Pub Date : 2020-02-13DOI: 10.5772/intechopen.90482
P. Gusin, Andy T. Augousti, A. Radosz
The supermassive black hole located in the galaxy M87 (BH M87) is four times larger than our solar system. If it is spherically symmetric, then a capsule free falling from a distance of 1 light year would cross BHM87’s event horizon within some tens of years. Continuing that journey, any unfortunate astronomer traveling within the capsule would remain alive for a few further tens of hours; if the capsule were equipped with a powerful engine and could slow down, their lifetime inside the horizon beyond “the gates of Hell”would be slightly extended. How is this so?What are the other properties of the interior of BH M87? Maintaining the assumption of spherical symmetry of the exterior of BH M87, we briefly discuss some simple but intriguing properties of its interior, a region that turns out to be highly anisotropic, both expanding and contracting at the same time.
{"title":"BH M87: Beyond the Gates of Hell","authors":"P. Gusin, Andy T. Augousti, A. Radosz","doi":"10.5772/intechopen.90482","DOIUrl":"https://doi.org/10.5772/intechopen.90482","url":null,"abstract":"The supermassive black hole located in the galaxy M87 (BH M87) is four times larger than our solar system. If it is spherically symmetric, then a capsule free falling from a distance of 1 light year would cross BHM87’s event horizon within some tens of years. Continuing that journey, any unfortunate astronomer traveling within the capsule would remain alive for a few further tens of hours; if the capsule were equipped with a powerful engine and could slow down, their lifetime inside the horizon beyond “the gates of Hell”would be slightly extended. How is this so?What are the other properties of the interior of BH M87? Maintaining the assumption of spherical symmetry of the exterior of BH M87, we briefly discuss some simple but intriguing properties of its interior, a region that turns out to be highly anisotropic, both expanding and contracting at the same time.","PeriodicalId":270584,"journal":{"name":"Progress in Relativity","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117229398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-15DOI: 10.5772/intechopen.90282
Akuro Big-Alabo, C. Ossia
Conservative systems represent a large number of naturally occurring and artificially designed scientific and engineering systems. A key consideration in the theory and application of nonlinear conservative systems is the solution of the governing nonlinear ordinary differential equation. This chapter surveys the recent approximate analytical schemes for the periodic solution of nonlinear conservative systems and presents a recently proposed approximate analytical algorithm called continuous piecewise linearization method (CPLM). The advantage of the CPLM over other analytical schemes is that it combines simplicity and accuracy for strong nonlinear and large-amplitude oscillations irrespective of the complexity of the nonlinear restoring force. Hence, CPLM solutions for typical nonlinear Hamiltonian systems are presented and discussed. Also, the CPLM solution for an example of a non-Hamiltonian conservative oscillator was presented. The chapter is aimed at showcasing the potential and benefits of the CPLM as a reliable and easily implementable scheme for the periodic solution of conservative systems.
{"title":"Periodic Solution of Nonlinear Conservative Systems","authors":"Akuro Big-Alabo, C. Ossia","doi":"10.5772/intechopen.90282","DOIUrl":"https://doi.org/10.5772/intechopen.90282","url":null,"abstract":"Conservative systems represent a large number of naturally occurring and artificially designed scientific and engineering systems. A key consideration in the theory and application of nonlinear conservative systems is the solution of the governing nonlinear ordinary differential equation. This chapter surveys the recent approximate analytical schemes for the periodic solution of nonlinear conservative systems and presents a recently proposed approximate analytical algorithm called continuous piecewise linearization method (CPLM). The advantage of the CPLM over other analytical schemes is that it combines simplicity and accuracy for strong nonlinear and large-amplitude oscillations irrespective of the complexity of the nonlinear restoring force. Hence, CPLM solutions for typical nonlinear Hamiltonian systems are presented and discussed. Also, the CPLM solution for an example of a non-Hamiltonian conservative oscillator was presented. The chapter is aimed at showcasing the potential and benefits of the CPLM as a reliable and easily implementable scheme for the periodic solution of conservative systems.","PeriodicalId":270584,"journal":{"name":"Progress in Relativity","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126753564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-22DOI: 10.5772/intechopen.90360
M. Agop, C. Buzea, D. Vasincu, D. Timofte
A theory of space-time is built on a fractal/multifractal variety. Thus, consider-ing that both the spatial coordinates and the time are fractal/multifractal, it is shown that both the energy and the non-differentiable mass of any biostructure depend on both the “ state ” of the biostructure and a speed limit of constant value. For the dynamics on Peano fractal/multifractal curves and Compton scale resolutions, it is shown that our results are reduced to those of Einstein relativity. In such a context, it has been shown that the “ chameleon effect ” of cholesterol corresponds to the HDL-LDL state transfer dictated by the spontaneous symmetry breaking through a fractal/multifractal tunnel effect. Then both HDL and LDL become distinct states of the same biostructure as in nuclear physics where proton and neutron are distinct states of the same nucleon. time transfer probability HDL $ LDL, and we show that the HDL ! LDL process is more probable than the inverse one.
{"title":"Dynamics of Biostructures on a Fractal/Multifractal Space-Time Manifold","authors":"M. Agop, C. Buzea, D. Vasincu, D. Timofte","doi":"10.5772/intechopen.90360","DOIUrl":"https://doi.org/10.5772/intechopen.90360","url":null,"abstract":"A theory of space-time is built on a fractal/multifractal variety. Thus, consider-ing that both the spatial coordinates and the time are fractal/multifractal, it is shown that both the energy and the non-differentiable mass of any biostructure depend on both the “ state ” of the biostructure and a speed limit of constant value. For the dynamics on Peano fractal/multifractal curves and Compton scale resolutions, it is shown that our results are reduced to those of Einstein relativity. In such a context, it has been shown that the “ chameleon effect ” of cholesterol corresponds to the HDL-LDL state transfer dictated by the spontaneous symmetry breaking through a fractal/multifractal tunnel effect. Then both HDL and LDL become distinct states of the same biostructure as in nuclear physics where proton and neutron are distinct states of the same nucleon. time transfer probability HDL $ LDL, and we show that the HDL ! LDL process is more probable than the inverse one.","PeriodicalId":270584,"journal":{"name":"Progress in Relativity","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121123458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-13DOI: 10.5772/intechopen.88069
S. Yoo-Kong
The alternative Hamiltonians for systems with one degree of freedom are solved directly from the Hamilton ’ s equations. These new Hamiltonians produce the same equation of motion with the standard one (called the Newtonian Hamiltonian). Furthermore, new Hamiltonians come with an extra-parameter, which can be used to recover the standard Hamiltonian.
{"title":"On the Nonuniqueness of the Hamiltonian for Systems with One Degree of Freedom","authors":"S. Yoo-Kong","doi":"10.5772/intechopen.88069","DOIUrl":"https://doi.org/10.5772/intechopen.88069","url":null,"abstract":"The alternative Hamiltonians for systems with one degree of freedom are solved directly from the Hamilton ’ s equations. These new Hamiltonians produce the same equation of motion with the standard one (called the Newtonian Hamiltonian). Furthermore, new Hamiltonians come with an extra-parameter, which can be used to recover the standard Hamiltonian.","PeriodicalId":270584,"journal":{"name":"Progress in Relativity","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131168148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-03DOI: 10.5772/intechopen.90267
A. Kaczmarek, A. Radosz
Dark matter is an invisible substance that seems to make almost 85% of all the mass and roughly 26% of mass-energy content of our Universe. We briefly present the history of its discovery, and we discuss the main attempts to resolve the problem of the origin of dark matter. Those attempts are as follows: dark matter particles (WIMPs), unseen astrophysical objects (MACHOs), or interactions of dark matter with ordinary (luminous) matter. We also introduce a different approach claiming no need for existence of the dark matter (MOND) and recent findings about the ultra-diffuse galaxies. Finally we present 21-cm line observations of neutral hydrogen in the Milky Way made by using 3 m in diameter radio telescope in the Astronomical Observatory of the Jagiellonian University. These studies yield rotational curve of our galaxy. Rotational curve we obtained is compared to those present in literature and constitutes a proof of presence of dark matter in the Milky Way.
{"title":"Dark Matter within the Milky Way","authors":"A. Kaczmarek, A. Radosz","doi":"10.5772/intechopen.90267","DOIUrl":"https://doi.org/10.5772/intechopen.90267","url":null,"abstract":"Dark matter is an invisible substance that seems to make almost 85% of all the mass and roughly 26% of mass-energy content of our Universe. We briefly present the history of its discovery, and we discuss the main attempts to resolve the problem of the origin of dark matter. Those attempts are as follows: dark matter particles (WIMPs), unseen astrophysical objects (MACHOs), or interactions of dark matter with ordinary (luminous) matter. We also introduce a different approach claiming no need for existence of the dark matter (MOND) and recent findings about the ultra-diffuse galaxies. Finally we present 21-cm line observations of neutral hydrogen in the Milky Way made by using 3 m in diameter radio telescope in the Astronomical Observatory of the Jagiellonian University. These studies yield rotational curve of our galaxy. Rotational curve we obtained is compared to those present in literature and constitutes a proof of presence of dark matter in the Milky Way.","PeriodicalId":270584,"journal":{"name":"Progress in Relativity","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128223978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-27DOI: 10.5772/INTECHOPEN.86980
S. Prijmenko, K. Lukin
A finite-length segment of filamentous relativistic electron beam (REB), moving uniformly in vacuum, radiates hybrid electromagnetic waves, compound of potential and vortex electric fields, as well as a vortex magnetic field. The strengths of electric and magnetic fields radiated by the segment edges have the opposite signs. The electromagnetic fields in the wave zone are considered as superposition of the electromagnetic waves radiated by the beginning and the end of the REB segment, which, in particular, leads to formation of the field ’ s interference components . In both the near and the intermediate zones, there is a flow of electrical energy due to the electric potential field and the field of displacement current.
{"title":"Radiation and Energy Flux of Electromagnetic Fields by a Segment of Relativistic Electron Beam Moving Uniformly in Vacuum","authors":"S. Prijmenko, K. Lukin","doi":"10.5772/INTECHOPEN.86980","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.86980","url":null,"abstract":"A finite-length segment of filamentous relativistic electron beam (REB), moving uniformly in vacuum, radiates hybrid electromagnetic waves, compound of potential and vortex electric fields, as well as a vortex magnetic field. The strengths of electric and magnetic fields radiated by the segment edges have the opposite signs. The electromagnetic fields in the wave zone are considered as superposition of the electromagnetic waves radiated by the beginning and the end of the REB segment, which, in particular, leads to formation of the field ’ s interference components . In both the near and the intermediate zones, there is a flow of electrical energy due to the electric potential field and the field of displacement current.","PeriodicalId":270584,"journal":{"name":"Progress in Relativity","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129676850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-11DOI: 10.5772/intechopen.89179
Joás Venâncio, C. Batista
The exact electrically charged solutions to the Dirac equation in higher-dimensional generalized Nariai spacetimes are obtained. Using these solutions, the boundary conditions leading to quasinormal modes of the Dirac field are analyzed, and their correspondent quasinormal frequencies are analytically calculated.
{"title":"Quasinormal Modes of Dirac Field in Generalized Nariai Spacetimes","authors":"Joás Venâncio, C. Batista","doi":"10.5772/intechopen.89179","DOIUrl":"https://doi.org/10.5772/intechopen.89179","url":null,"abstract":"The exact electrically charged solutions to the Dirac equation in higher-dimensional generalized Nariai spacetimes are obtained. Using these solutions, the boundary conditions leading to quasinormal modes of the Dirac field are analyzed, and their correspondent quasinormal frequencies are analytically calculated.","PeriodicalId":270584,"journal":{"name":"Progress in Relativity","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131236226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-25DOI: 10.5772/intechopen.87946
V. Gladyshev, I. Fomin
In this chapter we consider the issues of the origin and evolution of relic gravitational waves (GW), which appear as a result of quantum fluctuations of the scalar field and the corresponding perturbations of the space-time metric at the early inflationary stage of the evolution of the universe. The main provisions of the inflationary paradigm and the methods of the construction of current cosmological models on its basis are considered. The influence of relic gravitational waves on the anisotropy and polarization of the relic radiation and the importance of estimating such an effect on the verification of cosmological models are discussed as well.
{"title":"The Early Universe as a Source of Gravitational Waves","authors":"V. Gladyshev, I. Fomin","doi":"10.5772/intechopen.87946","DOIUrl":"https://doi.org/10.5772/intechopen.87946","url":null,"abstract":"In this chapter we consider the issues of the origin and evolution of relic gravitational waves (GW), which appear as a result of quantum fluctuations of the scalar field and the corresponding perturbations of the space-time metric at the early inflationary stage of the evolution of the universe. The main provisions of the inflationary paradigm and the methods of the construction of current cosmological models on its basis are considered. The influence of relic gravitational waves on the anisotropy and polarization of the relic radiation and the importance of estimating such an effect on the verification of cosmological models are discussed as well.","PeriodicalId":270584,"journal":{"name":"Progress in Relativity","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130628579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-25DOI: 10.5772/intechopen.88085
G. Turchetti, F. Panichi
We present a survey on the recently introduced fast indicators for Hamiltonian systems, which measure the sensitivity of orbits to small initial displacements, Lyapunov error (LE), and to a small additive noise, reversibility error (RE). The LE and RE are based on variational methods and require the computation of the tangent flow or map. The modified reversibility error method (REM) measures the effect of roundoff and is computed by iterating a symplectic map forward and backward the same number of times. The smoothest indicator is RE since it damps the oscillations of LE. It can be proven that LE and RE grow following a power law for regular orbits and an exponential law for chaotic orbits. There is a numerical evidence that the growth of RE and REM follows the same law. The application to models of celestial and beam dynamics has shown the reliability of these indicators.
{"title":"Fast Indicators for Orbital Stability: A Survey on Lyapunov and Reversibility Errors","authors":"G. Turchetti, F. Panichi","doi":"10.5772/intechopen.88085","DOIUrl":"https://doi.org/10.5772/intechopen.88085","url":null,"abstract":"We present a survey on the recently introduced fast indicators for Hamiltonian systems, which measure the sensitivity of orbits to small initial displacements, Lyapunov error (LE), and to a small additive noise, reversibility error (RE). The LE and RE are based on variational methods and require the computation of the tangent flow or map. The modified reversibility error method (REM) measures the effect of roundoff and is computed by iterating a symplectic map forward and backward the same number of times. The smoothest indicator is RE since it damps the oscillations of LE. It can be proven that LE and RE grow following a power law for regular orbits and an exponential law for chaotic orbits. There is a numerical evidence that the growth of RE and REM follows the same law. The application to models of celestial and beam dynamics has shown the reliability of these indicators.","PeriodicalId":270584,"journal":{"name":"Progress in Relativity","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125703466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-09DOI: 10.5772/intechopen.86785
F. T. Yu
One of the important aspects of science must be the substantiated physical realities, which were built by the fundamental laws of physics that cannot be simply substituted by unsubstantiated virtual reality. In writing this chapter we have mostly based on the constraints of the current laws of physics to illustrate the enigmatic time as the origin for creating our physical space (i.e., temporal uni-verse). The differences between physical reality and virtual reality are that physical reality is existing within the rule of time and supported by the laws of science, while virtual reality is created without the constraints of time and mostly not substantiated by the laws of physics. One of the important aspects of temporal (i.e., t > 0) space is that any emerging science has to be proven to exist within our temporal universe; otherwise it is fictitious and virtual as mathematics is.
{"title":"From Relativity to Creation of Temporal (t > 0) Universe","authors":"F. T. Yu","doi":"10.5772/intechopen.86785","DOIUrl":"https://doi.org/10.5772/intechopen.86785","url":null,"abstract":"One of the important aspects of science must be the substantiated physical realities, which were built by the fundamental laws of physics that cannot be simply substituted by unsubstantiated virtual reality. In writing this chapter we have mostly based on the constraints of the current laws of physics to illustrate the enigmatic time as the origin for creating our physical space (i.e., temporal uni-verse). The differences between physical reality and virtual reality are that physical reality is existing within the rule of time and supported by the laws of science, while virtual reality is created without the constraints of time and mostly not substantiated by the laws of physics. One of the important aspects of temporal (i.e., t > 0) space is that any emerging science has to be proven to exist within our temporal universe; otherwise it is fictitious and virtual as mathematics is.","PeriodicalId":270584,"journal":{"name":"Progress in Relativity","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124935995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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