Numerical metric extraction in AdS/CFT

An iterative method for recovering the bulk information in asymptotically AdS spacetimes is presented. We consider zero energy spacelike geodesics and their relation to the entanglement entropy in three dimensions to determine the metric in certain symmetric cases. A number of comparisons are made with an alternative extraction method presented in arXiv:hep-th/0609202, and the two methods are then combined to allow metric recovery in the most general type of static, spherically symmetric setups. We conclude by extracting the mass and density profiles for a toy model example of a gas of radiation in (2 + 1)-dimensional AdS.     

Mass,action, and entropy of Taub-Bolt-de Sitter spacetimes

We apply a recent proposal for defining conserved mass in asymptotically de Sitter spacetimes to the class of Taub-Bolt-de Sitter spacetimes. We compute the action, entropy, and conserved mass of these spacetimes, and find that in certain instances the mass and entropy can exceed that of pure de Sitter spacetime, in violation of recent suggestive conjectures to the contrary.     

Gravitational radiation reaction on the motion of particles in general relativity

We examine the problem of deducing the geodesic motion of test particles from Einstein's vacuum field equations and its extension to include gravitational radiation reaction. In the latter case we obtain an equation of motion for a particle which incorporates radiation reaction of the electrodynamical type, but due to shearing radiation, together with a mass-loss formula of the Bondi-Sachs type.Work supported in part by the National Science Foundation under Grant PHY-8306104.     

Could a real (not virtual) static observer exist outside a Schwarzschild black hole?

We considered the static spherically symmetric ensemble of observers, having finite bare mass and trying to measure geometrical and physical properties of the environmental static (Schwarzschild) space–time. The word “virtual” in the title means the test particle serving as an observer, and the “real” is the observer whose mass and its influences on the space–time metric cannot be neglected. It is shown that, using the photon rockets (which the mass together with the mass of their fuel is also taken into account) they can managed to keep themselves on the fixed value of radius. The process of diminishing the total bare mass up to zero lasts infinitely long time. It is important that the problem is solved self-consistently, i.e., with full account for the back reaction of both bare mass and radiation from rockets on the space–time geometry.     

Time-Symmetric Quantization in Spacetimes with Event Horizons

The standard quantization formalism in spacetimes with event horizons implies a non-unitary evolution of quantum states, as initial pure states may evolve into thermal states. This phenomenon is behind the famous black hole information loss paradox which provoked long-standing debates on the compatibility of quantum mechanics and gravity. In this paper we demonstrate that within an alternative time-symmetric quantization formalism thermal radiation is absent and states evolve unitarily in spacetimes with event horizons. We also discuss the theoretical consistency of the proposed formalism. We explicitly demonstrate that the theory preserves the microcausality condition and suggest a “reinterpretation postulate” to resolve other apparent pathologies associated with negative energy states. Accordingly as there is a consistent alternative, we argue that choosing to use time-asymmetric quantization is a necessary condition for the black hole information loss paradox.     

Progressing wave perturbations of cosmological spacetimes

We determine the large class of Robertson-Walker spacetimes whose first-order, linear, isentropic perturbations can be expressed in closed form, and the closed form perturbations are written down. It is shown that the class includes several well-known spacetimes including, for example, spatially flat dust and the radiation filled universe.     

Asymptotic symmetries in general relativity

In the context of a recent reformulation of the theory of gravitational radiation from bounded sources in which both shearing and shear-free radiation is manifestly present, we derive the asymptotic symmetry group of the spacetime. The group we obtain contains the Bondi-Metzner-Sachs group as a subgroup. This observation is relevant to the problem of the mysterious role of shear-free radiation in the Bondi-Sachs approach to the theory of gravitational radiation from bounded sources.     

Positive mass from holographic causality

For (n+1)-dimensional asymptotically anti-de Sitter (AdS) spacetimes which have holographic duals on their n-dimensional conformal boundaries, we show that the imposition of causality on the boundary theory is sufficient to prove positivity of mass for the spacetime when n> or =3, without the assumption of any local energy condition. We make crucial use of a time-delay formula relating the Ashtekar-Magnon mass of the spacetime to the time delay of a bulk null curve relative to that of a boundary null geodesic. We also discuss holographic causality for the negative mass AdS soliton and its implications for the positive energy conjecture of Horowitz and Myers.     

Obtaining a class of type O pure radiation metrics with a negative cosmological constant,using invariant operators

Using the generalised invariant formalism we derive a special subclass of conformally flat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalar component. The method used is a development of the methods used earlier for pure radiation spacetimes of Petrov types O and N, respectively. In this paper we demonstrate how to handle, in the generalised invariant formalism, spacetimes with isotropy freedom and rich Killing vector structure. Once the spacetimes have been constructed, it is straightforward to deduce their Karlhede classification: the Karlhede algorithm terminates at the fourth derivative order, and the spacetimes all have one degree of null isotropy and three, four or five Killing vectors.     

A Definition of Total Energy-Momenta and the Positive Mass Theorem on Asymptotically Hyperbolic 3-Manifolds. I

Two sets of asymptotically hyperbolic initial data are defined, which correspond to the spatial infinity in asymptotically AdS spacetimes and to the null infinity in asymptotically Minkowski spacetimes respectively. The positive mass theorem involving the total energy, the total linear momentum and the total angular momentum is established for these initial data sets.Research partially supported by National Natural Science Foundation of China under grant 10231050 and the innovation project of the Chinese Academy of Sciences.     

Optimal choices of reference for a quasi-local energy

We propose a program for determining the reference for the covariant Hamiltonian boundary term quasi-local energy and test it on spherically symmetric spacetimes. For different observers the quasi-local energy can be positive, zero, or even negative, however the maximum value is positive for both the Schwarzschild and FLRW spacetimes.     

Abbott-Deser-Tekin Charge of Dilaton Black Holes with Squashed Horizons

We consider the conserved charge of static black holes with squashed horizons in the Einstein-Maxwell-dilaton theory via both the Abbott-Deser-Tekin(ADT)method and its off-shell generalization.We Grst make use of the original ADT method to compute the mass of the dilaton squashed black holes in terms of three different reference spacetimes,which are the asymptotic geometry,the flat background and the spacetime of the KaluzaKlein monopole with boundary matched to the original metric,respectively.Each mass satisfies the Grst law of black hole thermodynamics,although the mass computed on the basis of the boundary matching the KaluzaKlein monopole is different from that of the other two reference spacetimes.Then the mass of the black holes is evaluated through the off-shell generalized ADT method.     

On the Geometry and Mass of Static,Asymptotically AdS Spacetimes,and the Uniqueness of the AdS Soliton

We prove two theorems, announced in [6], for static spacetimes that solve Einstein's equation with negative cosmological constant. The first is a general structure theorem for spacetimes obeying a certain convexity condition near infinity, analogous to the structure theorems of Cheeger and Gromoll for manifolds of non-negative Ricci curvature. For spacetimes with Ricci-flat conformal boundary, the convexity condition is associated with negative mass. The second theorem is a uniqueness theorem for the negative mass AdS soliton spacetime. This result lends support to the new positive mass conjecture due to Horowitz and Myers which states that the unique lowest mass solution which asymptotes to the AdS soliton is the soliton itself. This conjecture was motivated by a nonsupersymmetric version of the AdS/CFT correspondence. Our results add to the growing body of rigorous mathematical results inspired by the AdS/CFT correspondence conjecture. Our techniques exploit a special geometric feature which the universal cover of the soliton spacetime shares with familiar ``ground state' spacetimes such as Minkowski spacetime, namely, the presence of a null line, or complete achronal null geodesic, and the totally geodesic null hypersurface that it determines. En route, we provide an analysis of the boundary data at conformal infinity for the Lorentzian signature static Einstein equations, in the spirit of the Fefferman-Graham analysis for the Riemannian signature case. This leads us to generalize to arbitrary dimension a mass definition for static asymptotically AdS spacetimes given by Chruciel and Simon. We prove equivalence of this mass definition with those of Ashtekar-Magnon and Hawking-Horowitz.     

Gravitational collapse: expanding and collapsing regions

We investigate the expanding and collapsing regions by taking two well-known spherically symmetric spacetimes. For this purpose, the general formalism is developed by using Israel junction conditions for arbitrary spacetimes. This has been used to obtain the surface energy density and the tangential pressure. The minimal pressure provides the gateway to explore the expanding and collapsing regions. We take Minkowski and Kantowski-Sachs spacetimes and use the general formulation to investigate the expanding and collapsing regions of the shell.     

静态 dilaton 黑洞中带电磁荷粒子的隧穿效应

利用Parikh 和 Wilczek的隧穿模型,在Gibbons-Maeda dilaton 黑洞时空中,通过计算带有电荷和磁荷的粒子在事件视界上的隧穿概率,研究了该黑洞的Hawking辐射.在粒子的隧穿过程中,强调了时空的能量守恒和电磁荷守恒,考虑了隧穿粒子对背景时空的反作用.计算表明,在Gibbons-Maeda dilaton 黑洞时空中,带电磁荷的粒子通过事件视界的隧穿概率取决于粒子出射前后黑洞熵的变化.这表示,黑洞辐射过程中可以满足信息守恒和量子理论的幺正性. 关键词： 黑洞 霍金辐射 量子理论     

Particle collisions near the cosmological horizon of a Reissner-Nordström-de Sitter black hole

It has recently been shown that black holes can act as particle accelerators and two particles can collide with arbitrarily high center-of-mass (CM) energy under certain critical conditions. In this paper, we investigate particle collisions outside a Reissner-Nordström-de Sitter (RN-dS) black hole. We find that infinite CM energy can be produced near the cosmological horizon for generic spacetime configurations. Remarkably, such infinite CM energy does not require the black hole to be extremal, in contrast to spacetimes in the absence of cosmological constants. However, since the charge of an astrophysical body is negligible, the required charge to mass ratio of the particle is extremely higher than that of any elementary particle.     

Geometric inequalities in spherically symmetric spacetimes

In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the Misner–Sharp mass and the concept of the Kodama vector field provides an ideal setting to the investigations of geometric inequalities. We applying the proposed new techniques to investigate the spacetimes containing black hole or cosmological horizons but we shall also apply them in context of normal bodies. Most of the previous investigations applied only the quasi-local charges and the area. Our main point is to include the quasi-local mass in the corresponding geometrical inequalities. This way we recover some known relations but new inequalities are also derived.     

Beyond the speed of light on Finsler spacetimes

As a prototypical massive field theory we study the scalar field on the recently introduced Finsler spacetimes. We show that particle excitations exist that propagate faster than the speed of light recognized as the boundary velocity of observers. This effect appears already in Finsler spacetime geometries with very small departures from Lorentzian metric geometry. It switches on for a sufficiently large ratio of the particle four-momentum and mass, and is the consequence of a modified version of the Coleman–Glashow velocity dispersion relation. The momentum dispersion relation on Finsler spacetimes is shown to be the same as on metric spacetimes, which differs from many quantum gravity models. If similar relations resulted for fermions on Finsler spacetimes, these generalized geometries could explain the potential observation of superluminal neutrinos claimed by the Opera Collaboration.     

Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets

We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisymmetric situation where a bound on the angular momentum by the mass has been shown to hold for black hole solutions. Our construction involves changing the solution at the linear level in a shell near infinity, and perturbing to impose the vacuum constraint equations. The procedure involves the perturbation correction of an approximate solution which is given explicitly.     

Twisted Lorentzian manifolds: a characterization with torse-forming time-like unit vectors

Robertson–Walker and generalized Robertson–Walker spacetimes may be characterized by the existence of a time-like unit torse-forming vector field, with other constrains. We show that Twisted manifolds may still be characterized by the existence of such (unique) vector field, with no other constrain. Twisted manifolds generalize RW and GRW spacetimes by admitting a scale function that depends both on time and space. We obtain the Ricci tensor, corresponding to the stress–energy tensor of an imperfect fluid.