Three-dimensional General Relativity Research Articles

Combined Screw and Wedge Dislocations

Elastic media with defects are considered manifold with nontrivial Riemann–Cartan geometry in the geometric theory of defects. We obtain the solution of three-dimensional Euclidean general relativity equations with an arbitrary number of linear parallel sources. It describes elastic media with parallel combined wedge and screw dislocations.

Formation of Episodic Jets and Associated Flares from Black Hole Accretion Systems

Episodic ejections of blobs (episodic jets) are widely observed in black hole sources and usually associated with flares. In this paper, by performing and analyzing three-dimensional general relativity magnetohydrodynamical numerical simulations of accretion flows, we investigate their physical mechanisms. We find that magnetic reconnection occurs in the accretion flow, likely due to the turbulent motion and differential rotation of the accretion flow, resulting in flares and formation of flux ropes. Flux ropes formed inside of 10–15 gravitational radii are found to mainly stay within the accretion flow, while flux ropes formed beyond this radius are ejected outward by magnetic forces and form the episodic jets. These results confirm the basic scenario proposed in Yuan et al. Moreover, our simulations find that the predicted velocity of the ejected blobs is in good consistency with observations of Sgr A*, M81, and M87. All of the processes were found to occur quasiperiodically, with the period being the orbital time at the radius where the flux rope is formed. The predicted period of the flares and ejections is consistent with those found from the light curves or image of Sgr A*, M87, and PKS 1510–089. The possible applications to protostellar accretion systems are discussed.

The Accretion Flow in M87 is Really MAD

Abstract The supermassive black holes in most galaxies in the universe are powered by hot accretion flows. Both theoretical analysis and numerical simulations have indicated that, depending on the degree of magnetization, black hole hot accretion flow is divided into two modes, namely SANE (standard and normal evolution) and MAD (magnetically arrested disk). It has been an important question which mode the hot accretion flows in individual sources should belong to in reality, SANE or MAD. This issue has been investigated in some previous works but they all suffer from various uncertainties. By using the measured rotation measure (RM) values in the prototype low-luminosity active galactic nuclei in M87 at 2, 5, and 8 GHz along the jet at various distances from the black hole, combined with three-dimensional general relativity magnetohydrodynamical numerical simulations of SANE and MAD, we show in this paper that the RM values predicted by MAD are well consistent with observations, while the SANE model overestimates the RM by over two orders of magnitude and thus is ruled out.

Fully extended BV-BFV description of General Relativity in three dimensions

We compute the extension of the BV theory for three-dimensional General Relativity to all higher-codimension strata - boundaries, corners and vertices - in the BV-BFV framework. Moreover, we show that such extension is strongly equivalent to (nondegenerate) BF theory at all codimensions.

Integrable Systems and Spacetime Dynamics.

It is shown that the Ablowitz-Kaup-Newell-Segur (AKNS) integrable hierarchy can be obtained as the dynamical equations of three-dimensional general relativity with a negative cosmological constant. This geometrization of the AKNS system is possible through the construction of novel boundary conditions for the gravitational field. These are invariant under an asymptotic symmetry group characterized by an infinite set of AKNS commuting conserved charges. Gravitational configurations are studied by means of SL(2,R) conjugacy classes. Conical singularities and black hole solutions are included in the boundary conditions.

Numerical Simulation of Hot Accretion Flows. IV. Effects of Black Hole Spin and Magnetic Field Strength on the Wind and the Comparison between Wind and Jet Properties

Abstract This is the fourth paper of our series studying winds from hot accretion flows around black holes. In the first two papers, we showed the existence of strong winds in hot accretion flows using hydrodynamical and magnetohydrodynamical (MHD) simulations. In the third paper, by using three-dimensional general relativity MHD numerical simulation data of hot accretion flows and adopting a “virtual particle trajectory” data analysis approach, we calculated the properties of wind, such as its mass flux and velocity. However, that paper focuses only on a nonspinning black hole and standard and normal accretion. In the present paper, we extend the third paper by including cases of a rapidly rotating black hole and magnetically arrested disk. We focus on investigating the effect of spin and magnetic field on the properties of the wind and jet. It is found that a larger spin and stronger magnetic field usually enhance the wind and jet. The formulae describing the mass flux, poloidal velocity, and fluxes of momentum, kinetic energy, and total energy of the wind and jet are presented. One interesting finding, among others, is that even in the case of a very rapidly spinning black hole, where the jet is supposed to be the strongest, the momentum flux of the jet is smaller than that of the wind, while the total energy flux of the jet is larger than that of the wind by at most a factor of 10. This result suggests that the wind potentially plays a more important role than the jet, at least for some problems in active galactic nucleus feedback.

Weyl charges in asymptotically locallyAdS3spacetimes

We discuss an enhancement of the Brown-Henneaux boundary conditions in three-dimensional AdS General Relativity to encompass Weyl transformations of the boundary metric. The resulting asymptotic symmetry algebra, after a field-dependent redefinition of the generators, is a direct sum of two copies of the Witt algebra and the Weyl abelian sector. The charges associated to Weyl transformations are non-vanishing, integrable but not conserved due to a flux driven by the Weyl anomaly coefficient. The charge algebra admits an additional non-trivial central extension in the Weyl sector, related to the well-known Weyl anomaly. We then construct the holographic Weyl current and show that it satisfies an anomalous Ward-Takahashi identity of the boundary theory.

Entropy in three-dimensional general relativity: Kerr-AdS black hole

Black hole thermodynamics of the Kerr-AdS spacetime in three-dimensional general relativity is analyzed using a Hamiltonian approach. The values of the conserved charges and entropy, obtained by a proper treatment of the AdS asymptotic conditions, are shown to satisfy the first law of black hole dynamics.

The gauge symmetries of first-order general relativity with matter fields

In n-dimensional spacetimes (n > 3), there exists an internal gauge symmetry of the Palatini action with a cosmological constant that is the natural generalization of the so-called ‘local translations’ of three-dimensional general relativity. We report the extension of this symmetry to include the minimal coupling of Yang–Mills and fermion fields to the Palatini action with a cosmological constant. We show that, as in the case of three-dimensional local translations, the extended symmetry depends on the energy–momentum tensor of the corresponding matter field and, for fermions, it contains an additional term that in four dimensions is proportional to the axial fermion current. We also report the extension of the analog of this internal gauge symmetry for the Holst action with a cosmological constant by incorporating minimally coupled scalar and Yang–Mills fields, as well as a non-minimally coupled fermion field. In the last case, the extended symmetry is affected by both the Immirzi parameter and the energy–momentum tensor and, for fermions, it also depends on the axial fermion current.

Smarr formula for BTZ black holes in general three-dimensional gravity models

Recent studies have presented the interpretation of thermodynamic enthalpy for the mass of BTZ black holes and the corresponding Smarr formula. All these are made in the background of three-dimensional (3D) general relativity. In this paper, we extend such interpretation into general 3D gravity models. It is found that the direct extension is unfeasible and some extra conditions are required to preserve both the Smarr formula and the first law of black hole thermodynamics. Thus, BTZ black hole thermodynamics enforces some constraints for general 3D gravity models, and these constraints are consistent with all previous discussions.

Three-Dimensional Extended Bargmann Supergravity.

We show that three-dimensional general relativity, augmented with two vector fields, allows for a nonrelativistic limit, different from the standard limit leading to Newtonian gravity, that results in a well-defined action which is of the Chern-Simons type. We show that this three-dimensional "extended Bargmann gravity," after coupling to matter, leads to equations of motion allowing a wider class of background geometries than the ones that one encounters in Newtonian gravity. We give the supersymmetric generalization of these results and point out an important application in the context of calculating partition functions of nonrelativistic field theories using localization techniques.

Rotating black holes in three-dimensional Hořava gravity

We study black holes in the infrared sector of three-dimensional Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity. It is shown that black hole solutions with anti--de Sitter asymptotics are admissible only in the sector of the theory in which the scalar degree of freedom propagates infinitely fast. We derive the most general class of stationary, circularly symmetric, asymptotically anti--de Sitter black hole solutions. We also show that the theory admits black hole solutions with de Sitter and flat asymptotics, unlike three-dimensional general relativity. For all these cases, universal horizons may or may not exist depending on the choice of parameters. Solutions with de Sitter asymptotics can have universal horizons that lie beyond the de Sitter horizon.

Topologically massive gravity and Ricci–Cotton flow

We consider topologically massive gravity (TMG), which is three-dimensional general relativity with a cosmological constant and a gravitational Chern–Simons term. When the cosmological constant is negative the theory has two potential vacuum solutions: anti-de Sitter space and warped anti-de Sitter space. The theory also contains a massive graviton state which renders these solutions unstable for certain values of the parameters and boundary conditions. We study the decay of these solutions due to the condensation of the massive graviton mode using Ricci–Cotton flow, which is the appropriate generalization of Ricci flow to TMG. When the Chern–Simons coupling is small the AdS solution flows to warped AdS by the condensation of the massive graviton mode. When the coupling is large the situation is reversed, and warped AdS flows to AdS. Minisuperspace models are constructed where these flows are studied explicitly.

Cutting-edge issues in core-collapse supernova theory

AbstractBased on our multi-dimensional neutrino-radiation hydrodynamic simulations, we report several cutting-edge issues about the long-veiled explosion mechanism of core-collapse supernovae (CCSNe). In this contribution, we pay particular attention to whether three-dimensional (3D) hydrodynamics and/or general relativity (GR) would or would not help the onset of explosions. Our results from the first generation of full GR 3D simulations including approximate neutrino transport are quite optimistic, indicating that both of the two ingredients can foster neutrino-driven explosions. We give an outlook with a summary of the most urgent tasks to draw a robust conclusion to our findings.

New massive gravity extended with an arbitrary number of curvature corrections

We consider new massive gravity (NMG) type models in the context of AdS/CFT. By demanding the existence of a holographic $c$ theorem, we construct an infinite family of three-dimensional quantum gravity models, generalizing the NMG Lagrangian to arbitrarily high order in curvatures. We calculate the central charge $c$ and show that using Cardy's formula it matches the entropy of black hole solutions. We also consider fluctuations about an anti-de Sitter background, finding ghostlike massive modes as in NMG. However, these can (a) be made massless by setting $c=0$, in which case these Lagrangians are expected to provide gravity duals for strongly coupled logarithmic conformal field theories, (b) be eliminated by imposing a single constraint on the parameters of the Lagrangian, thereby obtaining an infinite family of theories with the same perturbative content of three-dimensional general relativity.

Equivalence of three-dimensional spacetimes

A solution to the equivalence problem in three-dimensional gravity is given and a practically useful method to obtain a coordinate invariant description of local geometry is presented. The method is a nontrivial adaptation of the Karlhede invariant classification of spacetimes of general relativity. The local geometry is completely determined by the curvature tensor and a finite number of its covariant derivatives in a frame where the components of the metric are constants. The results are presented in the framework of real two-component spinors in three-dimensional spacetimes, where the algebraic classifications of the Ricci and Cotton–York spinors are given and their isotropy groups and canonical forms are determined. As an application we discuss Gödel-type spacetimes in three-dimensional general relativity. The conditions for local space and time homogeneity are derived and the equivalence of three-dimensional Gödel-type spacetimes is studied and the results compared with previous work on four-dimensional Gödel-type spacetimes.

Quadratic gravity theories in 2+1 dimensions and the topological Chern-Simons term

It is astonishing that a locally trivial and globally nontrivial Einstein-type gravitational theory can be built only by lowering the dimension of our space-time—which is supposed to be four dimensional—by one unit. In fact, threedimensional general relativity is dynamically trivial: outside sources, spacetime is flat—all effects of the localized sources are on the global geometry, which is fixed by the singularities of the worldlines of the particles @1#. The quantum mechanical analogue of this triviality emerges when the HilbertEinstein action related to this theory is quantized. It is easy to establish that the theory does not possess any propagating degrees of freedom. In other words, there are no gravitons. The preceding considerations lead us to raise the following important question: Is it possible to build a nontrivial generally covariant three-dimensional gravity theory having propagating degrees of freedom? The answer is affirmative. Actually, this can be done at least in two different ways: ~i! Adding a topological nontrivial term to general relativity in ~211!D @2#. Ordinary Einstein gravity which is trivial acquires now a propagating, massive, spin-2 mode. This theory is ghost-free and causal, although of the thirdderivative order. ~ii! Including the four-derivatives terms *R 2 Agd 3 x and

Stationary black holes in a generalized three-dimensional theory of gravity

We consider a generalized three-dimensional theory of gravity which is specified by two fields, the graviton and the dilaton, and one parameter. This theory contains, as particular cases, three-dimensional General Relativity and three-dimensional String Theory. Stationary black hole solutions are generated from the static ones using a simple coordinate transformation. The stationary black holes solutions thus obtained are locally equivalent to the corresponding static ones, but globally distinct. The mass and angular momentum of the stationary black hole solutions are computed using an extension of the Regge and Teitelboim formalism. The causal structure of the black holes is described.

Statistical mechanics of the three-dimensional Euclidean black hole

In its formulation as a Chern-Simons theory, three-dimensional general relativity induces a Wess-Zumino-Witten action on spatial boundaries. Treating the horizon of the three-dimensional Euclidean black hole as a boundary, I count the states of the resulting WZW model, and show that when analytically continued back to Lorentzian signature, they yield the correct Bekenstein-Hawking entropy. The relevant states can be understood as ``would-be gauge'' degrees of freedom that become dynamical at the horizon.

Dualities of 3D dilaton gravity.

We investigate Brans-Dicke dilaton gravity theories in 2+1 dimensions. We show that the reduced field equations for solutions with diagonal metric and depending only on one spacetime coordinate have a continuous O(2) symmetry. Using this symmetry we derive general static and cosmological solutions of the theory. The action of the discrete group O(2,Z) on the space of the solutions is discussed. Three-dimensional string effective theory and three-dimensional general relativity are discussed in detail. In particular, we find that the previously discovered black string solution is dual to a spacetime with a conical singularity.