This document is due to reviewing an article by Maydanyuk and Olkhovsky, of a Nova Science conpendium as of “The big bang, theory assumptions and Problems”, as of 2012, which uses the Wheeler De Witt equation as an ...This document is due to reviewing an article by Maydanyuk and Olkhovsky, of a Nova Science conpendium as of “The big bang, theory assumptions and Problems”, as of 2012, which uses the Wheeler De Witt equation as an evolution equation assuming a closed universe. Having the value of k, not as the closed universe, but nearly zero of a nearly flat universe, which leads to serious problems of interpretation of what initial conditions are. These problems of interpretations of initial conditions tie in with difficulties in using QM as an initial driver of inflation. And argue in favor of using a different procedure as far as forming a wave function of the universe initially. The author wishes to thank Abhay Ashtekar for his well thought out criticism but asserts that limitations in space-time geometry largely due to when is formed from semi classical reasoning, i.e. Maxwell’s equation involving a close boundary value regime between Octonionic geometry and flat space non Octonionic geometry is a datum which Abhay Ashekhar may wish to consider in his quantum bounce model and in loop quantum gravity in the future.展开更多
The Heun functions have wide application in modern physics and are expected to succeed the hypergeometrical functions in the physical problems of the 21st century. The numerical work with those functions, however, is ...The Heun functions have wide application in modern physics and are expected to succeed the hypergeometrical functions in the physical problems of the 21st century. The numerical work with those functions, however, is complicated and requires filling the gaps in the theory of the Heun functions and also, creating new algorithms able to work with them efficiently. We propose a new algorithm for solving a system of two nonlinear transcendental equations with two complex variables based on the Müller algorithm. The new algorithm is particularly useful in systems featuring the Heun functions and for them, the new algorithm gives distinctly better results than Newton’s and Broyden’s methods. As an example for its application in physics, the new algorithm was used to find the quasi-normal modes (QNM) of Schwarzschild black hole described by the Regge-Wheeler equation. The numerical results obtained by our method are compared with the already published QNM frequencies and are found to coincide to a great extent with them. Also discussed are the QNM of the Kerr black hole, described by the Teukolsky Master equation.展开更多
A new 'twice loose shoe' method in the Wheeler–DeWitt equation of the universe wavefunction on the cosmic scale factor and a scalar field is suggested. We analyze both the affections coming from the tunnell...A new 'twice loose shoe' method in the Wheeler–DeWitt equation of the universe wavefunction on the cosmic scale factor and a scalar field is suggested. We analyze both the affections coming from the tunnelling effect of and the potential well effect of , and obtain the initial values and about a primary closed universe which is born with the largest probability in the quantum manner. Our result is able to overcome the 'large field difficulty' of the universe quantum creation probability with only tunnelling effect. This new born universe has to suffer a startup of inflation, and then comes into the usual slow rolling inflation. The universe with the largest probability maybe has a 'gentle' inflation or an eternal chaotic inflation, this depends on a new parameter which describes the tunnelling character.展开更多
Using Hall and Reginatto’s condition for a Wheeler De Witt Equation for a Friedman-Walker metric coupled to a (Inflaton) scalar field Φ, we delineate the outer boundary of the value of a scale factor a (t) for quant...Using Hall and Reginatto’s condition for a Wheeler De Witt Equation for a Friedman-Walker metric coupled to a (Inflaton) scalar field Φ, we delineate the outer boundary of the value of a scale factor a (t) for quantum effects, in an expanding universe. The inflaton field is from Padmanabhan’s reference, “An Invitation to Astrophysics” which yields a nonstandard Potential U (a, Φ) which will lead to an algebraic expression for a (t) for the value of the outer boundary of quantum effects in the universe. Afterwards, using the scale factor a (t)=ainitial·tα, with alpha given different values, we give an estimation as to a time, t (time) which is roughly the boundary of the range of quantum effects. How this is unusual? We use the Wheeler De Witt Equation, as a coupling to a given inflaton field Φ and find a different way as to delineate a time regime for the range of quantum effects in an expanding universe.展开更多
The stability problem of the Rindler spacetime is carefully studies by using the scalar wave perturbation. Using two different coordinate systems, the scalar wave equation is investigated. The results are different in...The stability problem of the Rindler spacetime is carefully studies by using the scalar wave perturbation. Using two different coordinate systems, the scalar wave equation is investigated. The results are different in the two cases. They are analysed and compared with each other in detail. The following conclusions are obtained： （a） the Rindler spacetime as a whole is not stable; （b） the Rindler spacetime can exist stably only as part of the Minkowski spacetime, and the Minkowski spacetime can be a real entity independently; （c） there are some defects for the scalar wave equation written by the Rindler coordinates, and it is unsuitable for the investigation of the stability properties of the Rindler spacetime. All these results may shed some light on the stability properties of the Schwarzschild black hole. It is natural and reasonable for one to infer that： （a） perhaps the Regge-Wheeler equation is not sufficient to determine the stable properties; （b） the Schwarzschild black hole as a whole might be really unstable; （c） the Kruskal spacetime is stable and can exist as a real physical entity; whereas the Schwarzschild black hole can occur only as part of the Kruskal spacetime.展开更多
In this paper we will analyze the third quantization of gravity in path integral formalism. We will use the time-dependent version of Wheeler–DeW itt equation to analyze the multiverse in this formalism. We will prop...In this paper we will analyze the third quantization of gravity in path integral formalism. We will use the time-dependent version of Wheeler–DeW itt equation to analyze the multiverse in this formalism. We will propose a mechanism for baryogenesis to occur in the multiverse, without violating the baryon number conservation.展开更多
The quantum cosmology with the scalar-spinor interaction of σ model is analyzed by means of Hartle and Hawking’s method. The Wheeler-DeWitt equation is obtained and the corresponding wave function of the universe so...The quantum cosmology with the scalar-spinor interaction of σ model is analyzed by means of Hartle and Hawking’s method. The Wheeler-DeWitt equation is obtained and the corresponding wave function of the universe solved. The obtained asymptotic solution of the wave function indicates that in the σ model the contribution of the spinor part is notable when the scalar factor α is very small, and the expression of the solution is related to the initial conditions. When the scalar factor α is great, the contribution of the spinor part is not significant and has the same conduct as the scalar part.展开更多
文摘This document is due to reviewing an article by Maydanyuk and Olkhovsky, of a Nova Science conpendium as of “The big bang, theory assumptions and Problems”, as of 2012, which uses the Wheeler De Witt equation as an evolution equation assuming a closed universe. Having the value of k, not as the closed universe, but nearly zero of a nearly flat universe, which leads to serious problems of interpretation of what initial conditions are. These problems of interpretations of initial conditions tie in with difficulties in using QM as an initial driver of inflation. And argue in favor of using a different procedure as far as forming a wave function of the universe initially. The author wishes to thank Abhay Ashtekar for his well thought out criticism but asserts that limitations in space-time geometry largely due to when is formed from semi classical reasoning, i.e. Maxwell’s equation involving a close boundary value regime between Octonionic geometry and flat space non Octonionic geometry is a datum which Abhay Ashekhar may wish to consider in his quantum bounce model and in loop quantum gravity in the future.
文摘The Heun functions have wide application in modern physics and are expected to succeed the hypergeometrical functions in the physical problems of the 21st century. The numerical work with those functions, however, is complicated and requires filling the gaps in the theory of the Heun functions and also, creating new algorithms able to work with them efficiently. We propose a new algorithm for solving a system of two nonlinear transcendental equations with two complex variables based on the Müller algorithm. The new algorithm is particularly useful in systems featuring the Heun functions and for them, the new algorithm gives distinctly better results than Newton’s and Broyden’s methods. As an example for its application in physics, the new algorithm was used to find the quasi-normal modes (QNM) of Schwarzschild black hole described by the Regge-Wheeler equation. The numerical results obtained by our method are compared with the already published QNM frequencies and are found to coincide to a great extent with them. Also discussed are the QNM of the Kerr black hole, described by the Teukolsky Master equation.
文摘A new 'twice loose shoe' method in the Wheeler–DeWitt equation of the universe wavefunction on the cosmic scale factor and a scalar field is suggested. We analyze both the affections coming from the tunnelling effect of and the potential well effect of , and obtain the initial values and about a primary closed universe which is born with the largest probability in the quantum manner. Our result is able to overcome the 'large field difficulty' of the universe quantum creation probability with only tunnelling effect. This new born universe has to suffer a startup of inflation, and then comes into the usual slow rolling inflation. The universe with the largest probability maybe has a 'gentle' inflation or an eternal chaotic inflation, this depends on a new parameter which describes the tunnelling character.
文摘Using Hall and Reginatto’s condition for a Wheeler De Witt Equation for a Friedman-Walker metric coupled to a (Inflaton) scalar field Φ, we delineate the outer boundary of the value of a scale factor a (t) for quantum effects, in an expanding universe. The inflaton field is from Padmanabhan’s reference, “An Invitation to Astrophysics” which yields a nonstandard Potential U (a, Φ) which will lead to an algebraic expression for a (t) for the value of the outer boundary of quantum effects in the universe. Afterwards, using the scale factor a (t)=ainitial·tα, with alpha given different values, we give an estimation as to a time, t (time) which is roughly the boundary of the range of quantum effects. How this is unusual? We use the Wheeler De Witt Equation, as a coupling to a given inflaton field Φ and find a different way as to delineate a time regime for the range of quantum effects in an expanding universe.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10475013, 10375087 and 10373003）, the National Basic Research Program （Grant No 2004CB318000） and National Science Foundation for Post-Doctoral Scientists of China.
文摘The stability problem of the Rindler spacetime is carefully studies by using the scalar wave perturbation. Using two different coordinate systems, the scalar wave equation is investigated. The results are different in the two cases. They are analysed and compared with each other in detail. The following conclusions are obtained： （a） the Rindler spacetime as a whole is not stable; （b） the Rindler spacetime can exist stably only as part of the Minkowski spacetime, and the Minkowski spacetime can be a real entity independently; （c） there are some defects for the scalar wave equation written by the Rindler coordinates, and it is unsuitable for the investigation of the stability properties of the Rindler spacetime. All these results may shed some light on the stability properties of the Schwarzschild black hole. It is natural and reasonable for one to infer that： （a） perhaps the Regge-Wheeler equation is not sufficient to determine the stable properties; （b） the Schwarzschild black hole as a whole might be really unstable; （c） the Kruskal spacetime is stable and can exist as a real physical entity; whereas the Schwarzschild black hole can occur only as part of the Kruskal spacetime.
文摘In this paper we will analyze the third quantization of gravity in path integral formalism. We will use the time-dependent version of Wheeler–DeW itt equation to analyze the multiverse in this formalism. We will propose a mechanism for baryogenesis to occur in the multiverse, without violating the baryon number conservation.
文摘The quantum cosmology with the scalar-spinor interaction of σ model is analyzed by means of Hartle and Hawking’s method. The Wheeler-DeWitt equation is obtained and the corresponding wave function of the universe solved. The obtained asymptotic solution of the wave function indicates that in the σ model the contribution of the spinor part is notable when the scalar factor α is very small, and the expression of the solution is related to the initial conditions. When the scalar factor α is great, the contribution of the spinor part is not significant and has the same conduct as the scalar part.
