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
This paper reports that the directional temperature is used to present a scheme for deducing the velocity of the reference frame where the black-body which produces the 2.7 K radiation background is at rest. The new r...This paper reports that the directional temperature is used to present a scheme for deducing the velocity of the reference frame where the black-body which produces the 2.7 K radiation background is at rest. The new renormalized relativistic thermodynamics lays the foundations of the method.展开更多
Taking a black hole as a black body system, using general black body radiation theory, a Schwarzschild black hole and a Kerr-Newman black hole are investigated respectively. It is concluded that a black hole can be re...Taking a black hole as a black body system, using general black body radiation theory, a Schwarzschild black hole and a Kerr-Newman black hole are investigated respectively. It is concluded that a black hole can be regarded as an ideal general black body system exactly for the changing process only. However, a stationary global black hole cannot be smoothly regarded as a general black body system. A black hole has some special characteristics which different from a general thermodynamics system. This conclusion means that a black hole should be inherently dynamical, at least when it is taken as a black body system.展开更多
The inverse black body radiation problem, which is to reconstruct the area temperature distribution from the measurement of power spectrum distribution, is a well-known ill-posed problem. In this paper, a variational ...The inverse black body radiation problem, which is to reconstruct the area temperature distribution from the measurement of power spectrum distribution, is a well-known ill-posed problem. In this paper, a variational expectation-maximization （EM） method is developed and its convergence is studied. Numerical experiments demonstrate that the variational EM method is more efficient and accurate than the traditional methods, including the Tikhonov regularization method, the Landweber method and the conjugate gradient method.展开更多
We present the results obtained from detailed timing and spectral studies of a black hole candidate MAXI J1813-095 using Swift,NICER,and NuSTAR observations during its 2018 outburst.The timing behavior of the source i...We present the results obtained from detailed timing and spectral studies of a black hole candidate MAXI J1813-095 using Swift,NICER,and NuSTAR observations during its 2018 outburst.The timing behavior of the source is mainly studied by examining NICER light curves in the 0.5−10 keV range.We did not find any signature of quasi-periodic oscillations in the power density spectra of the source.We carry out spectral analysis with a combined disk blackbody&power law model,and physical two-component advective flow(TCAF)model.From the combined disk blackbody&power-law model,we extracted thermal and non-thermal fluxes,photon index and inner disk temperature.We also find evidence for weak reflection in the spectra.We have tested the physical TCAF model on a broadband spectrum from NuSTAR and Swift/XRT.The parameters like mass accretion rates,the size of Compton clouds and the shock strength are extracted.Our result affirms that the source remained in the hard state during the entire outburst which indicates a‘failed’outburst.We estimate the mass of the black hole as 7.4±1.5M⊙from the spectral study with the TCAF model.We apply the LAOR model for the Fe K line emission.From this,the spin parameter of the black hole is ascertained as a^(∗)>0.76.The inclination angle of the system is estimated to be in the range of 28°−45°from the reflection model.We find the source distance to be∼6 kpc.展开更多
The radical hypothesis concerning the physics of gravitational black-body radiation is placed on a more solid statistical mechanics foundation in this study. As the concepts and formalism in the former presentation ar...The radical hypothesis concerning the physics of gravitational black-body radiation is placed on a more solid statistical mechanics foundation in this study. As the concepts and formalism in the former presentation are only partially developed and furthermore, suffer from an unfortunate misstep regarding Hawking radiation and the hypothetical gravitational black-body temperature of a parcel or distribution of energy;this paper aims to fill in some of the theoretical gaps in the derivation of the Planck radiation formula for gravity (or non-Euclidean space-time), and there by provide a more complete and transparent quantum theory of thermal gravitational radiation.展开更多
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Project partially supported by COFFA and EDI,IPN
文摘This paper reports that the directional temperature is used to present a scheme for deducing the velocity of the reference frame where the black-body which produces the 2.7 K radiation background is at rest. The new renormalized relativistic thermodynamics lays the foundations of the method.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10773002 and 10875012)the National Basic Research Program of China (Grant No. 2003CB716302)
文摘Taking a black hole as a black body system, using general black body radiation theory, a Schwarzschild black hole and a Kerr-Newman black hole are investigated respectively. It is concluded that a black hole can be regarded as an ideal general black body system exactly for the changing process only. However, a stationary global black hole cannot be smoothly regarded as a general black body system. A black hole has some special characteristics which different from a general thermodynamics system. This conclusion means that a black hole should be inherently dynamical, at least when it is taken as a black body system.
基金the National Basic Research Program of China (2006CB705700)the National Science Foundation of China(60532080)Microsoft Research of Asia
文摘The inverse black body radiation problem, which is to reconstruct the area temperature distribution from the measurement of power spectrum distribution, is a well-known ill-posed problem. In this paper, a variational expectation-maximization （EM） method is developed and its convergence is studied. Numerical experiments demonstrate that the variational EM method is more efficient and accurate than the traditional methods, including the Tikhonov regularization method, the Landweber method and the conjugate gradient method.
基金This research has made use of data and/or software provided by the High Energy Astrophysics Science Archive Research Center(HEASARC)which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory+5 种基金This research has made use of the NuSTAR Data Analysis Software(NuSTARDAS)jointly developed by the ASI Science Data Center(ASDC,Italy)California Institute of Technology(Caltech,USA)This work has made use of XRT data supplied by the UK Swift Science Data Centre at the University of Leicester,UK.A.J.and N.K.acknowledge support from the research fellowship from Physical Research Laboratory,Ahmedabad,Indiafunded by the Department of Space,Government of India for this work.K.C.acknowledges support from the DST/INSPIRE Fellowship(IF170233)R.B.acknowledges support from the CSIR-UGC NET qualified UGC fellowship(June-2018,527223)Research by S.K.C.and D.D.is supported in part by the Higher Education Dept.of the Govt.of West Bengal,India.S.K.C.and D.D.also acknowledge partial support from ISRO sponsored RESPOND project(ISRO/RES/2/418/17-18)fund.H.-K.C.is supported by MOST of Taiwan under grants MOST/106-2923-M-007-002-MY3 and MOST/108-2112-M-007-003.D.D.acknowledges support from DST/GITA sponsored India-Taiwan collaborative project(GITA/DST/TWN/P-76/2017)fund.
文摘We present the results obtained from detailed timing and spectral studies of a black hole candidate MAXI J1813-095 using Swift,NICER,and NuSTAR observations during its 2018 outburst.The timing behavior of the source is mainly studied by examining NICER light curves in the 0.5−10 keV range.We did not find any signature of quasi-periodic oscillations in the power density spectra of the source.We carry out spectral analysis with a combined disk blackbody&power law model,and physical two-component advective flow(TCAF)model.From the combined disk blackbody&power-law model,we extracted thermal and non-thermal fluxes,photon index and inner disk temperature.We also find evidence for weak reflection in the spectra.We have tested the physical TCAF model on a broadband spectrum from NuSTAR and Swift/XRT.The parameters like mass accretion rates,the size of Compton clouds and the shock strength are extracted.Our result affirms that the source remained in the hard state during the entire outburst which indicates a‘failed’outburst.We estimate the mass of the black hole as 7.4±1.5M⊙from the spectral study with the TCAF model.We apply the LAOR model for the Fe K line emission.From this,the spin parameter of the black hole is ascertained as a^(∗)>0.76.The inclination angle of the system is estimated to be in the range of 28°−45°from the reflection model.We find the source distance to be∼6 kpc.
文摘The radical hypothesis concerning the physics of gravitational black-body radiation is placed on a more solid statistical mechanics foundation in this study. As the concepts and formalism in the former presentation are only partially developed and furthermore, suffer from an unfortunate misstep regarding Hawking radiation and the hypothetical gravitational black-body temperature of a parcel or distribution of energy;this paper aims to fill in some of the theoretical gaps in the derivation of the Planck radiation formula for gravity (or non-Euclidean space-time), and there by provide a more complete and transparent quantum theory of thermal gravitational radiation.
基金Supported by the National Natural Science Foundation of China(60572125)the Basic Scientific Research Foundation of Harbin Engineering University(002110260736)
