Chiang-Mei Chen

PSEUDOTENSORS AND QUASILOCAL ENERGY-MOMENTUM

Early energy-momentum investigations for gravitating systems gave reference frame dependent pseudotensors; later the quasilocal idea was developed. Quasilocal energy-momentum can be determined by the Hamiltonian boundary term, which also identifies the variables to be held fixed on the boundary. We show that a pseudotensor corresponds to a Hamiltonian boundary term. Hence they are quasilocal and acceptable; each is the energy-momentum density for a definite physical situation with certain boundary conditions. These conditions are identified for well-known pseudotensors.

Hyperbolic space cosmologies

We present a systematic study of accelerating cosmologies obtained from M/string theory compactifications of hyperbolic spaces with time-varying volume. A set of vacuum solutions where the internal space is a product of hyperbolic manifolds is found to give qualitatively the same accelerating four-dimensional FLRW universe behavior as a single hyperbolic space. We also examine the possibility that our universe is a hyperbolic space and provide exact Milne type solutions, as well as intersecting S-brane solutions. When both the usual 4D spacetime and the m-dimensional internal space are hyperbolic, we find eternally accelerating cosmologies for m ≥ 7, with and without form field backgrounds. In particular, the effective potential for a magnetic field background in the large 3 dimensions is positive definite with a local minimum and thus enhances the eternally accelerating expansion.

A note on acceleration from product space compactification

We study compactifications of Einstein gravity on product spaces in vacuum and their acceleration phases. Scalar potentials for the dimensionally reduced effective theory are found to be of exponential form and exact solutions are obtained for a class of product spaces. The inflation in our solutions is not sufficient for the early universe. We comment on the possibility of obtaining sufficient inflation by compactification in general.

Quasilocal quantities for general relativity and other gravity theories

From a covariant Hamiltonian formulation, by using symplectic ideas, we obtain certain covariant boundary expressions for the quasilocal quantities of general relativity and other geometric gravity theories. The contribution from each of the independent dynamic geometric variables (the frame, metric or connection) has two possible covariant forms associated with the selected type of boundary condition. The quasilocal expressions also depend on a reference value for each dynamic variable and a displacement vector field. Integrating over a closed 2-surface with suitable choices for the vector field gives the quasilocal energy, momentum and angular momentum. For the special cases of Einsteins theory and the Poincare gauge theory our expressions are similar to some previously known expressions and give good values for the total ADM and Bondi quantities. We apply our formalism to black hole thermodynamics obtaining the first law and an associated entropy expression for these general gravity theories. For Einsteins theory our quasilocal expressions are evaluated on static spherically symmetric solutions and compared with the findings of some other researchers. The choices needed for the formalism to associate a quasilocal expression with the boundary of a region are discussed.

Holographic Duals of Black Holes in Five-dimensional Minimal Supergravity

We examine the dual conformal field theory for extremal charged black holes in five-dimensional minimal supergravity with two independent angular momenta. The conformal field theory Virasoro algebra, central charge and temperature are calculated. Additionally the conformal field theory entropy is calculated using the Cardy formula and agrees with the Bekenstein–Hawking black hole entropy. The central charges are directly proportional to the angular momentum components of the black hole. In five and higher dimensions, rotations of the spacetime correspond to rotations of the central charges leading to an apparent symmetry relating the conformal field theories dual to each black hole. A rotationally invariant central charge, which is proportional to the total angular momentum, is used to discuss the supersymmetric Breckenridge–Myers–Peet–Vafa black hole limits.

Hidden conformal symmetry of the Reissner-Nordström black holes

Motivated by recent progresses in the holographic descriptions of the Kerr and Reissner-Nordström (RN) black holes, we explore the hidden conformal symmetry of the nonextremal uplifted 5D RN black hole by studying the near horizon wave equation of a massless scalar field propagating in this background. Similar to the Kerr black hole case, this hidden conformal symmetry is broken by the periodicity of the associated angle coordinate in the background geometry. Nevertheless, the probe massless scalar field somehow can reveal the dual CFT description of the nonextremal RN black holes. The duality is further supported by matching of the entropies and absorption cross sections calculated from both the CFT and gravity sides.

Holography of charged dilaton black holes in general dimensions

We study several aspects of charged dilaton black holes with planar symmetry in (d + 2)-dimensional spacetime, generalizing the four-dimensional results investigated in arXiv:0911.3586 [hep-th]. We revisit the exact solutions with both zero and finite temperature and discuss the thermodynamics of the near-extremal black holes. We calculate the AC conductivity in the zero-temperature background by solving the corresponding Schrödinger equation and find that the AC conductivity behaves like ωδ, where the exponent δ is determined by the dilaton coupling α and the spacetime dimension parameter d. Moreover, we also study the Gauss-Bonnet corrections to η/s in a five-dimensional finite-temperature background.

Holographic dual of the dyonic Reissner-Nordström black hole

It is shown that the hidden conformal symmetry, namely SO(2,2) ∼ SL(2,R)L × SL(2,R)R symmetry, of the non-extremal dyonic Reissner-Nordstrblack hole can be probed by a charged massless scalar field at low frequencies. The existence of such hidden conformal symmetry suggests that the field theory holographically dual to the 4D Reissner-Nordstrom black hole indeed should be a 2D CFT. Although the associated AdS3 structure does not explicitly appear in the near horizon geometry, the primary parameters of the dual CFT2 can be exactly obtained without the necessity of embedding the 4D Reissner-Nordstrblack hole into 5D spacetime. The duality is further supported by comparing the absorption cross sections and real-time correlators obtained from both the CFT and the gravity sides.

The RN/CFT Correspondence Revisited

We reconsidered the quantum gravity description of the near horizon extremal Reissner-Nordstrøm black hole in the viewpoint of the AdS2/CFT1 correspondence. We found that, for pure electric case, the right moving central charge of dual 1D CFT is 6Q2 which is different from the previous result 6Q3 of left moving sector obtained by warped AdS3/CFT2 description. We discussed the discrepancy in these two approaches and examined novel properties of our result.

Quasilocal energy-momentum for geometric gravity theories

Abstract From a covariant Hamiltonian formulation, using symplectic ideas, we obtain covariant quasilocal energy-momentum boundary expressions for general gravity theories. The expressions depend on which variables are fixed on the boundary, on a reference configuration and a displacement vector field. We consider applications to Einsteins theory, black hole thermodynamics and alternate spinor expressions.