The Concept of MOND (Modifying Newtonian Dynamics) was proposed by Mordehai Milgrom as a possible way to reconcile the difference between the experimentally observed high values and the calculated values using Newton...The Concept of MOND (Modifying Newtonian Dynamics) was proposed by Mordehai Milgrom as a possible way to reconcile the difference between the experimentally observed high values and the calculated values using Newton’s Law of Gravity for the dynamical parameters of orbiting stars in a galaxy, without having to introduce the concept of dark matter. Milgrom’s MOND concept challenges the need for dark matter to account for the above difference. The experimentally observed velocity rotation curves of stars in a galaxy show that for small values of r (distance of the star from the centre of the galaxy), the velocity observed (VO) for the orbiting star fairly agrees with values (VN) calculated using Newton’s law of gravity. But as r increases, the difference between VO and VN gradually increases. For very large values of r, VO increases with a constant slope. Finally, VO becomes fairly constant with distance. The above features of VO cannot be explained by Newton’s law of gravity. Milgrom successfully showed that the above features can be explained by modifying Newton’s law of gravity as F=GMmr2μwhere μ is a function just added by Milgrom without a supporting theory behind and is assumed to have certain special properties to suit the purpose. In this paper, it is shown that when the attenuation of dark energy by the space medium is taken into account, Newton’s law of gravity gets modified with a correction term in it. This correction term surprisingly gives rise to the required properties of the function μ added by Milgrom to the existing conventional law of gravity. The work presented here therefore can be considered as a theoretical support for the successful phenomenological scheme proposed by Milgrom.展开更多
In recent papers [1] [2] [3], we framed suitable axioms for Space called Super Space by Wheeler [4]. Using our axioms in Newtonian formalism and considering the density of the universe to be constant in time, we showe...In recent papers [1] [2] [3], we framed suitable axioms for Space called Super Space by Wheeler [4]. Using our axioms in Newtonian formalism and considering the density of the universe to be constant in time, we showed in the above references that at t = 0 the radius of the universe need not be zero. And thus, we avoided the problem of singularity. We further showed that the Hubble factor is no longer constant in time and goes on decreasing as confirmed by experiments. We pointed out in the above references that Space is the source of dark energy which is responsible for the accelerated expansion of the universe. With a view to improving the above-mentioned results quantitatively, in this paper, we are discussing the consequences of our axioms using Einstein’s field equations of general theory of relativity. Friedmann-like Cosmological equations with Dark Energy built-in are derived. This derivation is obtained using Robertson-Walker line element and by introducing a suitable expression for Energy-Momentum tensor in terms of matter and Dark energy contents of the universe. The solutions of our cosmological equations obtained here, show that the radius of the universe cannot reach zero but has a minimum value and there is also maximum value for the radius of the universe. The inflationary expansion of the very early universe emerges from our theory.展开更多
The topological study of connectedness is heavily geometric or visual. Connectedness and connectedness-like properties play an important role in most topological characterization theorems, as well as in the study of o...The topological study of connectedness is heavily geometric or visual. Connectedness and connectedness-like properties play an important role in most topological characterization theorems, as well as in the study of obstructions to the extension of functions. In this paper, the behaviour of these properties in the realm of closure spaces is investigated using the class of perfect mappings. A perfect mapping is a type of map under which the image generally inherits the properties of the mapped space. It turns out that the general behaviour of connectedness properties in topological spaces extends to the class of isotone space.展开更多
文摘The Concept of MOND (Modifying Newtonian Dynamics) was proposed by Mordehai Milgrom as a possible way to reconcile the difference between the experimentally observed high values and the calculated values using Newton’s Law of Gravity for the dynamical parameters of orbiting stars in a galaxy, without having to introduce the concept of dark matter. Milgrom’s MOND concept challenges the need for dark matter to account for the above difference. The experimentally observed velocity rotation curves of stars in a galaxy show that for small values of r (distance of the star from the centre of the galaxy), the velocity observed (VO) for the orbiting star fairly agrees with values (VN) calculated using Newton’s law of gravity. But as r increases, the difference between VO and VN gradually increases. For very large values of r, VO increases with a constant slope. Finally, VO becomes fairly constant with distance. The above features of VO cannot be explained by Newton’s law of gravity. Milgrom successfully showed that the above features can be explained by modifying Newton’s law of gravity as F=GMmr2μwhere μ is a function just added by Milgrom without a supporting theory behind and is assumed to have certain special properties to suit the purpose. In this paper, it is shown that when the attenuation of dark energy by the space medium is taken into account, Newton’s law of gravity gets modified with a correction term in it. This correction term surprisingly gives rise to the required properties of the function μ added by Milgrom to the existing conventional law of gravity. The work presented here therefore can be considered as a theoretical support for the successful phenomenological scheme proposed by Milgrom.
文摘In recent papers [1] [2] [3], we framed suitable axioms for Space called Super Space by Wheeler [4]. Using our axioms in Newtonian formalism and considering the density of the universe to be constant in time, we showed in the above references that at t = 0 the radius of the universe need not be zero. And thus, we avoided the problem of singularity. We further showed that the Hubble factor is no longer constant in time and goes on decreasing as confirmed by experiments. We pointed out in the above references that Space is the source of dark energy which is responsible for the accelerated expansion of the universe. With a view to improving the above-mentioned results quantitatively, in this paper, we are discussing the consequences of our axioms using Einstein’s field equations of general theory of relativity. Friedmann-like Cosmological equations with Dark Energy built-in are derived. This derivation is obtained using Robertson-Walker line element and by introducing a suitable expression for Energy-Momentum tensor in terms of matter and Dark energy contents of the universe. The solutions of our cosmological equations obtained here, show that the radius of the universe cannot reach zero but has a minimum value and there is also maximum value for the radius of the universe. The inflationary expansion of the very early universe emerges from our theory.
文摘The topological study of connectedness is heavily geometric or visual. Connectedness and connectedness-like properties play an important role in most topological characterization theorems, as well as in the study of obstructions to the extension of functions. In this paper, the behaviour of these properties in the realm of closure spaces is investigated using the class of perfect mappings. A perfect mapping is a type of map under which the image generally inherits the properties of the mapped space. It turns out that the general behaviour of connectedness properties in topological spaces extends to the class of isotone space.
