Generalized Stefan-Boltzmann law

Thermodynamics arguments have been employed to derive how the energy density depends on the temperatureT for a fluid whose pressurep obeys the equation of statep = ( –1), where is a constant. Three different methods, among them the one considered by Boltzmann (Carnot cycle), lead to the expression = T/( –1), where is a constant. This result also appears naturally in the framework of general relativity for spacetimes with constant spatial curvature. Some particular cases are vacuum (p = –), cosmic strings (p= –1/3), radiation (p = 1/3), and stiff matter (p = ). It is also shown that such results can be adapted for blackbody radiation inN spatial dimensions.     

Understanding first law of thermodynamics of black holes

We approach the thermodynamic properties of the d-dimensional RN black holes, discuss the three expressions for the first law of thermodynamics for black holes and calculate the energies in the three regions of the black hole spacetimes. Some remarks of the first law of thermodynamics and the thermal properties for the black holes are given.     

Thermodynamic surface system of static black holes and area law

We propose a new picture of black holes through a special holographic screen. This holographic screen contains all the degrees of freedom of a black hole. We find that this holographic screen is similar to the ordinary thermodynamic surface system. Meanwhile, through the "white-wall box" and the formula of sound velocity, we find some similarities between gravitons and photons. We further assume that such a holographic screen is a kind of Bose-Einstein condensate of gravitons. Through this assumption and those similarities, we finally get the area law of static black holes.     

On gravitational Stefan-Boltzmann law and Casimir effect in FRW universe

General Relativity and Gravitation - We perform, in a manifestly $$\mathrm{SO}(n-1,1)$$ [ $$\mathrm{SO}(n)$$ ] covariant fashion, the Hamiltonian analysis of general relativity in n dimensions...     

Effective first law of thermodynamics of black holes with two horizons

For a black hole with two horizons, the effective entropy is assumed to be a linear combination of the two entropies of the outer and inner horizons. In terms of the effective thermodynamic quantities the effective Bekenstein-Smarr formula and the effective first law of thermodynamics are derived.     

Physical process first law and increase of horizon entropy for black holes in Einstein-Gauss-Bonnet gravity

We establish the physical process version of the first law by studying small perturbations of a stationary black hole with a regular bifurcation surface in Einstein-Gauss-Bonnet gravity. Our result shows that when the stationary black hole is perturbed by a matter stress energy tensor and finally settles down to a new stationary state, the Wald entropy increases as long as the matter satisfies the null energy condition.     

Connecting black holes and black strings

Static vacuum spacetimes with one compact dimension include black holes with localized horizons but also uniform and nonuniform black strings where the horizon wraps over the compact dimension. We present new numerical solutions for these localized black holes in 5 and 6 dimensions. Combined with previous 6D nonuniform string results, these provide evidence that the black hole and nonuniform string branches join at a topology changing solution.     

静态球对称黑洞Dirac场的Stefan-Boltzmann定律

利用静态球对称黑洞Dirac场的统计熵，导出静态球对称黑洞的Stefan-Boltzmann定律，得 到黑洞的辐出度与视界温度的四次方成正比的结论.发现Stefan-Boltzmann常数不同于平直 时空的值，并且在不同时空度规中该常数有不同的值. 关键词： 黑洞 统计熵 薄层模型 辐出度     

Fragile black holes

The AdS/CFT correspondence may give a new way of understanding field theories in extreme conditions, as in the quark–gluon plasma phase of quark matter. The correspondence normally involves asymptotically AdS black holes with dual field theories which are defined on locally flat boundary spacetimes; the implicit assumption is that the distortions of spacetime which occur under extreme conditions do not affect the field theory in any unexpected way. However, AdS black holes are [to varying degrees] fragile, in the sense that they become unstable to stringy effects when their event horizons are sufficiently distorted. This implies that field theories on curved backgrounds may likewise be unstable in a suitable sense. We investigate this phenomenon, focussing on the “fragility” of AdS₅ black holes with flat event horizons. We find that, when they are distorted, these black holes are always unstable in string theory. This may have consequences for the detailed structure of the quark matter phase diagram at extreme values of the spacetime curvature.     

Energy conservation for dynamical black holes

An energy conservation law is described, expressing the increase in mass-energy of a general black hole in terms of the energy densities of the infalling matter and gravitational radiation. This first law of black-hole dynamics describes how a black hole grows and is regular in the limit where it ceases to grow. An effective gravitational-radiation energy tensor is obtained, providing measures of both ingoing and outgoing, transverse and longitudinal gravitational radiation on and near a black hole. Corresponding energy-tensor forms of the first law involve a preferred time vector which plays the role of a stationary Killing vector. Identifying an energy flux, vanishing if and only if the horizon is null, allows a division into energy supply and work terms. The energy supply can be expressed in terms of area increase and a newly defined surface gravity, yielding a Gibbs-like equation.