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 blackbody 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, 2 2.725 K T = . 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,

A model is presented where the quintessence parameter, w, is related to a time-varying gravitational constant. Assuming a present value of w = -.98, we predict a current variation of Ġ/G = -.06 H0, a value within current observational bounds. H0 is Hubble's parameter, G is Newton's constant and Ġ is the derivative of G with respect to time. Thus, G has a cosmic origin, is decreasing with respect to cosmological time, and is proportional to H0, as originally proposed by the Dirac-Jordan hypothesis, albeit at a much slower rate. Within our model, we can explain the cosmological constant fine-tuning problem, the discrepancy between the present very weak value of the cosmological constant, and the much greater vacuum energy found in earlier epochs (we assume a connection exists). To formalize and solidify our model, we give two distinct parametrizations of G with respect to "a", the cosmic scale parameter. We treat G -1 as an order parameter, which vanishes at high energies; at low temperatures, it reaches a saturation value, a value we are close to today. Our first parametrization for G -1 is motivated by a charging capacitor; the second treats G -1 (a) by analogy to a magnetic response, i.e., as a Langevin function. Both parametrizations, even though very distinct, give a remarkably similar tracking behavior for w(a), but not of the conventional form, w(a) = w0 + wa (1-a), which can be thought of as only holding over a limited range in "a". Interestingly, both parametrizations indicate the onset of G formation at a temperature of approximately 7 *10 21 degrees Kelvin, in contrast to the ΛCDM model where G is taken as a constant all the way back to the Planck temperature, 1.42 * 10 32 degrees Kelvin. At the temperature of formation, we find that G has increased to roughly 4*10 20 times its present value. For most of cosmic evolution, however, our variable G model gives results similar to the predictions of the ΛCDM model, except in the very early universe, as we shall demonstrate. In fact, in the limit where w approaches -1, Ġ/G vanishes, and we are left with the concordance model. Within our framework, the emergence of dark energy over matter at a scale of a ≈ .5 is that point where G -1 increases noticeably to its current value G0 -1 . This weakening of G to its current value G0 is speculated as the true cause for the observed unanticipated acceleration of the universe.

Based on previous work, it is shown how a time varying gravitational constant can account for the apparent tension between Hubble's constant and a newly predicted age of the universe. The rate of expansion, about nine percent greater than previously estimated, can be accommodated by two specific models, treating the gravitational constant as an order parameter. The deviations from ΛCDM are slight except in the very early universe, and the two time varying parametrizations for G lead to precisely the standard cosmological model in the limit where, 0 G G → , as well as offering a possible explanation for the observed tension. It is estimated that in the current epoch, 0 0.06 G G H = − , where 0 H is Hubble's parameter, a value within current observational bounds. Keywords Universe, Gravitational Constant, Hubble's Constant, Standard Cosmological ModelRecently, it has been observed that the universe is much less old than previouslyThe latest galaxy studies indicate that the rate of expansion is about 9 percent faster than previous estimates. Instead of being 13.8 billion years old, current estimates would indicate the age of the universe at a more modest age of, 12.5 -13 Gyr. As stated by members of the research team concerning the latest findings, "there becomes a very strong likelihood that we're missing something in the cosmological model". As indicated in the title of the work, there now is "stronger evidence for physics beyond ΛCDM".In this short note, we would like to bring to the attention of the reader that a cosmologically time-varying G can accommodate such a result. As a particular

A black hole is treated as a self-contained, steady state, spherically symmetric, 4-dimensional spatial ball filled with blackbody radiation, which is embedded in 3-D space. To model the interior distribution of radiation, we invoke two stellar-like equations, generalized to 4-D space, and a probability distribution function (pdf) for the actual radiative mass distribution within its interior. For our purposes, we choose a truncated Gaussian distribution, although other pdf's with support, ( ), s x γ , and interestingly, scales with a more complicated function of radius.Thus, within our framework, the black hole is a highly-ordered state, in sharp 2 0.1 R M c . This factor of 0.1 is specific to 4-D space. Keywords Black Hole, 4-D Spatial Blackbody Radiation Model, Internal Structure, Radiative Pressure * g T . See references [1] [2] [3] [4]. The black hole, being defined as a steady state ball of radiation in 4-D space, is embedded in 3-D space, much like a gas bubble within a liquid, or, a liquid droplet within a gas. However, the droplet is 4-dimensional, and, as we shall see, not of uniform density. There are three central issues regarding black holes for which we seek an answer. First, what is the nature of the event horizon? Second, what does the internal structure of a black hole look like? And third, can we calculate key thermodynamic variables within the black hole itself? As examples of ther-modynamic quantities, what are the radiative pressure, the internal energy density, the total (radiative mass) energy density, the entropy density, and the gravitational strength within the black hole as functions of, r, the 4-D radius? In the C. Pilot first paper [5], we focused on giving an answer to the first question. In this paper, we will address questions two, and three.In a previous work [5], we presented a model to answer question one. We argued that the event horizon can be thought of as a membrane, where we have a discontinuity in space, which separates the 4-D black hole from the surrounding 3-D space. Access from one space to the other is through the event horizon, which acts as flexible membrane, and which allows for zero or net radiative heat inflow, but no net outflow. The event horizon was assumed to be infinitely thin.The temperature, 1 T , just inside the event horizon in 4-D space is given strictly in terms of the black hole mass, or radius. If the temperature just outside, 2 T , equals 2.725 K, then we will assume that there is no inflow. For higher temperatures, where, 2 2.725 K T > , we will assume net inflow. The amount of radiative heat inflow, d d Q t , depends on the temperature 2 T , as well as on the size, or mass, of the black hole. It can be determined using a generalized version of the Stefan-Boltzmann equation, derived in reference [5], to take into account radiative transfers between adjoining spatial dimensions. With or without net inflow of radiative heat energy, we saw that the temperature drops precipitously upon entering the black hole. This is due to the change in the dimension...

If we assume a closed universe with slight positive curvature, cosmic expansion can modeled as a heat engine where we define the "system", collectively, as those regions of space within the observable universe, which will later evolve into voids/ empty space. We identify the "surroundings", collectively, as those pockets of space, which will eventually develop into matter-filled galaxies, clusters, super-clusters and filament walls. Using this model, we can find the energy needed for cosmic expansion using basic thermodynamic principles, and prove that cosmic expansion had as its origin, a finite initial energy density, pressure, volume, and temperature. Inflation in the traditional sense, with the inflaton field, may also not be required. We will argue that homogeneities and in-homogeneities in the WMAP temperature profile is attributable to quantum mechanical fluctuations about a fixed background temperature in the initial isothermal expansion phase. Fluctuations in temperature can cause certain regions of space to lose heat. Other regions will absorb that heat. The voids are those regions which absorb the heat forcing, i.e., fueling expansion of the latter and creating slightly cooler temperatures in the former, where matter will later congregate. Upon freeze-out, this could produce the observed WMAP signature with its associated CBR fluctuation in magnitude. Finally, we estimate that the freeze-out temperature and the freeze-out time for WMAP in-homogeneities, occurred at roughly 3.02 * 10 27 K and 2.54 * 10 -35 s, respectively, after first initiation of volume expansion. This is in line with current estimates for the end of the inflationary epoch. The heat input in the inflationary phase is estimated to be Q = 1.81 * 10 94 J, and the void volume increases by a factor of only 5.65. The bubble voids in the observable universe increase, collectively, in size from about .046 m 3 to .262 m 3 within this inflationary period.