arXiv subjects

Guihua Tian

Publications and source records attributed to Guihua Tian.

21 records · Page 2Linked to original sources

arXiv2005

Is the Schwarzschild black hole really stable?

The stability of the Schwarzschild black hole is studied. Regge and Wheeler treated the problem first at 1957 and obtained the dynamical equations for the small perturbation. There are two kinds of perturbations: odd one and even one. Using the Painlevé coordinate, we reconsider the odd perturbation and find that: the white-hole-connected universe(r>2m, see text) is unstable. Because the odd perturbation may be regarded as the angular perturbation, therefore, the physical mean to it may be that the white-hole-connected universe is unstable with respect to the rotating perturbation.

gr-qc↗

arXiv2004

Integral equations for the spin-weighted spheroidal wave function

Integral equations for the spin-weighted spheroidal wave functions is given. For the prolate spheroidal wave function with m=0, there exists the integral equation whose kernel is(sin x)/x, and the sinc function kernel (sin x)/x is of great mathematical significance. In the paper, we also extend the similar sinc function kernel (sin x)/x to the case m and s both are not zero, which interestingly turn out as some kind of Hankel transformation.

gr-qc↗

arXiv2002

Can an observer really catch up with light

Given a null geodesic $γ_0(λ)$ with a point $r$ in $(p,q)$ conjugate to $p$ along $γ_0(λ)$, there will be a variation of $γ_0(λ)$ which will give a time-like curve from $p$ to $q$. This is a well-known theory proved in the famous book\cite{2}. In the paper we prove that the time-like curves coming from the above-mentioned variation have a proper acceleration which approaches infinity as the time-like curve approaches the null geodesic. This means no observer can be infinitesimally near the light and begin at the same point with the light and finally catch the light. Only separated from the light path finitely, does the observer can begin at the same point with the light and finally catch the light.

gr-qc↗