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Register a new userFunctions of State for Spinor Gas in General Relativity
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Ying-Qiu Gu
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The energy momentum tensor of perfect fluid is a simplified but successful model in astrophysics. In this paper, assuming the particles driven by gravity and moving along geodesics, we derived the functions of state in detail. The results show that, these functions have a little correction for the usual thermodynamics. The new functions naturally satisfy the causal condition and consist with relativity. For the self potentials of the particles we introduce an extra function $W$, which acts like negative pressure and can be used to describe dark matter. The results are helpful to understand the relation and interaction between space-time and matter.
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If there is a null gradient field in 1+3 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is much helpful for simplifying and solving the Einsteins field equation. This light-cone coordinate system has wonderful properties and has been widely used in astrophysics to calculate parameters. In this paper, we give a detailed discussion for the structure of space-time with light-cone coordinate system. We derive the conditions for existence of such coordinate system, and show how to construct the light-cone coordinate system from usual ones, then explain their geometrical and physical meanings by examples.
The concept of oscillatory Universe appears to be realistic and buried in the dynamic dark energy equation of state. We explore its evolutionary history under the frame work of general relativity. We observe that oscillations do not go unnoticed with such an equation of state and that their effects persist later on in cosmic evolution. The `classical general relativity seems to retain the past history of oscillatory Universe in the form of increasing scale factor as the classical thermodynamics retains this history in the form of increasing cosmological entropy.
We examine two far-reaching and somewhat heretic consequences of General Relativity. (i) It requires a cosmology which includes a preferred rest frame, absolute space and time. (ii) A rotating universe and time travel are strict solutions of General Relativity.
This Letter, i.e. for the first time, proves that a general invariant velocity is originated from the principle of special relativity, namely, discovers the origin of the general invariant velocity, and when the general invariant velocity is taken as the invariant light velocity in current theories, we get the corresponding special theory of relativity. Further, this Letter deduces triple special theories of relativity in cosmology, and cancels the invariant presumption of light velocity, it is proved that there exists a general constant velocity K determined by the experiments in cosmology, for K > 0, = 0 and < 0, they correspond to three kinds of possible relativistic theories in which the special theory of relativity is naturally contained for the special case of K > 0, and this Letter gives a prediction that, for K < 0, there is another likely case satisfying the principle of special relativity for some special physical systems in cosmology, in which the relativistic effects observed would be that the moving body would be lengthened, moving clock would be quickened. And the point of K = 0 is a bifurcation point, through which it gives out three types of possible universes in the cosmology (or multiverse). When a kind of matter with the maximally invariant velocity that may be superluminal or equal to light velocity is determined by experiments, then the invariant velocity can be taken as one of the general invariant velocity achieved in this Letter, then all results of current physical theories are consistent by utilizing this Letters theory.
We study how a strong gravity affects the equation of state of matters. For this purpose, we employ a canonical ensemble of classical monoatomic ideal gas inside a box in a Rindler spacetime. The total energy decreases monotonically with the increase of the external gravity representing its attractiveness. It is however bounded below, which is different from that of the Newtonian gravity case. As for the entropy, it decreases with the external gravity in the Newtonian regime. However, in the presence of strong gravity or ultra-relativistic high temperature, the entropy increases with the gravity. This result can be a resolution of the negative entropy problem of the ideal gas in the Newtonian gravity. In the presence of strong gravity, the bottom of the box is very close to the event horizon of the Rindler spacetime mimicking a blackhole and the gas behaves as if it is on an effective two dimensional surface located at the bottom of the box. Investigating the equation of state in the strong gravity regime, the temperature of the system is found to be not a free parameter but to approach a fixed value proportional to the external gravity, which is reminiscent of the Unruh temperature.
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