| Summary: | The minimum entropy is responsible for the formation of dark matter bubbles in a black hole, while the variation in the density of dark matter allows these bubbles to leave the event horizon. Some experimental evidence supports the dark matter production model in the inner vicinity of the border of a black hole. The principle of minima entropy explains how cavitation occurs on the event horizon, which in turn complies with the Navier–Stokes 3D equations. Moreover, current works in an axiomatic way show that in the event horizon Einstein’s equations are equivalent to Navier–Stokes’ equations. Thus, The solutions of Einstein combined with the boundary conditions establish a one-to-one correspondence with solutions of incompressible Navier–Stokes and in the near-horizon limit it provides a precise mathematical sense in which horizons are always incompressible fluids. It is also essential to understand that Cavitation by minimum entropy is the production of dark matter bubbles, by variation of the pressure inside or on the horizon of a black hole, in general <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Δ</mi> <mi>p</mi> <mo>=</mo> <msub> <mi>p</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>p</mi> <mi>n</mi> </msub> <mo>=</mo> <mfenced separators="" open="(" close=")"> <mfrac> <msub> <mi>σ</mi> <mi>n</mi> </msub> <msub> <mi>σ</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mfrac> <mo>−</mo> <mn>1</mn> </mfenced> <msub> <mi>p</mi> <mi>n</mi> </msub> </mrow> </semantics> </math> </inline-formula> or in particular <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Δ</mi> <mi>p</mi> <mo>=</mo> <mo>−</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>−</mo> <mi>P</mi> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mn>0</mn> </msub> </mrow> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mrow> <mfrac> <mrow> <mi>∂</mi> <mi>P</mi> </mrow> <mrow> <mi>∂</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>Δ</mi> <mi>p</mi> </mrow> <msub> <mi>ρ</mi> <mn>0</mn> </msub> </mfrac> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>. Finally, fluctuations in the density of dark matter can facilitate its escape from a black hole, if and only if there is previously dark matter produced by cavitation inside or on the horizon of a black hole and also <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>ρ</mi> <mrow> <mi>D</mi> <mi>M</mi> </mrow> </msub> <mo><</mo> <msub> <mi>ρ</mi> <mi>B</mi> </msub> <mo>.</mo> </mrow> </semantics> </math> </inline-formula>
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