Area products for stationary black hole horizons

Area products for multi-horizon stationary black holes often have intriguing properties, and are often (though not always) independent of the mass of the black hole itself (depending only on various charges, angular momenta, and moduli). Such products are often formulated in terms of the areas of inner (Cauchy) horizons and outer (event) horizons, and sometimes include the effects of unphysical "virtual" horizons. But the conjectured mass-independence sometimes fails. Specifically, for the Schwarzschild-de Sitter [Kottler] black hole in (3+1) dimensions it is shown by explicit exact calculation that the product of event horizon area and cosmological horizon area is not mass independent. (Including the effect of the third "virtual" horizon does not improve the situation.) Similarly, in the Reissner-Nordstrom-anti-de Sitter black hole in (3+1) dimensions the product of inner (Cauchy) horizon area and event horizon area is calculated (perturbatively), and is shown to be not mass independent. That is, the mass-independence of the product of physical horizon areas is not generic. In spherical symmetry, whenever the quasi-local mass m(r) is a Laurent polynomial in aerial radius, r=sqrt{A/4\pi}, there are significantly more complicated mass-independent quantities, the elementary symmetric polynomials built up from the complete set of horizon radii (physical and virtual). Sometimes it is possible to eliminate the unphysical virtual horizons, constructing combinations of physical horizon areas that are mass independent, but they tend to be considerably more complicated than the simple products and related constructions currently being mooted in the literature.Comment: V1: 16 pages; V2: 9 pages (now formatted in PRD style). Minor change in title. Extra introduction, background, discussion. Several additional references; other references updated. Minor typos fixed. This version accepted for publication in PRD; V3: Minor typos fixed. Published versio

Lovelock Thin-Shell Wormholes

We construct the asymptotically flat charged thin-shell wormholes of Lovelock gravity in seven dimensions by cut-and-paste technique, and apply the generalized junction conditions in order to calculate the energy-momentum tensor of these wormholes on the shell. We find that for negative second order and positive third order Lovelock coefficients, there are thin-shell wormholes that respect the weak energy condition. In this case, the amount of normal matter decreases as the third order Lovelock coefficient increases. For positive second and third order Lovelock coefficients, the weak energy condition is violated and the amount of exotic matter decreases as the charge increases. Finally, we perform a linear stability analysis against a symmetry preserving perturbation, and find that the wormholes are stable provided the derivative of surface pressure density with respect to surface energy density is negative and the throat radius is chosen suitable.Comment: 13 pages, 6 figure

From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture

The recent interest in ``time machines'' has been largely fueled by the apparent ease with which such systems may be formed in general relativity, given relatively benign initial conditions such as the existence of traversable wormholes or of infinite cosmic strings. This rather disturbing state of affairs has led Hawking to formulate his Chronology Protection Conjecture, whereby the formation of ``time machines'' is forbidden. This paper will use several simple examples to argue that the universe appears to exhibit a ``defense in depth'' strategy in this regard. For appropriate parameter regimes Casimir effects, wormhole disruption effects, and gravitational back reaction effects all contribute to the fight against time travel. Particular attention is paid to the role of the quantum gravity cutoff. For the class of model problems considered it is shown that the gravitational back reaction becomes large before the Planck scale quantum gravity cutoff is reached, thus supporting Hawking's conjecture.Comment: 43 pages,ReV_TeX,major revision

Sensitivity of Hawking radiation to superluminal dispersion relations

We analyze the Hawking radiation process due to collapsing configurations in the presence of superluminal modifications of the dispersion relation. With such superluminal dispersion relations, the horizon effectively becomes a frequency-dependent concept. In particular, at every moment of the collapse, there is a critical frequency above which no horizon is experienced. We show that, as a consequence, the late-time radiation suffers strong modifications, both quantitative and qualitative, compared to the standard Hawking picture. Concretely, we show that the radiation spectrum becomes dependent on the measuring time, on the surface gravities associated with different frequencies, and on the critical frequency. Even if the critical frequency is well above the Planck scale, important modifications still show up.Comment: 14 pages, 7 figures. Extensive paragraph added in conclusions to clarify obtained result

The vacuum state of quantum gravity contains large virtual masses

In the functional integral approach to quantum gravity, the quantum configurations are usually treated to order hbar through a stationary phase approximation around the saddle point of the action where spacetime is flat. We show that from this point a "level line" in functional space departs, which comprises a family of static non-flat metrics with zero scalar curvature, depending on a continuous mass parameter. Furthermore, each of these metrics can be perturbed by an arbitrary function in such a way to still satisfy the condition Int(gR)d4x=0. We thus find a set of zero-modes of the gravitational action which has non-vanishing measure in the functional space. These metrics will contribute to the functional integral as vacuum fluctuations, on the same footing as those near the saddle point.Comment: 13 pages, 4 figures; to appear in Class. Q. Gravit

Dirty black holes: Entropy versus area

Considerable interest has recently been expressed in the entropy versus area relationship for ``dirty'' black holes --- black holes in interaction with various classical matter fields, distorted by higher derivative gravity, or infested with various forms of quantum hair. In many cases it is found that the entropy is simply related to the area of the event horizon: S = k A_H/(4\ell_P^2). For example, the ``entropy = (1/4) area'' law *holds* for: Schwarzschild, Reissner--Nordstrom, Kerr--Newman, and dilatonic black holes. On the other hand, the ``entropy = (1/4) area'' law *fails* for: various types of (Riemann)^n gravity, Lovelock gravity, and various versions of quantum hair. The pattern underlying these results is less than clear. This paper systematizes these results by deriving a general formula for the entropy: S = {k A_H/(4\ell_P^2)} + {1/T_H} \int_\Sigma [rho - {L}_E ] K^\mu d\Sigma_\mu + \int_\Sigma s V^\mu d\Sigma_\mu. (K^\mu is the timelike Killing vector, V^\mu the four velocity of a co--rotating observer.) If no hair is present the validity of the ``entropy = (1/4) area'' law reduces to the question of whether or not the Lorentzian energy density for the system under consideration is formally equal to the Euclideanized Lagrangian. ****** To appear in Physical Review D 15 July 1993 ****** [Stylistic changes, minor typos fixed, references updated, discussion of the Born-Infeld system excised]Comment: plain LaTeX, 17 pages, minor revision

Causal structure of acoustic spacetimes

The so-called ``analogue models of general relativity'' provide a number of specific physical systems, well outside the traditional realm of general relativity, that nevertheless are well-described by the differential geometry of curved spacetime. Specifically, the propagation of acoustic disturbances in moving fluids are described by ``effective metrics'' that carry with them notions of ``causal structure'' as determined by an exchange of sound signals. These acoustic causal structures serve as specific examples of what can be done in the presence of a Lorentzian metric without having recourse to the Einstein equations of general relativity. (After all, the underlying fluid mechanics is governed by the equations of traditional hydrodynamics, not by the Einstein equations.) In this article we take a careful look at what can be said about the causal structure of acoustic spacetimes, focusing on those containing sonic points or horizons, both with a view to seeing what is different from standard general relativity, and to seeing what the similarities might be.Comment: 51 pages, 39 figures (23 colour figures, colour used to convey physics information.) V2: Two references added, some additional discussion of maximal analytic extension, plus minor cosmetic change

Analog gravity from field theory normal modes?

We demonstrate that the emergence of a curved spacetime ``effective Lorentzian geometry'' is a common and generic result of linearizing a field theory around some non-trivial background. This investigation is motivated by considering the large number of ``analog models'' of general relativity that have recently been developed based on condensed matter physics, and asking whether there is something more fundamental going on. Indeed, linearization of a classical field theory (a field theoretic ``normal mode analysis'') results in fluctuations whose propagation is governed by a Lorentzian-signature curved spacetime ``effective metric''. For a single scalar field, this procedure results in a unique effective metric, which is quite sufficient for simulating kinematic aspects of general relativity (up to and including Hawking radiation). Quantizing the linearized fluctuations, the one-loop effective action contains a term proportional to the Einstein--Hilbert action, suggesting that while classical physics is responsible for generating an ``effective geometry'', quantum physics can be argued to induce an ``effective dynamics''. The situation is strongly reminiscent of Sakharov's ``induced gravity'' scenario, and suggests that Einstein gravity is an emergent low-energy long-distance phenomenon that is insensitive to the details of the high-energy short-distance physics. (We mean this in the same sense that hydrodynamics is a long-distance emergent phenomenon, many of whose predictions are insensitive to the short-distance cutoff implicit in molecular dynamics.)Comment: Revtex 4 (beta 5); 12 pages in single-column forma

Evolution of thin-wall configurations of texture matter

We consider the free matter of global textures within the framework of the perfect fluid approximation in general relativity. We examine thermodynamical properties of texture matter in comparison with radiation fluid and bubble matter. Then we study dynamics of thin-wall selfgravitating texture objects, and show that classical motion can be elliptical (finite), parabolical or hyperbolical. It is shown that total gravitational mass of neutral textures in equilibrium equals to zero as was expected. Finally, we perform the Wheeler-DeWitt's minisuperspace quantization of the theory, obtain exact wave functions and discrete spectra of bound states with provision for spatial topology.Comment: intermediate research on nature of dual-radiation matter; LaTeX, 12 pages, 1 figure and epsfig style file included; slightly shortened version was published in December issue of GR

Might some gamma ray bursts be an observable signature of natural wormholes?

The extragalactic microlensing scenario for natural wormholes is examined. It is shown that the main features of wormhole lensing events upon the light of distant Active Galactic Nuclei (AGNs) are similar to some types of already observed Gamma Ray Bursts (GRBs). Using recent satellite data on GRBs, an upper limit to the negative mass density -- ${\cal O} (10^{-36})$ g cm$^{-3}$ -- under the form of wormhole-like objects is presented.Comment: extended version, additions on GRB physics, background sources and cosmological consequences. Two ps figures. Accpeted for publication in Phys. Rev.