Umpei Miyamoto

High and low dimensions in the black hole negative mode

The negative mode of the Schwarzschild black hole is central to Euclidean quantum gravity around hot flat space and for the Gregory–Laflamme black string instability. We analyze the eigenvalue as a function of spacetime dimension λ = λ(d) by constructing two perturbative expansions: one for large d and the other for small d − 3, and determining as many coefficients as we are able to compute analytically. By joining the two expansions, we obtain an interpolating rational function accurate to better than 2% through the whole range of dimensions including d = 4.

Hawking radiation from black rings

We calculate the quantum radiation from the 5-dimensional charged rotating black rings by demanding the radiation eliminate the possible anomalies on the horizons. It is shown that the temperature, energy flux, and angular-momentum flux exactly coincide with those of the Hawking radiation. The black rings considered in this paper contain the Myers-Perry black hole as a limit, and the quantum radiation for this black hole, obtained in the literature, is recovered in the limit. The results support the picture that the Hawking radiation can be regarded as the anomaly eliminator on horizons and suggest its general applicability to the higher-dimensional black holes discovered recently.

Hawking radiation of a vector field and gravitational anomalies

Recently, the relation between Hawking radiation and gravitational anomalies has been used to estimate the flux of Hawking radiation for a large class of black objects. In this paper, we extend the formalism, originally proposed by Robinson and Wilczek, to the Hawking radiation of vector particles (photons). It is explicitly shown, with the Hamiltonian formalism, that the theory of an electromagnetic field on d-dimensional spherical black holes reduces to one of an infinite number of massive complex scalar fields on 2-dimensional spacetime, for which the usual anomaly-cancellation method is available. It is found that the total energy emitted from the horizon for the electromagnetic field is just (d - 2) times that for a scalar field. The results support the picture that Hawking radiation can be regarded as an anomaly eliminator on horizons. Possible extensions and applications of the analysis are discussed.

On non-uniform smeared black branes

We investigate charged dilatonic black p-branes smeared on a transverse circle. The system can be reduced to neutral vacuum black branes, and we perform static perturbations for the reduced system to construct non-uniform solutions. At each order a single master equation is derived, and the Gregory–Laflamme critical wavelength is determined. Based on the non-uniform solutions, we discuss thermodynamic properties of this system and argue that in a microcanonical ensemble the non-uniform smeared branes are entropically disfavoured even near the extremality, if the spacetime dimension is D ≤ 13 + p, which is the critical dimension for the vacuum case. However, the critical dimension is not universal. In a canonical ensemble, the vacuum non-uniform black branes are thermodynamically favourable at D > 12 + p, whereas the non-uniform smeared branes are favourable at D > 14 + p near the extremality.

New stable phase of non-uniform charged black strings

Non-uniform black strings coupled to a gauge field are constructed by a perturbative method in a wide range of spacetime dimensions. At the linear order of perturbations, we see that the Gregory-Laflamme instability vanishes at the point where the background solution becomes thermodynamically stable. The emergence/vanishing of the static mode resembles phase transitions, and in fact we find that its critical exponent is nearly 1/2, which means a second-order transition. By employing higher-order perturbations, the physical properties of the non-uniform black strings are investigated in detail. For fixed spacetime dimensions, we find the critical charges at which the stability of non-uniform states changes. For some range of charge, non-uniform black strings are entropically favored over uniform ones. The gauge charge works as a control parameter that controls not only the stability of uniform black strings but also the non-uniform states. In addition, we find that for a fixed background charge the uniform state is not necessarily the state carrying the largest tension. The phase diagram and a comparison with the critical dimension are also discussed.

Have we already detected astrophysical symptoms of space-time noncommutativity?

We discuss astrophysical implications of

Particle velocity in noncommutative space-time

kappa

Analytic evidence for the Gubser–Mitra conjecture

-Minkowski space-time, in which there appears space-time noncommutativity. We first derive a velocity formula for particles based on the motion of a wave packet. The result is that a massless particle moves at a constant speed as in the usual Minkowski space-time, which implies that an arrival time analysis by

Generic features of Einstein-Aether black holes

gamma

On the resolution of negative mass naked singularities

-rays from Markarian (Mk) 421 does not exclude space-time noncommutativity. Based on this observation, we analyze reaction processes in