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Register a new userGravity Waves from Kerr/CFT
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Added by
Achilleas Porfyriadis
Publication date
2014
fields
Physics
and research's language is
English
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Dynamics at large redshift near the horizon of an extreme Kerr black hole are governed by an infinite-dimensional conformal symmetry. This symmetry may be exploited to analytically, rather than numerically, compute a variety of potentially observable processes. In this paper we compute and study the conformal transformation properties of the gravitational radiation emitted by an orbiting mass in the large-redshift near-horizon region.
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Massive objects orbiting a near-extreme Kerr black hole quickly plunge into the horizon after passing the innermost stable circular orbit. The plunge trajectory is shown to be related by a conformal map to a circular orbit. Conformal symmetry of the near-horizon region is then used to compute the gravitational radiation produced during the plunge phase.
Quantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by J=GM^2) is considered. It is shown that consistent boundary conditions exist, for which the asymptotic symmetry generators form one copy of the Virasoro algebra with central charge c_L=12J / hbar. This implies that the near-horizon quantum states can be identified with those of (a chiral half of) a two-dimensional conformal field theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with dimensionless temperature T_L=1/2pi and conjugate energy given by the zero mode generator, L_0, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy S_{micro}=2pi J / hbar for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy S_{macro}=Area / 4hbar G. The results apply to any consistent unitary quantum theory of gravity with a Kerr solution. We accordingly conjecture that extreme Kerr black holes are holographically dual to a chiral two-dimensional conformal field theory with central charge c_L=12J / hbar, and in particular that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with c_L sim 2 times 10^{79}.
We calculate the amplitude of gravitational waves produced by inflation on a de Sitter brane embedded in five-dimensional anti-de Sitter bulk spacetime, extending previous calculations in Randall-Sundrum type cosmology to include the effect of induced gravity corrections on the brane. These corrections arise via a term in the brane action that is proportional to the brane Ricci scalar. We find that, as in the Randall-Sundrum case, there is a mass gap between the discrete zero-mode and a continuum of massive bulk modes, which are too heavy to be excited during inflation. We give the normalization of the zero-mode as a function of the Hubble rate on the brane and are thus able to calculate the high energy correction to the spectrum of gravitational wave (tensor) modes excited on large scales during inflation from initial vacuum fluctuations on small scales. We also calculate the amplitude of density (scalar) perturbations expected due to inflaton fluctuations on the brane, and show that the usual four-dimensional consistency relation for the tensor/scalar ratio remains valid for brane inflation with induced gravity corrections.
Most extreme-mass-ratio-inspirals of small compact objects into supermassive black holes end with a fast plunge from an eccentric last stable orbit. For rapidly rotating black holes such fast plunges may be studied in the context of the Kerr/CFT correspondence because they occur in the near-horizon region where dynamics are governed by the infinite dimensional conformal symmetry. In this paper we use conformal transformations to analytically solve for the radiation emitted from fast plunges into near-extreme Kerr black holes. We find perfect agreement between the gravity and CFT computations.
Any abundance of black holes that was present in the early universe will evolve as matter, making up an increasingly large fraction of the total energy density as space expands. This motivates us to consider scenarios in which the early universe included an era that was dominated by low-mass ($M < 5times 10^8$ g) black holes which evaporate prior to primordial nucleosynthesis. In significant regions of parameter space, these black holes will become gravitationally bound within binary systems, and undergo mergers before evaporating. Such mergers result in three potentially observable signatures. First, any black holes that have undergone one or more mergers will possess substantial angular momentum, causing their Hawking evaporation to produce significant quantities of high-energy gravitons. These products of Hawking evaporation are predicted to constitute a background of hot ($sim$eV-keV) gravitons today, with an energy density corresponding to $Delta N_{rm eff} sim 0.01-0.03$. Second, these mergers will produce a stochastic background of high-frequency gravitational waves. And third, the energy density of these gravitational waves can be as large as $Delta N_{rm eff} sim 0.3$, depending on the length of time between the mergers and evaporation. These signals are each potentially within the reach of future measurements.
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