Uniqueness of the Reissner-Nordstrom metric near the null infinity

In the Newman-Penrose formalism,we prove that the Reissner-Nordstrom metric is the only asymptotically fat,static,axially symmetric,Petrov type-D analytic solution of the electro-vacuum Einstein-Maxwell equations near the null infinity.

Binary black hole systems do not interact in the Kastor-Traschen spacetime

The laser-interferometer gravitational-wave observatory (LIGO) has reported several observations of binary black hole mergers. Unfortunately, no exact solutions to the equations describing binary black hole systems exist. In particular, no exact solutions are available for the case in which a binary black hole system undergoes a merger;hence, we must rely on numerical calculations of the Maxwell-Einstein equations to construct the templates used to analyze gravitational wave data about suspected binary black hole systems [1,2].

On the angular momentum of compact binary coalescence

The supertranslation ambiguity issue of angular momentum is a long-standing problem in general relativity.Recently,there appeared the first definition of angular momentum at null infinity that is supertranslation invariant.However,in the compact binary coalescence community,supertranslation ambiguity is often ignored.This paper demonstrates that we have the happy circumstance that the newly defined angular momentum coincides with the classical definition at the quadrupole level.

Self-consistent effective-one-body theory for spinless binaries based on post-Minkowskian approximation I:Hamiltonian and decoupled equation forψ^(B)_(4)

To build a self-consistent effective-one-body(EOB)theory,in which the Hamiltonian,radiation-reaction force and waveform for the“plus”and“cross”modes of the gravitational wave should be based on the same effective background spacetime,the key step is to look for the decoupled equation forψ^(B)_(4)=h_(+)−ih_(×),which seems a very difficult task because there are non-vanishing tetrad components of the tracefree Ricci tensor for such spacetime.Fortunately,based on an effective spacetime obtained in this paper by using the post-Minkowskian(PM)approximation,we find the decoupled equation forψ^(B)_(4)by dividing the perturbation part of the metric into the odd and even parities.With the effective metric and decoupled equation at hand,we set up a frame of self-consistent EOB model for spinless binaries.

Newtonian limit of Einstein equation with a cosmological constant

Traditionally,the cosmological constant has been viewed as dark energy that mimics matter with negative energy.Given that matter with negative energy provides a repulsive force,which fundamentally differs from typical gravitational forces,it has been believed that the cosmological constant effectively contributes a repulsive force.However,it is important to note that the concept of gravitational force is valid only within the framework of Newtonian dynamics.In this study,we demonstrate that the traditional understanding of the gravitational force contributed by the cosmological constant is not entirely correct.Our approach involves investigating the Newtonian limit of the Einstein equation with a cosmological constant.The subtleties involved in this analysis are discussed in detail.Interestingly,we find that the effect of the cosmological constant on Newtonian gravity is an attractive force rather than a repulsive one for ordinary matter.As expected,this corrective force is negligibly small.However,our findings may offer a way to distinguish between dark energy and the cosmological constant,as one contributes a repulsive force while the other contributes an attractive force.

Generalized gravitomagnetic field and gravitational waves

Synge was the first to derive the geodesic deviation entirely mathematically (1)Only later did people realize its importance [2] for describing the physical behavior of curved spacetime [3], particularly that it can unambiguously manifest gravitational waves (4, 5)The geodesic deviation relates purely to the 'electric' part of a curved spacetime, while the complementary 'magnetic' part is related to the way gyroscopes adapt to geodesics. For Ricci flat spacetimes.

On limit behavior of quasi-local mass for ellipsoids at spatial infinity

We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime.These ellipsoids are not nearly round but they are of interest as an admissible parametrized foliation defining the Arnowitt–Deser–Misner mass.The Hawking mass of this family of ellipsoids tends to-∞.In contrast,we show that the Hayward mass converges to a finite value.Moreover,a positive mass type theorem is established.The limit of the mass has a uniform positive lower bound no matter how oblate these ellipsoids are.This result could be extended for asymptotically Schwarzschild manifolds.And numerical simulation in the Schwarzschild spacetime illustrates that the Hayward mass is monotonically increasing near infinity.

Lorentz transformation of three dimensional gravitational wave tensor

Recently there has been more and more interest in the gravitational wave(GW) of moving sources. This paper introduces a Lorentz transformation problem of GWs. Although the BondiMetzner-Sachs(BMS) theory has in principle already included the Lorentz transformation of GWs, the transformation of the three-dimensional GW tensor has not been explicitly calculated before. Within four-dimensional spacetime, GWs have the properties of ‘boost weight zero’ and‘spin weight 2’. This fact makes the Lorentz transformation of GWs difficult to understand. In the current paper, we adopt the traditional three-dimensional tensor description of a GW. Such a transverse-traceless tensor describes the GW freedom directly. We derive the explicit Lorentz transformation of the GW tensor. The transformation is similar to the Lorentz transformation for an electric field vector and a magnetic field vector which are three-dimensional vectors. Based on the deduced Lorentz transformation of the GW three-dimensional tensor, we can construct the gravitational waveform of a moving source with high speed if only the waveform of the corresponding rest waveform is given.

Hayward Quasilocal Energy of Tori

In this paper, the authors show that one cannot dream of the positivity of the Hayward energy in the general situation. They consider a scenario of a spherically symmetric constant density star matched to the Schwarzschild solution, representing momentarily static initial data. It is proved that any topological tori within the star, distorted or not,have strictly positive Hayward energy. Surprisingly we find analytic examples of ‘thin’ tori with negative Hayward energy in the outer neighborhood of the Schwarzschild horizon.These tori are swept out by rotating the standard round circles in the static coordinates but they are distorted in the isotropic coordinates. Numerical results also indicate that there exist horizontally dragged tori with strictly negative Hayward energy in the region between the boundary of the star and the Schwarzschild horizon.