Kai Lin

Bio: Kai Lin is an academic researcher from China University of Geosciences (Wuhan). The author has contributed to research in topics: Black hole & Schwarzschild radius. The author has an hindex of 13, co-authored 65 publications receiving 518 citations. Previous affiliations of Kai Lin include Zhejiang University of Technology & Universidade Federal de Itajubá.

Dirac quasinormal modes in spherically symmetric regular black holes

Abstract: Using the WKB approximation, massless and massive Dirac quasinormal modes (QNMs) are studied in spherically symmetric regular spacetimes. We analyze the relationships between QNM frequencies and the parameters (angular momentum number $l$, magnetic monopole charge $\ensuremath{\beta}$, and the mass of the field $m$) and discuss the extreme charge of magnetic monopole ${\ensuremath{\beta}}_{e}$ for spherically symmetric regular black holes. Furthermore, we apply an expansion method to expand QNMs in inverse powers of $L=l+1/2$ and confirm good precision with $lgn$. Finally, we improve the traditional finite difference method to be available in the massive Dirac case and illuminate the dynamical evolution of the massive Dirac field.

Universal horizons and black holes in gravitational theories with broken Lorentz symmetry

Abstract: In this paper, we first show that the definition of the universal horizons studied recently in the khronometric theory of gravity can be straightforwardly generalized to other theories that violate the Lorentz symmetry, by simply considering the khronon as a probe field and playing the same role as a Killing vector field. As an application, we study static charged (D + 1)-dimensional spacetimes in the framework of the healthy (nonprojectable) Horava–Lifshitz (HL) gravity in the infrared (IR) limit, and find various solutions. Some of them represent Lifshitz spacetimes with hyperscaling violations, and some have black hole structures. In the latter, universal horizons always exist inside the Killing horizons. The surface gravity on them can be either larger or smaller than the surface gravity on the Killing horizons, depending on the spacetimes considered. Although such black holes are found only in the IR, we argue that black holes with universal horizons also exist in the full theory of the HL gravity. A simple example is the Schwarzschild solution written in the Painleve–Gullstrand coordinates, which is also a solution of the full theory of the HL gravity and has a universal horizon located inside the Schwarzschild Killing horizon.

High-dimensional Lifshitz-type spacetimes, universal horizons, and black holes in Hořava-Lifshitz gravity

Abstract: In this paper, we present all $[(d+1)+1]$-dimensional static diagonal vacuum solutions of the nonprojectable Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity in the IR limit and show that they give rise to very rich Lifshitz-type structures, depending on the choice of the free parameters of the solutions. These include the Lifshitz space-times with or without hyperscaling violation, Lifshitz solitons, and black holes. Remarkably, even the theory breaks explicitly the Lorentz symmetry and allows generically instantaneous propagations, universal horizons still exist, which serve as one-way membranes for signals moving with any large velocities. In particular, particles even with infinitely large velocities would just move around on these boundaries and would not be able to escape to infinity. Another remarkable feature appearing in the Lifshitz-type space-times is that the dynamical exponent $z$ can take its values only in the ranges $1\ensuremath{\le}zl2$ for $d\ensuremath{\ge}3$ and $1\ensuremath{\le}zl\ensuremath{\infty}$ for $d=2$, due to the stability and ghost-free conditions of the theory.

A Matrix Method for Quasinormal Modes: Schwarzschild Black Holes in Asymptotically Flat and (Anti-) de Sitter Spacetimes

Abstract: In this work, we study the quasinormal modes of Schwarzschild and Schwarzschild (Anti-) de Sitter black holes by a matrix method. The proposed method involves discretizing the master field equation and expressing it in form of a homogeneous system of linear algebraic equations. The resulting homogeneous matrix equation furnishes a non-standard eigenvalue problem, which can then be solved numerically to obtain the quasinormal frequencies. A key feature of the present approach is that the discretization of the wave function and its derivatives are made to be independent of any specific metric through coordinate transformation. In many cases, it can be carried out beforehand which in turn improves the efficiency and facilitates the numerical implementation. We also analyze the precision and efficiency of the present method as well as compare the results to those obtained by different approaches.

A Matrix Method for Quasinormal Modes: Schwarzschild Black Holes in Asymptotically Flat and (Anti-) de Sitter Spacetimes

Abstract: In this work, we study the quasinormal modes of Schwarzschild and Schwarzschild (Anti-) de Sitter black holes by a matrix method The proposed method involves discretizing the master field equation and expressing it in the form of a homogeneous system of linear algebraic equations The resulting homogeneous matrix equation furnishes a non-standard eigenvalue problem, which can then be solved numerically to obtain the quasinormal frequencies A key feature of the present approach is that the discretization of the wave function and its derivatives is made to be independent of any specific metric through coordinate transformation In many cases, it can be carried out beforehand, which in turn improves the efficiency and facilitates the numerical implementation We also analyze the precision and efficiency of the present method as well as compare the results to those obtained by different approaches

The Observation of Gravitational Waves from a Binary Black Hole Merger

Abstract: On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160) Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

Black Hole Explosions

Abstract: QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Introducing the Black-Hole

Abstract: According to present cosmology, certain stars end their careers in a total gravitational collapse that transcends the ordinary laws of physics.