Behavior of vacuum and naked singularity under smooth gauge function in Lyra geometry

Lyra geometry is a conformal geometry originated from Weyl geometry. In this article, we derive the exterior field equation under spherically symmetric gauge function $x^0(r)$ and metric in Lyra geometry. When we impose a specific form of the gauge function $x^0(r)$, the radial differential equation of the metric component $g_{00}$ will possess an irregular singular point(ISP) at $r=0$. Moreover, we apply the method of dominant balance and then get the asymptotic behavior of the new spacetime solution. The significance of this work is that we could use a series of smooth gauge functions $x^0(r)$ to modulate the degree of divergence of the singularity at $r=0$ and the singularity will become a naked singularity under certain conditions. Furthermore, we investigate the physical meaning of this novel behavior of spacetime in Lyra geometry and find out that no spaceship with finite integrated acceleration could arrive at this singularity at $r=0$. The physical meaning of gauge function and integrability is also discussed.Comment: 24 pages, 1 figure

A new global 1-form in Lyra geometric cosmos model

Dark energy phenomena has inspired lots of investigations on the cosmological constant problems. In order to understand its origin and properties as well as its impacts on universe's evolutions, there are many approaches to modify the well-known General Relativity, such as the Weyl-Lyra Geometry. In the well studied cosmology model within Lyra geometry, there is a problem that the first law of thermodynamics is violated. To unravel this issue, if we use the effective density and pressure in the Lyra cosmology model to preserve the first law of thermodynamics in the cosmos, the former 1-form $(\beta,0,0,0)$ cannot give a proper vacuum behavior. In this paper, the auxiliary 1-form is modified to overcome this difficulty. It can be shown that the complex terms in the field equation derived from the regime of Lyra Geometric$\frac{3}{2}{\phi}^{\mu}{\phi}_{\nu}-\frac{3}{4}{\delta}^{\mu}_{\nu}{\phi}^{\alpha}{\phi}_{\alpha}$with our new 1-form could behave just as the cosmological constant. This work can be regarded as a new exploration on a possible origin of the cosmological constant from a Lyra cosmology model.Comment: 8 pages. Accepted for publication in IJT

INVESTIGATION OF DEVICE PHYSICS OF MnPS3/MnPSe3 BASED PHOTODETECTOR

Ph.DDOCTOR OF PHILOSOPHY (FOS

Optimal Guidance Laws for a Hypersonic Multiplayer Pursuit-Evasion Game Based on a Differential Game Strategy

The guidance problem of a confrontation between an interceptor, a hypersonic vehicle, and an active defender is investigated in this paper. As a hypersonic multiplayer pursuit-evasion game, the optimal guidance scheme for each adversary in the engagement is proposed on the basis of linear-quadratic differential game strategy. In this setting, the angle of attack is designed as the output of guidance laws, in order to match up with the nonlinear dynamics of adversaries. Analytical expressions of the guidance laws are obtained by solving the Riccati differential equation derived by the closed-loop system. Furthermore, the satisfaction of the saddle-point condition of the proposed guidance laws is proven mathematically according to the minimax principle. Finally, nonlinear numerical examples based on 3-DOF dynamics of hypersonic vehicles are presented, to validate the analytical analysis in this study. By comparing different guidance schemes, the effectiveness of the proposed guidance strategies is demonstrated. Players in the engagement could improve their performance in confrontation by employing the proposed optimal guidance approaches with appropriate weight parameters

Optimal Guidance Laws for a Hypersonic Multiplayer Pursuit-Evasion Game Based on a Differential Game Strategy

The guidance problem of a confrontation between an interceptor, a hypersonic vehicle, and an active defender is investigated in this paper. As a hypersonic multiplayer pursuit-evasion game, the optimal guidance scheme for each adversary in the engagement is proposed on the basis of linear-quadratic differential game strategy. In this setting, the angle of attack is designed as the output of guidance laws, in order to match up with the nonlinear dynamics of adversaries. Analytical expressions of the guidance laws are obtained by solving the Riccati differential equation derived by the closed-loop system. Furthermore, the satisfaction of the saddle-point condition of the proposed guidance laws is proven mathematically according to the minimax principle. Finally, nonlinear numerical examples based on 3-DOF dynamics of hypersonic vehicles are presented, to validate the analytical analysis in this study. By comparing different guidance schemes, the effectiveness of the proposed guidance strategies is demonstrated. Players in the engagement could improve their performance in confrontation by employing the proposed optimal guidance approaches with appropriate weight parameters