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# Contour plot of the Kretchmann scalar tanh(σ −4 R αβγδ R αβγδ ) in the (ρ, z) plane for p = 1/3. The centre of the flower-shaped region is the ring singularity.

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We analyze the $\delta=2$ Tomimatsu-Sato spacetime in the context of the
proposed Kerr/CFT correspondence. This 4-dimensional vacuum spacetime is
asymptotically flat and has a well-defined ADM mass and angular momentum, but
also involves several exotic features including a naked ring singularity, and
two disjoint Killing horizons separated by a reg...

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## Citations

Recently double black hole vacuum and electrovacuum metrics attracted attention as exact solutions suitable for visualization of ultra-compact objects beyond the Kerr paradigm. However, many of the proposed systems are plagued with ring curvature singularities. Here we present a new simple solution of this type which is asymptotically Kerr, has zero electric and magnetic charges, but is endowed with magnetic dipole moment and electric quadrupole moment. It is manifestly free of ring singularities, and contains only a mild string-like singularity on the axis corresponding to a distributional energy-momentum tensor. Its main constituents are two extreme co-rotating black holes carrying equal electric and opposite magnetic and NUT charges.

We study the extremal rotating spacetimes with a NUT twist in the context of recently proposed Kerr/CFT correspondence. The Kerr/CFT correspondence states that the near-horizon states of an extremal four (or higher) dimensional black hole could be identified with a certain chiral conformal field theory. The corresponding Virasoro algebra is generated with a class of diffeomorphism which preserves an appropriate boundary condition on the near-horizon geometry. We combine the calculated central charges with the expected form of the temperature, using the Cardy formula to obtain the microscopically entropy of the extremal rotating spacetimes with a NUT twist. All results are in agreement with the macroscopic entropy of the extremal spacetimes.

We model the spacetime of low-mass X-ray binaries with the Tomimatsu-Sato
{\delta} = 2 (TS2) metric and study the properties of the orbital and the
epicyclic frequencies. The numerical analysis shows that the properties of the
characteristic frequencies of oscillation do not differ qualitatively from
those of the Kerr black hole. Estimates for the angular momenta of the three
stellar mass black hole candidates GRO 1655-40, XTE 1550-564 and GRS 1915+105
are made with the application of the nonlinear resonance model. We find
agreement between the predictions based on the 3 : 2 nonlinear resonance model
for a TS2 background and the current estimates found in the literature.

We have investigated the hidden conformal symmetry of generic non-extremal rotating black holes in the five-dimensional Gödel universe. In a range of parameters, the low-frequency massless scalar wave equation in the “near region” can be described by an SL(2, R)L
× SL(2, R)R
conformal symmetry. We further found that the microscopic entropy via Cardy formula matches the macroscopic Bekenstein-Hawking entropy and the absorption cross section for the massless scalar also agrees with the one for the two dimensional finite temperature conformal field theory (CFT). All these evidences support the conjecture that the generic non-extremal rotating black hole immersed in the Gödel universe can be dual to a two dimensional finite temperature CFT. In addition, we have reformulated the first laws of thermodynamics associated with the inner and outer horizons of the rotating Gödel-type black holes into the forms of conformal thermodynamics.

The physical properties of the Tomimatsu-Sato delta=2 spacetime are analyzed,
with emphasis on the issues of the negative mass distribution in this spacetime
and the origin of a massless ring singularity which are treated with the aid of
an equatorially asymmetric two-body configuration arising within the framework
of the analytically extended double-Kerr solution. As a by-product of this
analysis it is proved analytically that the Kerr spacetime with negative mass
always has a massless naked ring singularity off the symmetry axis accompanied
by a region with closed timelike curves, and it is also pointed out that the
Boyer-Lindquist coordinates in that case should be introduced in a different
manner than in the case of the Kerr solution with positive mass.

We study the hidden conformal symmetry of four-dimensional extremal
Kaluza-Klein black hole. The scalar Laplacian corresponding to the radial
equation in the near-region is rewritten in terms of the $SL(2,\mathbb R)$
quadratic Casimir. Using the first law of black hole thermodynamics, this
symmetry enables us to obtain the conjugate charges for the CFT side. The
real-time correlators are also found to agree with the CFT expectations.

The extremal Kerr black hole with the angular momentum J is conjectured to be
dual to CFT with central charges c_L=c_R=12J. However, the central charge in
the right sector remains to be explicitly derived so far. In order to
investigate this issue, we introduce new near horizon limits of (near) extremal
Kerr and five-dimensional Myers-Perry black holes. We obtain Virasoro algebras
as asymptotic symmetries and calculate the central charges associated with
them. One of them is equivalent to that of the previous studies, and the other
is non-zero, but still the order of near extremal parameter. Redefining the
algebras to take the standard form, we obtain a finite value as expected by the
Kerr/CFT correspondence.