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.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

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.

Black Hole Explosions

在2007年以前,几乎没有人会意识到弦论和凝聚态理论这两个看上去毫不相关的理论会被联系在一起,并且成为相互关联互为对偶的两个体系。作为现代高能理论物理最激动人心的进展之一的弦理论,诞生于上个世纪60年代末,并从上世纪70年代中期起被期望于作为描述量子引力并且统一自然界中各种相互作用的理论。

新书推荐：Holographic Duality in Condensed Matter Physics

Motivated by recent developments of BTZ black holes and interesting results of massive gravity, we investigate massive BTZ black holes in the presence of Maxwell and Born-Infeld (BI) electrodynamics. We study geometrical properties such as type of singularity and asymptotical behavior as well as thermodynamic structure of the solutions through canonical ensemble. We show that despite the existence of massive term, obtained solutions are asymptotically (a)dS and have a curvature singularity at the origin. Then, we regard varying cosmological constant and examine the Van der Waals like behavior of the solutions in extended phase space. In addition, we employ geometrical thermodynamic approaches and show that using Weinhold, Ruppeiner and Quevedo metrics leads to existence of ensemble dependency while HPEM metric yields consistent picture. For neutral solutions, it will be shown that generalization to massive gravity leads to the presence of non-zero temperature and heat capacity for vanishing horizon radius. Such behavior is not observed for linearly charged solutions while generalization to nonlinearly one recovers this property.

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Massive charged BTZ black holes in asymptotically (a)dS spacetimes

Motivated by high interest in the close relation between string theory and black hole solutions, in this paper, we take into account the Einstein-Gauss-Bonnet Lagrangian in the context of massive gravity. We examine the possibility of black hole in this regard, and discuss the types of horizons. Next, we calculate conserved and thermodynamic quantities and check the validity of the first law of thermodynamics. In addition, we investigate the stability of these black holes in context of canonical ensemble. We show that number, type and place of phase transition points may be significantly affected by different parameters. Next, by considering cosmological constant as thermodynamical pressure, we will extend phase space and calculate critical values. Then, we construct thermodynamical spacetime by considering mass as thermodynamical potential. We study geometrical thermodynamics of these black holes in context of heat capacity and extended phase space. We show that studying heat capacity, geometrical thermodynamics and critical behavior in extended phase space lead to consistent results. Finally, we will employ a new method for obtaining critical values and show that the results of this method are consistent with those of other methods.

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Charged black hole solutions in Gauss-Bonnet-massive gravity

An auxiliary metric (reference metric) is inevitable in massive gravity theory. In the scenario of the gauge/gravity duality, massive gravity with a singular reference metric is used to study momentum dissipation, which describes the electric and heat conductivity for normal conductors. We demonstrate in detail that the de Rham-Gabadadze-Tolley (dRGT) massive gravity with a singular reference metric is ghost free.

Ghost free massive gravity with singular reference metrics

We study the Misner-Sharp mass for the f(R) gravity in an n-dimensional (n >= 3) spacetime which permits three-type (n - 2)-dimensional maximally symmetric subspace We obtain the Misner-Sharp mass via two approaches One is the inverse unified first law method and the other is the conserved charge method, which uses a generalized Kodama vector In the first approach, we assume the unified first law still holds in n-dimensional f(R) gravity, which requires a quasilocal mass form (we define it as the generalized Misner-Sharp mass) In the second approach, the conserved charge corresponding to the generalized local Kodama vector is the generalized Misner-Sharp mass The two approaches, which are bridged by a constraint, are equivalent This constraint determines the existence of a well-defined Misner-Sharp mass In an important special case, we present the explicit form for the static space, and we calculate the Misner-Sharp mass for the Clifton-Barrow solution as an example

Misner-Sharp mass in n-dimensional f (R) gravity

We obtain the Misner-Sharp mass in the massive gravity for a four dimensional spacetime with a two dimensional maximally symmetric subspace via the inverse unified first law method. Significantly, the stress energy is conserved in this case with a widely used reference metric. Based on this property we confirm the derived Misner-Sharp mass by the conserved charge method. We find that the existence of the Misner-sharp mass in this case does not lead to extra constraint for the massive gravity, which is notable in modified gravities. In addition, as a special case, we also investigate the Misner-Sharp mass in the static spacetime. Especially, we take the FRW universe into account for investigating the thermodynamics of the massive gravity. The result shows that the massive gravity can be in thermodynamic equilibrium, which fills in the gap in the previous studies of thermodynamics in the massive gravity.

Misner-Sharp mass and the unified first law in massive gravity

Dynamical solutions are always of interest to people in gravity theories. We derive a series of generalized Vaidya solutions in the $n$-dimensional de Rham-Gabadadze-Tolley massive gravity with a singular reference metric. Similar to the case of the Einstein gravity, the generalized Vaidya solution can describe shining/absorbing stars. Moreover, we also find a more general Vaidya-like solution by introducing a more generic matter field than the pure radiation in the original Vaidya spacetime. As a result, the above generalized Vaidya solution is naturally included in this Vaidya-like solution as a special case. We investigate the thermodynamics for this Vaidya-like spacetime by using the unified first law and present the generalized Misner-Sharp mass. Our results show that the generalized Minser-Sharp mass does exist in this spacetime. In addition, the usual Clausius relation $\ensuremath{\delta}Q=TdS$ holds on the apparent horizon, which implicates that the massive gravity is in a thermodynamic equilibrium state. We find that the work density vanishes for the generalized Vaidya solution, while it appears in the more general Vaidya-like solution. Furthermore, the covariant generalized Minser-Sharp mass in the $n$-dimensional de Rham-Gabadadze-Tolley massive gravity is also derived by taking a general metric ansatz into account.

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Generalized Vaidya Solutions and Misner-Sharp mass for $n$-dimensional massive gravity

Gravity is believed to have a deep and inherent relation to thermodynamics. We study phase transitions and critical behaviors in the extended phase space of asymptotic anti--de Sitter black holes in Einstein-Horndeski gravity. We demonstrate that the black hole in Einstein-Horndeski gravity undergoes a phase transition and $P\ensuremath{-}V$ criticality mimicking the van der Waals gas-liquid system. The key approach in our study is to introduce a more reasonable pressure instead of the previous pressure $P=\ensuremath{-}\mathrm{\ensuremath{\Lambda}}/8\ensuremath{\pi}$ related to the cosmological constant $\mathrm{\ensuremath{\Lambda}}$, and this proper pressure is motivated by the asymptotical behavior of the black hole. Moreover, we also obtain $P\ensuremath{-}V$ criticality in the two cases with $\mathrm{\ensuremath{\Lambda}}=0$ and $\mathrm{\ensuremath{\Lambda}}g0$ for the first time, which implies that the cosmological constant $\mathrm{\ensuremath{\Lambda}}$ may not be a necessary pressure candidate for black holes at the microscopic level. We present critical exponents for these phase transition processes.

Hongsheng Zhang

Papers

Ghost free massive gravity with singular reference metrics

Misner-Sharp mass in n-dimensional f (R) gravity

Misner-Sharp mass and the unified first law in massive gravity

Generalized Vaidya Solutions and Misner-Sharp mass for $n$-dimensional massive gravity

P-V criticality in the extended phase space of black holes in Einstein-Horndeski gravity