Is there a black hole minimum mass?

Applying the first and generalised second laws of thermodynamics for a realistic process of near critical black hole formation, we derive an entropy bound, which is identical to Bekenstein's one for radiation. Relying upon this bound, we derive an absolute minimum mass $\sim0.04 \sqrt{g_{*}}m_{\rm Pl}$, where $g_{*}$ and $m_{\rm Pl}$ is the effective degrees of freedom for the initial temparature and the Planck mass, respectively. Since this minimum mass coincides with the lower bound on masses of which black holes can be regarded as classical against the Hawking evaporation, the thermodynamical argument will not prohibit the formation of the smallest classical black hole. For more general situations, we derive a minimum mass, which may depend on the initial value for entropy per particle. For primordial black holes, however, we show that this minimum mass can not be much greater than the Planck mass at any formation epoch of the Universe, as long as $g_{*}$ is within a reasonable range. We also derive a size-independent upper bound on the entropy density of a stiff fluid in terms of the energy density.Comment: 4 pages, accepted for publication in Physical Review D, minor correctio

The depletion in Bose Einstein condensates using Quantum Field Theory in curved space

Using methods developed in Quantum Field Theory in curved space we can estimate the effects of the inhomogeneities and of a non vanishing velocity on the depletion of a Bose Einstein condensate within the hydrodynamical approximation.Comment: 4 pages, no figure. Discussion extended and references adde

Born-Infeld type Gravity

Generalizations of gravitational Born-Infeld type lagrangians are investigated. Phenomenological constraints (reduction to Einstein-Hilbert action for small curvature, spin two ghost freedom and absence of Coulomb like Schwarschild singularity) select one effective lagrangian whose dynamics is dictated by the tensors g_{\mu\nu} and R_{\mu\nu\rho\sigma}(not R_{\mu\nu} or the scalar R).Comment: 7 pages, 3 figures, revte

Back-reaction effects in acoustic black holes

Acoustic black holes are very interesting non-gravitational objects which can be described by the geometrical formalism of General Relativity. These models can be useful to experimentally test effects otherwise undetectable, as for example the Hawking radiation. The back-reaction effects on the background quantities induced by the analogue Hawking radiation could be the key to indirectly observe it. We briefly show how this analogy works and derive the backreaction equations for the linearized quantum fluctuations in the background of an acoustic black hole. A first order in hbar solution is given in the near horizon region. It indicates that acoustic black holes, unlike Schwarzschild ones, get cooler as they radiate phonons. They show remarkable analogies with near-extremal Reissner-Nordstrom black holes.Comment: 10 pages, 1 figure; Talk given at the conference ``Constrained Dynamics and Quantum Gravity (QG05)", Cala Gonone (Italy), September 200

Regularization of fluctuations near the sonic horizon due to the quantum potential and its influence on the Hawking radiation

We consider dynamics of fluctuations in transonically accelerating Bose-Einstein condensates and luminous liquids (coherent light propagating in a Kerr nonlinear medium) using the hydrodynamic approach. It is known that neglecting the quantum potential (QP) leads to a singular behavior of quantum and classical fluctuations in the vicinity of the Mach (sonic) horizon, which in turn gives rise to the Hawking radiation. The neglect of QP is well founded at not too small distances $|x| \gg l_h$ from the horizon, where $l_h$ is the healing length. Taking the QP into account we show that a second characteristic length $l_r > l_h$ exists, such that the linear fluctuation modes become regularized for $|x| \ll l_r$. At $|x| \gg l_r$ the modes keep their singular behavior, which however is influenced by the QP. As a result we find a deviation of the high frequency tail of the spectrum of Hawking radiation from Planck's black body radiation distribution. Similar results hold for the wave propagation in Kerr nonlinear media where the length $l_h$ and $l_r$ exist due to the nonlinearity.Comment: 23 pages, 2 figure

Quantum radiation reaction force on a one-dimensional cavity with two relativistic moving mirrors

We consider a real massless scalar field inside a cavity with two moving mirrors in a two-dimensional spacetime, satisfying Dirichlet boundary condition at the instantaneous position of the boundaries, for arbitrary and relativistic laws of motion. Considering vacuum as the initial field state, we obtain formulas for the exact value of the energy density of the field and the quantum force acting on the boundaries, which extend results found in previous papers. For the particular cases of a cavity with just one moving boundary, non-relativistic velocities, or in the limit of infinity length of the cavity (a single mirror), our results coincide with those found in the literature.Comment: 6 pages 9 figure

Tunnelling, Temperature and Taub-NUT Black Holes

We investigate quantum tunnelling methods for calculating black hole temperature, specifically the null geodesic method of Parikh and Wilczek and the Hamilton-Jacobi Ansatz method of Angheben et al. We consider application of these methods to a broad class of spacetimes with event horizons, inlcuding Rindler and non-static spacetimes such as Kerr-Newman and Taub-NUT. We obtain a general form for the temperature of Taub-NUT-Ads black holes that is commensurate with other methods. We examine the limitations of these methods for extremal black holes, taking the extremal Reissner-Nordstrom spacetime as a case in point.Comment: 22 pages, 3 figures; added references, fixed figures, added comments to extremal section, added footnot

Quantum effects in Acoustic Black Holes: the Backreaction

We investigate the backreaction equations for an acoustic black hole formed in a Laval nozzle under the assumption that the motion of the fluid is one-dimensional. The solution in the near-horizon region shows that as phonons are (thermally) radiated the sonic horizon shrinks and the temperature decreases. This contrasts with the behaviour of Schwarzschild black holes, and is similar to what happens in the evaporation of (near-extremal) Reissner-Nordstrom black holes (i.e. infinite evaporation time). Finally, by appropriate boundary conditions the solution is extended in both the asymptotic regions of the nozzle.Comment: 23 pages, latex, 1 figure; revised version, to appear in Phys. Rev.

Bound states due to an accelerated mirror

We discuss an effect of accelerated mirrors which remained hitherto unnoticed, the formation of a field condensate near its surface for massive fields. From the view point of an observer attached to the mirror, this is effect is rather natural because a gravitational field is felt there. The novelty here is that since the effect is not observer dependent even inertial observers will detect the formation of this condensate. We further show that this localization is in agreement with Bekenstein's entropy bound.Comment: Final version to appear in PR

The Power Spectrum in de Sitter Inflation, Revisited

We find that the amplitude of quantum fluctuations of the invariant de Sitter vacuum coincides exactly with that of the vacuum of a comoving observer for a massless scalar (inflaton) field. We propose redefining the actual physical power spectrum as the difference between the amplitudes of the above vacua. An inertial particle detector continues to observe the Gibbons-Hawking temperature. However, although the resulting power spectrum is still scale-free, its amplitude can be drastically reduced since now, instead of the Hubble's scale at the inflationary period, it is determined by the square of the mass of the inflaton fluctuation field.Comment: 4 page