We found that it is possible to stay conscious falling through the event horizon of aBlack Hole if the mass exceeds 19,000M_sol. This assumes the average person is ofgood health and can stay conscious with a relative force less than 5 g acting upon them

Benham, T J.

Dodds, C

Foxcroft, B

Waters, S J. W.

English

University of Leicester Open Journals

Journal of Physics Special TopicsAn undergraduate physics journalP5 2 Spaghettification: Surviving a Black Hole Event Hori-zonDodds, C. J. C., Benham, T. J., Foxcroft, B., Waters, S. J. WDepartment of Physics and Astronomy, University of Leicester, Leicester, LE1 7RHNovember 8, 2016AbstractWe found that it is possible to stay conscious while falling across the event horizon of a black hole if themass exceeds ≈ 19, 000 Msol. This assumes the average person is of good health and can stay consciouswith a relative force less than 5 g acting upon them.IntroductionBlack holes are among the most mysterious ob-jects in the universe, appearing to devour bothmatter and light, and allowing neither to escapeits enormous gravity. They have a number of fea-tures unique to the extreme environments theycreate, such as the infinitely dense singularitytheorised to be in the centre of the black hole,and the event horizon, the boundary at which ra-diation and matter cannot leave or be observedfrom outside the black hole.In this article we explore the possibility of sur-vival for a human passing through the event hori-zon of various mass black holes. We consider therelative g-forces that may act upon the personfor a given range of black hole masses, and findwhether this reaches a lethal level. Other physi-cal phenomena which may make such a journeydangerous are not considered in depth in this pa-per, as such we are assuming the person appearsinstantly at the event horizon and thus ignor-ing special and general relativity. For simplicitythe body of the person falls feet first perpendic-ular to the event horizon, where ‘inside the eventhorizon’ is the point at which the person’s headhas just passed through the event horizon.Excessive and sustained g-forces can drainblood away from the brain causing cerebral hy-poxia, leading to a loss of consciousness. This isknown as g-force induced loss of consciousness orG-LOC [1]. The g thresholds at which this oc-curs depends on an individual’s fitness, trainingand age, but a figure of 5 g is reasonable [2].TheoryThe acceleration (g) due to gravity is given byEquation (1) [3].g =GMr2(1)Where G is the gravitational constant and isequal to 6.67×10-11 m3kg-1s-2, and M is the massof the object, in this case the black hole. This isused along side Equation (2), the Schwarzschildradius [4] rs - the radius of the black hole’s eventhorizon, which also uses c = 3 × 108 ms-1, thespeed of light - to find expressions (Equations(3) & (4)) to express the gravitational accelera-tion at the head and feet of a person of heightH, where we use a height of 1.65 m.rs =2GMc2(2)Equations (3) and (4) express the gravitationalacceleration at the top of the person’s head atheight H and at the bottom of their feet, respec-tively, falling past the event horizon.ghead =GMr2s(3)gfeet =GM(rs −H)2 (4)Due to the extreme gravitational gradient be-tween the head and the feet, the body would ex-perience severe tidal forces (Equation (5)) caus-ing the phenomenon termed spaghettification,where the body would be severely stretched.∆g = |ghead − gfeet| (5)ResultsAs the mathematics to find a suitable black holemass via analytical methods becomes complex,we employed a graphical method to find the rel-evant masses by inputting varying masses intoEquations (3), (4) and (5) and plotting the ∆g,as shown in Figure 1.Figure 1: This graph shows the range of blackhole masses which would produce tidal forces un-der the g-force limits typical to a human.From this graph, it is clear that a falling personwould still be conscious whilst passing throughthe event horizon of a black hole with a massgreater than ≈ 19, 000 Msol, assuming that theaverage person can withstand less than 5 g.ConclusionThe findings suggest that the larger the blackhole the greater the liklihood of making it pastthe event horizon in good health, when only con-sidering the gravitational effects of a black hole;the force gradient on the infalling human bodyis more gradual the more massive the black holeis. As mentioned previously, a black hole of massgreater than ≈ 19, 000 Msol produces tidal forcesnot lethal to an average healthy human who isexpected to survive less than 5 g of force. Manypeople are capable of surviving forces greaterthan 5 g, such as fighter pilots and astronauts,but to do so have extensive training and equip-ment to help avoid G-LOC. By contrast, theextreme gravitational gradient of a small blackhole would be lethal to the human body, and theaforementioned spaghettification will occur.Though in theory the g-forces experienced asone falls through the event horizon of a mas-sive black hole are gentle enough to survive for ashort period, current models of black holes wouldsuggest that survival is ultimately futile as oneapproaches the infinitely dense singularity in thecentre. Other risks of such an extreme environ-ment must also be considered, such as high ra-diation emissions or other infalling matter whichwould likely pose a serious risk. As such, theauthors recommend future astronauts take pre-cautions to avoid falling into black holes.References[1] https://goo.gl/s3Y4GX (12/10/16)[2] https://goo.gl/5xvrIv (13/10/16)[3] https://goo.gl/WidP0B (13/10/16)[4] Carroll, B, W. and Ostlie, D, A. (2007) AnIntroduction to Modern Astrophysics SecondEdition. San Francisco: Pearson. p. 635

P5_2 Spaghettification: Surviving a Black Hole Event Horizon

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P5_2 Spaghettification: Surviving a Black Hole Event Horizon

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