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Register a new userA note on the fuzzy sphere area spectrum, black hole luminosity, and the quantum nature of spacetime
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Added by
Carlos A. S. Almeida
Publication date
2014
fields
Physics
and research's language is
English
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Non-commutative corrections to the classical expression for the fuzzy sphere area are found out through the asymptotic expansion for its heat kernel trace. As an important consequence, some quantum gravity deviations in the luminosity of black holes must appear. We calculate these deviations for a static, spherically symmetric, black-hole with a horizon modeled by a fuzzy sphere. The results obtained could be verified through the radiation of black holes formed in the Large Hadron Collider (LHC).
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Using a graphical analysis, we show that for the horizon radius $r_hgtrsim 4.8sqrttheta$, the standard semiclassical Bekenstein-Hawking area law for noncommutative Schwarzschild black hole exactly holds for all orders of $theta$. We also give the corrections to the area law to get the exact nature of the Bekenstein-Hawking entropy when $r_h<4.8sqrttheta$ till the extremal point $r_h=3.0sqrt{theta}$.
We study the quantum geometry of the fuzzy sphere defined as the angular momentum algebra $[x_i,x_j]=2imathlambda_p epsilon_{ijk}x_k$ modulo setting $sum_i x_i^2$ to a constant, using a recently introduced 3D rotationally invariant differential structure. Metrics are given by symmetric $3 times 3$ matrices $g$ and we show that for each metric there is a unique quantum Levi-Civita connection with constant coefficients, with scalar curvature $ frac{1}{2}({rm Tr}(g^2)-frac{1}{2}{rm Tr}(g)^2)/det(g)$. As an application, we construct Euclidean quantum gravity on the fuzzy unit sphere. We also calculate the charge 1 monopole for the 3D differential structure.
We investigate quantum corrections in non-commutative gauge theory on fuzzy sphere. We study translation invariant models which classically favor a single fuzzy sphere with U(1) gauge group. We evaluate the effective actions up to the two loop level. We find non-vanishing quantum corrections at each order even in supersymmetric models. In particular the two loop contribution favors U(n) gauge group over U(1) contrary to the tree action in a deformed IIB matrix model with a Myers term. We further observe close correspondences to 2 dimensional quantum gravity.
We investigate the Teichm{u}ller parameters for a Euclidean multiple BTZ black hole spacetime. To induce a complex structure in the asymptotic boundary of such a spacetime, we consider the limit in which two black holes are at a large distance from each other. In this limit, we can approximately determine the period matrix (i.e., the Teichm{u}ller parameters) for the spacetime boundary by using a pinching parameter. The Teichm{u}ller parameters are essential in describing the partition function for the boundary conformal field theory (CFT). We provide an interpretation of the partition function for the genus two extremal boundary CFT proposed by Gaiotto and Yin that it is relevant to double BTZ black hole spacetime.
A distinct visual signature occurs in black holes that are surrounded by optically thin and geometrically thick emission regions. This signature is a sharp-edged dip in brightness that is coincident with the black-hole shadow, which is the projection of the black holes unstable-photon region on the observers sky. We highlight two key mechanisms responsible for producing the sharp-edged dip: i) the reduction of intensity observed in rays that intersect the unstable-photon region, and thus the perfectly absorbing event horizon, versus rays that do not (blocking), and ii) the increase of intensity observed in rays that travel along extended, horizon-circling paths near the boundary of the unstable-photon region (path-lengthening). We demonstrate that the black-hole shadow is a distinct phenomenon from the photon ring, and that models exist in which the former may be observed, but not the latter. Additionally, we show that the black-hole shadow and its associated visual signature differ from the more model-dependent brightness depressions associated with thin-disk models, because for geometrically thick and optically thin emission regions, the blocking and path-lengthening effects are quite general. Consequentially, the black-hole shadow is a robust and fairly model-independent observable for accreting black holes that are in the deep sub-Eddington regime, such as low-luminosity active galactic nuclei (LLAGN).
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