Inspired by the recent proposal of soft hair on black holes in Hawking et al (2016 Phys. Rev. Lett. 116 231301), we have shown that an isolated horizon carries soft hairs implanted by electromagnetic fields. The solution space and the asymptotic symmetries of Einstein–Maxwell theory have been worked out explicitly near the isolated horizon. The conserved current has been computed and an infinite number of near horizon charges have been introduced from the electromagnetic fields associated with the asymptotic U(1) symmetry near the horizon, which indicates the fact that the isolated horizon carries a large amount of soft electric hairs. The soft electric hairs, i.e. asymptotic U(1) charges, are shown to be equivalent to the electric multipole moments of isolated horizons. It is further argued that the isolated horizon supertranslation is from the ambiguity of its foliation and an analogue of memory effect on horizon can be expected.

It is highlighted by Prigogine that there are two additional universal behaviors associated with the entropy production rate besides the four laws of thermodynamics. One is that the entropy production rate decreases when the system approaches the steady state, and the other is that the entropy production rate reaches its minimal value at the steady state. Motivated by the black hole thermodynamics and AdS/CFT correspondence, we resort to the Raychaudhuri equation to prove that these two universal behaviors are also obeyed by the black hole entropy. In particular, our result together with the four laws of black hole thermodynamics further indicates that the holographic gravity should be universal, not restricted only within the context of AdS/CFT correspondence.

With the attempt to find the holographic description of the usual acoustic black holes in fluid, we construct an acoustic black hole formed in the d-dimensional fluid located at the timelike cutoff surface of a neutral black brane in asymptotically AdSd+1 spacetime.

In this paper, we investigate the fluid/gravity correspondence in spacetime with general non-rotating weakly isolated horizon. With the help of a Petrov-like boundary condition and large mean curvature limit, we show that the dual hydrodynamical system is described by a generalized forced incompressible Navier–Stokes equation. Specially, for stationary black holes or those spacetime with some asymptotically stationary conditions, such a system reduces to a standard forced Navier–Stokes system.

Almost a century ago, Einstein, after Newton, shed new light on gravity by claiming that gravity is geometry. There has been no deeper insight beyond that later on except the recent suspicion that gravity may also be holographic, dual to some sort of quantum field theory living on the boundary with one less dimension. Such a suspicion has been supported mainly by a variety of specific examples from string theory. This paper is intended to purport the holographic gravity from a different perspective. Namely, we shall show that such a holography can actually be observed by working merely within the context of Einstein's gravity through promoting Brown–York's formalism, where neither is the spacetime required to be asymptotically AdS nor the boundary to be located at conformal infinity, which also conforms to the spirit inherited from Wilson's effective field theory. In particular, we show that our holography works remarkably well at least at the level of thermodynamics and hydrodynamics, where a perfect matching between the bulk gravity and boundary fluid is found for entropy and its production by the conserved current method.

The second Poincaré kinematical group serves as one of new ones in addition to the known possible kinematics. The geometries with the second Poincaré symmetry is presented and their properties are analyzed. On the geometries, the new mechanics based on the principle of relativity with two universal constants (c, l) can be established.

The dual fluid description for a general cutoff surface at radius r=rc outside the horizon in the charged AdS black brane bulk space–time is investigated, first in the Einstein–Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter ϵ, the coupled Einstein–Maxwell equations are solved up to O(ϵ2). The incompressible Navier–Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density η/s is independent of both the cutoff rc and the black brane charge. Then, we extend our discussion to the Gauss–Bonnet–Maxwell case, where the incompressible Navier–Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio η/s is independent of the cutoff rc but dependent on the charge density of the black brane.

We generalize the framework in arXiv:1104.5502 to the case that an embedding may have a non-vanishing intrinsic curvature. Directly employing the Brown-York stress tensor as the fundamental variables, we study the effect of finite perturbations of the extrinsic curvature while keeping the intrinsic metric fixed. We show that imposing a Petrov type I condition on the hypersurface geometry may reduce to the incompressible Navier–Stokes equation for a fluid moving in spatially curved spacetime in the near-horizon limit.

A theorem related to the Newman-Penrose constants is proven. The theorem states that all the Newman-Penrose constants of asymptotically flat, stationary, asymptotically algebraically special electrovacuum space-times are zero. Straightforward application of this theorem shows that all the Newman-Penrose constants of the Kerr-Newman space-time must vanish.

We reexpress the Kerr metric in standard Bondi-Sachs coordinates near null infinity

Wilczek and his collaborators' anomaly cancellation approach is applied to the 3D Schwarzschild- and BTZ-like braneworld black holes induced by the generalized metrics in the Randall–Sundrum scenario. Based on the fact that the horizon of braneworld black hole will extend into the bulk spacetime, calculation is done from the bulk generalized metrics side and it is shown that this approach also reproduces the correct Hawking radiation for these braneworld black holes. Besides, since this approach does not involve the dynamical equation, it is also shown that the Hawking radiation is only a kinematic effect.

The entropy bound conjecture concerning black hole dynamical horizons is proved. The conjecture states, if a dynamical horizon, DH, is bounded by two surfaces with areas of AB and AB' (AB' > AB), then the entropy, SD, that crosses DH must satisfy SD ≤ ¼(AB'−AB). We show that this conjecture is implied by the generalized Bousso bound. Consequently, the generalized second law holds for dynamical horizons. Finally, we show that the lightlike Bousso bound and its spacelike counterpart can be unified as one bound.

We consider the general asymptotic expression of stationary spacetime. Using the Killing equation, we reduce the dynamical freedom of the Einstein equation to the in-going gravitational wave Ψ0. The general form of this function can be obtained. With the help of an asymptotically algebraic special condition, we prove that all Newman–Penrose constants vanish.

The null infinity limit of the gravitational energy-momentum and energy flux determined by the covariant Hamiltonian quasilocal expressions is evaluated using the Newman-Penrose spin coefficients. The reference contribution is considered by three different embedding approaches. All of them give the expected Bondi energy and energy flux

The Noether-charge and the Hamiltonian realizations for the diff(M)algebra in diffeomorphism-invariant gravitational theories without a cosmological constant in any dimension are studied in a covariant formalism.