equation needed is placed below [8]:

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Here, V is the velocity of the satellite or object, M is the mass of the central object, in this case the Earth or a black hole, and R is the radius of the object. G is the gravitational force (in newtons) of the Earth which can be calculated using [8]:

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Where Fg is the gravitational force, G is gravity, M1 is the mass of object one and M2 is the mass of object two. R defines the radius of the body in which the artificial or natural satellite is orbiting.

Now, In order to calculate the increase in momentum or inertia, we can use a basic equation that I have constructed. The equation is based off the original method of calculating inertia, but has been slightly changed in order to suit our requirements.

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Where delta is “change in,” m is mass, R is a given radius and T is time. Although, this equation doesn’t necessarily apply to non-spherical objects. In order to avoid issues, I have created an equation for just that:

4. Conversion of mass to energy

As objects collapse in a black hole, a conversion or transfer of some sort is essential to understanding where the mass ends its journey at. Since the gravity of a black hole is too strong to keep an elementary particle at its original state, and to strong to release it in some sort of way, we can assume that it is converted through energy through fission or other reactions that occur due to the strong gravitational field of the particles desired destination (in our case a black hole) [9, 6, 3]. As the object splits, it eventually reaches a point in which it is the size of an atom. Since the gravity of the black hole will continue to pull the atom, it will continue to split and decay, releasing energy in the form of radiation as its by-product. This could explain the reason large amounts of radiation are measured near black holes. Radiation occurs when an unstable particle performs either nuclear actions: Fusion, Fission. Fission is the main method used in modern Nuclear power plants. It is when an atom is split. Fusion is somewhat the opposite and is when an element combines and crushes into another, forming a completely new element. Both methods release energy in the form of radiation as their by product.

As far as we know, Quarks are the smallest known item. It is believed that the mass of a quark is reflected by the properties of a higgs field. Furthermore, we stated that it is impossible for an object to reach zero mass, although, using Albert Einstein’s special theory of relativity [5], we can theoretically easily convert mass into energy.

Since the object is already moving at extremely high speeds (see part 3), it is already being converted from mass to energy. The conversion can be calculated with Einstein’s popular equation below [5]:

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In the above equation, E represents energy, m stands for mass and c is the speed of light. Meaning that the energy given to us by our conversions, can be calculated by multiplying our objects mass by the speed of light squared. This proves to us that matter can escape as energy from a black hole. I believe this was discussed in Stephen Hawking’s paper “The Information paradox for black holes.” Where Hawking states “I propose that the information loss paradox can be resolved by considering the supertranslation of the horizon caused by the ingoing particles. Information can be recovered in principle, but it is lost for all practical purpose ” [9]

Information is recovered in an energy state. Where the particles have no mass and are released in the form of radiation. This radiation, is in a scrambled state, making it impossible for us to recover or recreate an image of the fallen object.

5. Rate of Collapse

In this part, we will attempt to create an equation that will calculate the rate in which an object collapses in. The equation will likely be proven wrong since sufficient data isn’t provided by modern research. Hopefully, we will be able to consider all the above factors to create a potentially viable equation.

First, we begin by noting the gravitational pull (in Newtons) of the black hole. To make it easier for us, we will assume the black hole has the mass of the Earth. We will now use the same equation we previously used for momentum to help us calculate this equation:

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The change in momentum is above. Explanations to what the letters refer to can be found in part 3. Due to an effect named Hawking radiation, the mass of the black hole is constantly decreasing causing it to slowly destroy it self. Therefore, we will assume that every second, our mass of 5972 x 10^24kg is depleting by 3 KG. Of course, this represents the Earth, a black hole would have much larger proportions of mass and depletion rate. To avoid possible confusion, the Earth Is not depleting by 3KG per second, this is just an example to help explain this equation. Using the equation, we can calculate the inertia of our object. Since our object probably has mass, we will create a slightly different version of Einstein’s mass-energy equation, in order to continue.

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Above, E stands for energy, M refers to mass and v2 is for velocity squared. Using the equation for inertia, we can calculate the speed of an object entering the black hole, and then find the conversion rate using the equation above.

6. Conclusion

In conclusion, it is not as difficult to calculate different properties that are exhibited in black holes. With the above content, it should be of no difficult to predict various occurances that may occur in interactions between physical objects and black holes.

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^[1] "Event Horizon and Accretion Disk - Black Holes and Wormholes - The Physics of the Universe."Event Horizon and Accretion Disk - Black Holes and Wormholes - The Physics of the Universe. N.p., n.d. Web. Fall 2016. <http://www.physicsoftheuniverse.com/topics_blackholes_event.html>.

^[2] Das, Santabrata, Idranil Chattopadhyay, Anuj Nandi, and Biplob Sarkar. On the Possibilities of Mass Loss from an Advective Accretion Disc around Stationary Black Holes (2014): n. pag. Arxiv. Web. Winter 2015. <http://arxiv.org/pdf/1405.6895.pdf>.

^[3] Non-occurrence of Trapped Surfaces and Black Holes in Spherical Gravitational Collapse: An Abridged Version (2000): n. pag. Arxiv. Web.

^[4] Evolution of Accretion Disks around Massive Black Holes: Constraints from the Demography of Active Galactic Nuclei (2005): n. pag. Arxiv. Web.

^[5] General Theory of Relativity (1905): n. pag. Web. Fall 2015.

^[6] HAWKING RADIATION AND BLACK HOLE THERMODYNAMICS (2004): n. pag. Web.

^[7] CERN. CERN, n.d. Web. Fall 2016. <http://home.cern/>.

^[8] "Mathematics of Satellite Motion."Mathematics of Satellite Motion. N.p., n.d. Web. Winter 2016. <http://www.physicsclassroom.com/class/circles/Lesson-4/Mathematics-of-Satellite-Motion>.

^[9] The Information Paradox for Black Holes. (2015): n. pag. Web.

^[10] "How Much Mass Makes a Black Hole? - Astronomers Challenge Current Theories."Www.eso.org. N.p., n.d. Web. Winter 2016. <http://www.eso.org/public/news/eso1034/>.