Wavefunction of a Black Hole and the Dynamical Origin of Entropy

Recently it was proposed to explain the dynamical origin of the entropy of a black hole by identifying its dynamical degrees of freedom with states of quantum fields propagating in the black-hole's interior. The present paper contains the further development of this approach. The no-boundary proposal (analogous to the Hartle-Hawking no-boundary proposal in quantum cosmology) is put forward for defining the wave function of a black hole. This wave function is a functional on the configuration space of physical fields (including the gravitational one) on the three-dimensional space with the Einstein-Rosen bridge topology.It is shown that in the limit of small perturbations on the Kruskal background geometry the no-boundary wave function coincides with the Hartle-Hawking vacuum state. The invariant definition of inside and outside modes is proposed. The density matrix describing the internal state of a black hole is obtained by averaging over the outside modes. This density matrix is used to define the entropy of a black hole, which is to be divergent. It is argued that the quantum fluctuations of the horizon which are internally present in the proposed formalism may give the necessary cut-off and provide a black hole with the finite entropy.Comment: 39 pages, LaTeX misprint is corrected, original text is not modifie

Entanglement entropy in curved spacetimes with event horizons

We consider the computation of the entanglement entropy in curved backgrounds with event horizons. We use a Hamiltonian approach to the problem and perform numerical computations on a spherical lattice of spacing $a$. We study the cosmological case and make explicit computations for the Friedmann-Robertson-Walker universe. Our results for a massless, minimally coupled scalar field can be summarized by $S_{ent}=0.30 r_H^2/a^2$,which resembles the flat space formula, although here the horizon radius, $r_H$, is time-dependent.Comment: 12 pages, RevTex 3.0, 2 figures as uuencoded compressed Postscript file

On the Entropy of a Quantum Field in the Rotating Black Holes

By using the brick wall method we calculate the free energy and the entropy of the scalar field in the rotating black holes. As one approaches the stationary limit surface rather than the event horizon in comoving frame, those become divergent. Only when the field is comoving with the black hole (i.e. $\Omega_0 = \Omega_H$) those become divergent at the event horizon. In the Hartle-Hawking state the leading terms of the entropy are $A \frac{1}{h} + B \ln(h) + finite$, where $h$ is the cut-off in the radial coordnate near the horizon. In term of the proper distance cut-off $\epsilon$ it is written as $S = N A_H/\epsilon^2$. The origin of the divergence is that the density of state on the stationary surface and beyond it diverges.Comment: Latex, 23 pages, 7 eps figure

Two-dimensional Quantum-Corrected Eternal Black Hole

The one-loop quantum corrections to geometry and thermodynamics of black hole are studied for the two-dimensional RST model. We chose boundary conditions corresponding to the eternal black hole being in the thermal equilibrium with the Hawking radiation. The equations of motion are exactly integrated. The one of the solutions obtained is the constant curvature space-time with dilaton being a constant function. Such a solution is absent in the classical theory. On the other hand, we derive the quantum-corrected metric (\ref{solution}) written in the Schwarzschild like form which is a deformation of the classical black hole solution \cite{5d}. The space-time singularity occurs to be milder than in classics and the solution admits two asymptotically flat black hole space-times lying at "different sides" of the singularity. The thermodynamics of the classical black hole and its quantum counterpart is formulated. The thermodynamical quantities (energy, temperature, entropy) are calculated and occur to be the same for both the classical and quantum-corrected black holes. So, no quantum corrections to thermodynamics are observed. The possible relevance of the results obtained to the four-dimensional case is discussed.Comment: Latex, 28 pges; minor corrections in text and abstract made and new references adde

Algebraic analysis of a model of two-dimensional gravity

An algebraic analysis of the Hamiltonian formulation of the model two-dimensional gravity is performed. The crucial fact is an exact coincidence of the Poisson brackets algebra of the secondary constraints of this Hamiltonian formulation with the SO(2,1)-algebra. The eigenvectors of the canonical Hamiltonian $H_{c}$ are obtained and explicitly written in closed form.Comment: 21 pages, to appear in General Relativity and Gravitatio

Can the "brick wall" model present the same results in different coordinate representations?

By using the 't Hooft's "brick wall" model and the Pauli-Villars regularization scheme we calculate the statistical-mechanical entropies arising from the quantum scalar field in different coordinate settings, such as the Painlev\'{e} and Lemaitre coordinates. At first glance, it seems that the entropies would be different from that in the standard Schwarzschild coordinate since the metrics in both the Painlev\'{e} and Lemaitre coordinates do not possess the singularity at the event horizon as that in the Schwarzschild-like coordinate. However, after an exact calculation we find that, up to the subleading correction, the statistical-mechanical entropies in these coordinates are equivalent to that in the Schwarzschild-like coordinate. The result is not only valid for black holes and de Sitter spaces, but also for the case that the quantum field exerts back reaction on the gravitational field provided that the back reaction does not alter the symmetry of the spacetime.Comment: 8 pages, Phys. Rev. D in pres

One-loop Quantum Corrections to the Entropy for an Extremal Reissner-Nordstr\"om Black Hole

The first quantum corrections to the entropy for an eternal 4-dimensional extremal Reissner-Nordstr\"om black hole is investigated at one-loop level, in the large mass limit of the black hole, making use of the conformal techniques related to the optical metric. A leading cubic horizon divergence is found and other divergences appear due to the singular nature of the optical manifold. The area law is shown to be violated.Comment: 10 pages, LaTe

Viral discovery and diversity in trypanosomatid protozoa with a focus on relatives of the human parasite <i>Leishmania</i>.

Knowledge of viral diversity is expanding greatly, but many lineages remain underexplored. We surveyed RNA viruses in 52 cultured monoxenous relatives of the human parasite &lt;i&gt;Leishmania&lt;/i&gt; ( &lt;i&gt;Crithidia&lt;/i&gt; and &lt;i&gt;Leptomonas&lt;/i&gt; ), as well as plant-infecting &lt;i&gt;Phytomonas&lt;/i&gt; &lt;i&gt;Leptomonas pyrrhocoris&lt;/i&gt; was a hotbed for viral discovery, carrying a virus (Leptomonas pyrrhocoris ostravirus 1) with a highly divergent RNA-dependent RNA polymerase missed by conventional BLAST searches, an emergent clade of tombus-like viruses, and an example of viral endogenization. A deep-branching clade of trypanosomatid narnaviruses was found, notable as &lt;i&gt;Leptomonas seymouri&lt;/i&gt; bearing Narna-like virus 1 (LepseyNLV1) have been reported in cultures recovered from patients with visceral leishmaniasis. A deep-branching trypanosomatid viral lineage showing strong affinities to bunyaviruses was termed " &lt;i&gt;Leishbunyavirus&lt;/i&gt; " (LBV) and judged sufficiently distinct to warrant assignment within a proposed family termed " &lt;i&gt;Leishbunyaviridae&lt;/i&gt; " Numerous relatives of trypanosomatid viruses were found in insect metatranscriptomic surveys, which likely arise from trypanosomatid microbiota. Despite extensive sampling we found no relatives of the totivirus &lt;i&gt;Leishmaniavirus&lt;/i&gt; (LRV1/2), implying that it was acquired at about the same time the &lt;i&gt;Leishmania&lt;/i&gt; became able to parasitize vertebrates. As viruses were found in over a quarter of isolates tested, many more are likely to be found in the &gt;600 unsurveyed trypanosomatid species. Viral loss was occasionally observed in culture, providing potentially isogenic virus-free lines enabling studies probing the biological role of trypanosomatid viruses. These data shed important insights on the emergence of viruses within an important trypanosomatid clade relevant to human disease

Euclidean Approach to the Entropy for a Scalar Field in Rindler-like Space-Times

The off-shell entropy for a massless scalar field in a D-dimensional Rindler-like space-time is investigated within the conical Euclidean approach in the manifold C_\be\times\M^N, C_\be being the 2-dimensional cone, making use of the zeta-function regularisation. Due to the presence of conical singularities, it is shown that the relation between the zeta-function and the heat kernel is non trivial and, as first pointed out by Cheeger, requires a separation between small and large eigenvalues of the Laplace operator. As a consequence, in the massless case, the (naive) non existence of the Mellin transform is by-passed by the Cheeger's analytical continuation of the zeta-function on manifold with conical singularities. Furthermore, the continuous spectrum leads to the introduction of smeared traces. In general, it is pointed out that the presence of the divergences may depend on the smearing function and they arise in removing the smearing cutoff. With a simple choice of the smearing function, horizon divergences in the thermodynamical quantities are recovered and these are similar to the divergences found by means of off-shell methods like the brick wall model, the optical conformal transformation techniques or the canonical path integral method.Comment: 17 pages, LaTex. A sign error corrected and few comments adde

Quasinormal modes of Schwarzschild black holes in four and higher dimensions

We make a thorough investigation of the asymptotic quasinormal modes of the four and five-dimensional Schwarzschild black hole for scalar, electromagnetic and gravitational perturbations. Our numerical results give full support to all the analytical predictions by Motl and Neitzke, for the leading term. We also compute the first order corrections analytically, by extending to higher dimensions, previous work of Musiri and Siopsis, and find excellent agreement with the numerical results. For generic spacetime dimension number D the first-order corrections go as $\frac{1}{n^{(D-3)/(D-2)}}$. This means that there is a more rapid convergence to the asymptotic value for the five dimensional case than for the four dimensional case, as we also show numerically.Comment: 12 pages, 5 figures, RevTeX4. v2. Typos corrected, references adde