Based on recent progress in quantum gravity and quantum cosmology, we are also presenting a way to estimate the temperature in the cosmos, the Hubble sphere, from a relation between the Planck temperature and the Hubb...Based on recent progress in quantum gravity and quantum cosmology, we are also presenting a way to estimate the temperature in the cosmos, the Hubble sphere, from a relation between the Planck temperature and the Hubble scale. Our analysis predicts the Hubble sphere temperature of 2.72 K with the one standard deviation confidence interval between 2.65 K and 2.80 K, which corresponds well with the measured temperature observed from the cosmic microwave background (CMB) of about 2.72 K. This adds evidence that there is a close connection between the Planck scale, gravity, and the cosmological scales as anticipated by Eddington already in 1918.1.展开更多
This brief note brings the reader up-to-date with the recent successes of the new Haug-Tatum cosmology model. In particular, the significance of recent proof that the Stefan-Boltzmann law applies to such a model is em...This brief note brings the reader up-to-date with the recent successes of the new Haug-Tatum cosmology model. In particular, the significance of recent proof that the Stefan-Boltzmann law applies to such a model is emphasized and a rationale for this is given. Remarkably, the proposed solutions of this model have incorporated all 580 supernova redshifts in the Union2 database. Therefore, one can usefully apply this thermodynamic law in the form of a continually expanding black-body universe model. To our knowledge, no other cosmological model has achieved such high-precision observational correlation.展开更多
This is the first paper in a two part series on black holes. In this work, we concern ourselves with the event horizon. A second follow-up paper will deal with its internal structure. We hypothesize that black holes a...This is the first paper in a two part series on black holes. In this work, we concern ourselves with the event horizon. A second follow-up paper will deal with its internal structure. We hypothesize that black holes are 4-dimensional spatial, steady state, self-contained spheres filled with black-body radiation. As such, the event horizon marks the boundary between two adjacent spaces, 4-D and 3-D, and there, we consider the radiative transfers involving black- body photons. We generalize the Stefan-Boltzmann law assuming that photons can transition between different dimensional spaces, and we can show how for a 3-D/4-D interface, one can only have zero, or net positive, transfer of radiative energy into the black hole. We find that we can predict the temperature just inside the event horizon, on the 4-D side, given the mass, or radius, of the black hole. For an isolated black hole with no radiative heat inflow, we will assume that the temperature, on the outside, is the CMB temperature, T2 = 2.725 K. We take into account the full complement of radiative energy, which for a black body will consist of internal energy density, radiative pressure, and entropy density. It is specifically the entropy density which is responsible for the heat flowing in. We also generalize the Young- Laplace equation for a 4-D/3-D interface. We derive an expression for the surface tension, and prove that it is necessarily positive, and finite, for a 4-D/3-D membrane. This is important as it will lead to an inherently positively curved object, which a black hole is. With this surface tension, we can determine the work needed to expand the black hole. We give two formulations, one involving the surface tension directly, and the other involving the coefficient of surface tension. Because two surfaces are expanding, the 4-D and the 3-D surfaces, there are two radiative contributions to the work done, one positive, which assists expansion. The other is negative, which will resist an increase in volume. The 4-D side promotes expansion whereas the 3-D side hinders it. At the surface itself, we also have gravity, which is the major contribution to the finite surface tension in almost all situations, which we calculate in the second paper. The surface tension depends not only on the size, or mass, of the black hole, but also on the outside surface temperature, quantities which are accessible observationally. Outside surface temperature will also determine inflow. Finally, we develop a “waterfall model” for a black hole, based on what happens at the event horizon. There we find a sharp discontinuity in temperature upon entering the event horizon, from the 3-D side. This is due to the increased surface area in 4-D space, AR(4) = 2π2R3, versus the 3-D surface area, AR(3) = 4πR2. This leads to much reduced radiative pressures, internal energy densities, and total energy densities just inside the event horizon. All quantities are explicitly calculated in terms of the outside surface temperature, and size of a black hole. Any net radiative heat inflow into the black hole, if it is non-zero, is restricted by the condition that, 0cdQ/dt FR(3), where, FR(3), is the 3-D radiative force applied to the event horizon, pushing it in. We argue throughout this paper that a 3-D/3-D interface would not have the same desirable characteristics as a 4-D/3-D interface. This includes allowing for only zero or net positive heat inflow into the black hole, an inherently positive finite radiative surface tension, much reduced temperatures just inside the event horizon, and limits on inflow.展开更多
In this paper, we correct the Stefan–Boltzmann law by considering the generalized uncertainty principle, and with this corrected Stefan–Boltzmann law, the lifespan of the Schwarzschild-de-sitter black holes is calcu...In this paper, we correct the Stefan–Boltzmann law by considering the generalized uncertainty principle, and with this corrected Stefan–Boltzmann law, the lifespan of the Schwarzschild-de-sitter black holes is calculated. We find that the corrected Stefan–Boltzmann law contains two terms, the 46 Tterm and the Tterm. Due to the modifications, at the end of the black hole radiation, it will arise a limited highest temperature and leave a residue. It is interesting to note that the mass of the residue and the Planck mass is in the same order of magnitude. The modified Stefan–Boltzmann law also gives a correction to the lifespan of the black hole, although it is very small.展开更多
文摘Based on recent progress in quantum gravity and quantum cosmology, we are also presenting a way to estimate the temperature in the cosmos, the Hubble sphere, from a relation between the Planck temperature and the Hubble scale. Our analysis predicts the Hubble sphere temperature of 2.72 K with the one standard deviation confidence interval between 2.65 K and 2.80 K, which corresponds well with the measured temperature observed from the cosmic microwave background (CMB) of about 2.72 K. This adds evidence that there is a close connection between the Planck scale, gravity, and the cosmological scales as anticipated by Eddington already in 1918.1.
文摘This brief note brings the reader up-to-date with the recent successes of the new Haug-Tatum cosmology model. In particular, the significance of recent proof that the Stefan-Boltzmann law applies to such a model is emphasized and a rationale for this is given. Remarkably, the proposed solutions of this model have incorporated all 580 supernova redshifts in the Union2 database. Therefore, one can usefully apply this thermodynamic law in the form of a continually expanding black-body universe model. To our knowledge, no other cosmological model has achieved such high-precision observational correlation.
文摘This is the first paper in a two part series on black holes. In this work, we concern ourselves with the event horizon. A second follow-up paper will deal with its internal structure. We hypothesize that black holes are 4-dimensional spatial, steady state, self-contained spheres filled with black-body radiation. As such, the event horizon marks the boundary between two adjacent spaces, 4-D and 3-D, and there, we consider the radiative transfers involving black- body photons. We generalize the Stefan-Boltzmann law assuming that photons can transition between different dimensional spaces, and we can show how for a 3-D/4-D interface, one can only have zero, or net positive, transfer of radiative energy into the black hole. We find that we can predict the temperature just inside the event horizon, on the 4-D side, given the mass, or radius, of the black hole. For an isolated black hole with no radiative heat inflow, we will assume that the temperature, on the outside, is the CMB temperature, T2 = 2.725 K. We take into account the full complement of radiative energy, which for a black body will consist of internal energy density, radiative pressure, and entropy density. It is specifically the entropy density which is responsible for the heat flowing in. We also generalize the Young- Laplace equation for a 4-D/3-D interface. We derive an expression for the surface tension, and prove that it is necessarily positive, and finite, for a 4-D/3-D membrane. This is important as it will lead to an inherently positively curved object, which a black hole is. With this surface tension, we can determine the work needed to expand the black hole. We give two formulations, one involving the surface tension directly, and the other involving the coefficient of surface tension. Because two surfaces are expanding, the 4-D and the 3-D surfaces, there are two radiative contributions to the work done, one positive, which assists expansion. The other is negative, which will resist an increase in volume. The 4-D side promotes expansion whereas the 3-D side hinders it. At the surface itself, we also have gravity, which is the major contribution to the finite surface tension in almost all situations, which we calculate in the second paper. The surface tension depends not only on the size, or mass, of the black hole, but also on the outside surface temperature, quantities which are accessible observationally. Outside surface temperature will also determine inflow. Finally, we develop a “waterfall model” for a black hole, based on what happens at the event horizon. There we find a sharp discontinuity in temperature upon entering the event horizon, from the 3-D side. This is due to the increased surface area in 4-D space, AR(4) = 2π2R3, versus the 3-D surface area, AR(3) = 4πR2. This leads to much reduced radiative pressures, internal energy densities, and total energy densities just inside the event horizon. All quantities are explicitly calculated in terms of the outside surface temperature, and size of a black hole. Any net radiative heat inflow into the black hole, if it is non-zero, is restricted by the condition that, 0cdQ/dt FR(3), where, FR(3), is the 3-D radiative force applied to the event horizon, pushing it in. We argue throughout this paper that a 3-D/3-D interface would not have the same desirable characteristics as a 4-D/3-D interface. This includes allowing for only zero or net positive heat inflow into the black hole, an inherently positive finite radiative surface tension, much reduced temperatures just inside the event horizon, and limits on inflow.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11273009 and 11303006
文摘In this paper, we correct the Stefan–Boltzmann law by considering the generalized uncertainty principle, and with this corrected Stefan–Boltzmann law, the lifespan of the Schwarzschild-de-sitter black holes is calculated. We find that the corrected Stefan–Boltzmann law contains two terms, the 46 Tterm and the Tterm. Due to the modifications, at the end of the black hole radiation, it will arise a limited highest temperature and leave a residue. It is interesting to note that the mass of the residue and the Planck mass is in the same order of magnitude. The modified Stefan–Boltzmann law also gives a correction to the lifespan of the black hole, although it is very small.
