Is it possible to quantify in General Relativity, GR, the entropy generated by Super-Massive Black Holes, SMBH, during its evaporation time, since the intrinsic Hawking radiation in the infinity that, although insignificant, is important in the effects on the thermal quantum atmosphere? The purpose was to develop a formula that allows us to measure the entropy generated during the evaporation time of different types of SMBH of: i. remnant BH of the binary black holes’ merger, BBH: GW150914, GW151226 and LTV151012 detected by the Laser Interferometer Gravitational-Wave Observatory, LIGO, and ii. Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman, and thus quantify in GR the “insignificant” quantum effects involved, in order to contribute to the validity of the generalized second law, GSL, that directly links the laws of black hole mechanics to the ordinary laws of thermodynamics, as a starting point for unifying quantum effects with GR. This formula could have some relationship with the detection of the shadow’s image of the event horizon of a BH. This formula was developed in dimensional analysis, using the constants of nature and the possible evaporation time of a black hole, to quantify the entropy generated during that time. The energy-stress tensor was calculated with the 4 metrics to obtain the material content and apply the proposed formula. The entropy of the evaporation time of SMBH proved to be insignificant, its temperature is barely above absolute zero, however, the calculation of this type of entropy allows us to argue about the importance of the quantum effects of Hawking radiation mentioned by authors who have studied the quantum effects with arguments that are fundamentally based on the presence of the surrounding thermal atmosphere of the BH.

Abstract. In a universe in indefinite expansion, undetermined amounts of dark material suspended in the space-time continuum exist. The case of 'sufficient' amount of material contracted throughout time due to its density can occur. Using relativistic equations, in the present work a thermodynamic system was considered whose volume of control is limited by a gigantic mass that is suspended in space in order to predict its behavior. Given the obtained results, evidence of a certain quantized dark material in process of collapse or collapsed into a black hole can be argued. The heat transfer of the black hole was measure through entropy change with respect to the time and other forms of energy, it was determined that the hole emits particles to surroundings from its event horizon (black hole 'shining'). The emissions are proportional to the disappearance of the hole; they are candidates to integrate the "baby universes" of Hawking with new histories that satisfy the theorem "a black hole has no hair". IntroductionSolutions of the relativistic equations that give place to singularities [1] in real time and/or in imaginary time, allow predicting a behavior of masses in space-time. Here the universe is a gigantic mass bordered by a volume of control in a thermodynamic system [2,3]. The simulation of the model obtained by means of relativistic equations [4][5][6][7][8][9], throws data of something similar to dark material that is scattered in the universe and confined in "baby universes" [10] probably constituent of black holes, white dwarfs or neutrinos stars, such as the particles of the gigantic mass were contracted to a field of enormous gravity [10][11][12]. The baby universes, that take the particles that fell into the hole, occur in what is called, imaginary time. Also, the obtained results allow predicting a closed link between the black holes and thermodynamic science by means of predictions of the entropy that presents the black hole when it emits particles from its event horizon [13]. The heat transfer in black holes measured through the entropy with respect to other forms of energy that take place during their emissions, is the responsible of the new histories of the particles thrown towards the surroundings. The solution obtained for the postulated metric give a place to imaginary numbers that allow glimpsing material with quantized energy. The theorem "a black hole has no hair" [14][15][16][17][18][19][20][21], concludes that the behavior of the gigantic mass compressed to a black hole with the mass of a mountain, is conceived by the quantum mechanics like a microscopic radius particle smaller than the radius of a neutron or a proton, which allows to demonstrate an intrinsic bond between General Relativity and the Quantum Theory through the Quantum Gravity.

Cosmic censorship!: black hole wrapped up by its entropy and hidden by its event horizon. In this paper, we postulate a metric to solve the Einstein equations of general relativity, which predicts the thermodynamic behavior of a gigantic mass that collapses to a black hole; taking into account the third law of thermodynamics that states that neither physical process can produce a naked singularity. However, under certain conditions, the model allows to evident violation to the cosmic censorship, exposing the hole nakedness. During the collapse of the hole, quantum effects appear: the area decrease and radiation produced has a high entropy, so that increases total entropy and expose the presence of the hole, while the appearance of the event horizon hide the singularity of the exterior gazes. It is verified that in certain circumstances, the model predicts that the hole mass is bigger than its angular momentum; and in all circumstances, this predicts an hole with enormous superficial graveness that satisfy a relationship of the three parameters that describe the hole (mass, charge and angular momentum); factors all indicative that the singularity is not naked. Then, there are no apparent horizons in accord with cosmic censorship conjecture. Even though the surface gravity of the hole prevents destroying its horizon wrapping singularity, there exists evidence of this singularity by the results of the spin-mass relationship and the escape velocity obtained. The lost information and the slow rate of rotation of the semi-major axis of the mass (dragging space and time around itself as it rotates), agree with Einstein's prediction, show the transport of energy through heat and mass transfer, which were measured by entropy of the hole by means of coordinated semi-spherical that include the different types of intrinsic energy to the process of radiation of the hole event horizon.

In this work it is presented the modeling and simulation of energy transfer and fluid flow of a stationary spherical arrangement of particles surrounding a gravitational body such as an astrophysical object that carries the curvature of space-time continuum in general relativity, taking into account the thermodynamics of the second law. This model also predicts the drag of space and time around an astrophysical object as it rotates, with results close to the experimental data reported by other authors. To model the energy transfer of the mass and the fluid flow in the space-time, it is used a 4-dimensional system. In order to make measurements of entropy in the arrow of time (past-present), tensors in General Relativity were used to calculate this thermodynamic quantity and with this, the big bang ́s low entropy condition in phase space of coarse graining (Hawking ́s box), according to Weyl curvature hypothesis (WCH) of Roger Penrose. Contribution of this paper is presented by tensors which carry information that has to do with something as non-distortion effect in fluid flow around the astrophysical object and the low entropy condition that is believed to exist in the past, in the big bang;what leads us to search for a new physical-mathematical science to continue. At this point, the Einstein field equations are out of context, which leads us to conclude that it is necessary a mathematical science that allows us to make calculations to rescue lost information due to collapse of matter to a black hole. This math should allow us to clear up physical phenomena (like origin of the universe) and their relationship, with the objective of unifying theories that lead to a physical science without uncertainties, as at the present time. In this regard, we propose a metric in hyperbolic coodinates to build a physical wormhole shaped object where gravitational bodies can be housed that allow us to link the past entropy with the present entropy according to the second law of thermodynamics, as a kind of mathematical space or alternative model to compensate in some way, the link between WCH and the phase space volume of the Hawking's box, and the link between WCH and the quantum-mechanical state-vector reduction, , proposed by Penrose which still have not been determined by any author. Nomenclature

In this paper it is presented a mathematical model in the context of physics/transport/diffusion/dispersion about a contaminant that is a product of wood fiber cooking in a pulp cellulose plant, which is currently being thrown in a lagoon that does not have any water treatment process. The objective is improving the environmental conditions prevailing according to an environmental technology program of water treatment process required by the Government of Mexico through regulations and certifications in water treatment industries, and the prediction of the involvement of the contaminant in fishes from the Lagoon.