Spherically symmetric solutions of Einstein + non-polynomial gravities

We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to maintain the (first) derivative order of the Einstein equations in Schwarzschild gauge. Generically, the solutions exhibit both horizons and a singularity at the origin, except for one model that forbids spherical symmetry altogether. Extensions to arbitrary dimension with a cosmological constant, Maxwell source and Gauss-Bonnet terms are also considered.Comment: 6 pages, no figures, REVTeX

Gauss-Bonnet Gravity with Scalar Field in Four Dimensions

We give all exact solutions of the Einstein-Gauss-Bonnet Field Equations coupled with a scalar field in four dimensions under certain assumptions.Comment: Latex file, 7 page

Exact solutions of Dirac equation on (1+1)-dimensional spacetime coupled to a static scalar field

We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.Comment: 7 pages, Late

Energy in Generic Higher Curvature Gravity Theories

We define and compute the energy of higher curvature gravity theories in arbitrary dimensions. Generically, these theories admit constant curvature vacua (even in the absence of an explicit cosmological constant), and asymptotically constant curvature solutions with non-trivial energy properties. For concreteness, we study quadratic curvature models in detail. Among them, the one whose action is the square of the traceless Ricci tensor always has zero energy, unlike conformal (Weyl) gravity. We also study the string-inspired Einstein-Gauss-Bonnet model and show that both its flat and Anti-de-Sitter vacua are stable.Comment: 18 pages, typos corrected, one footnote added, to appear in Phys. Rev.

Black Hole Configurations with Total Entropy Less than A/4

If one surrounds a black hole with a perfectly reflecting shell and adiabatically squeezes the shell inward, one can increase the black hole area A to exceed four times the total entropy S, which stays fixed during the process. A can be made to exceed 4S by a factor of order unity before the one enters the Planck regime where the semiclassical approximation breaks down. One interpretation is that the black hole entropy resides in its thermal atmosphere, and the shell restricts the atmosphere so that its entropy is less than A/4.Comment: 31 pages, LaTe

Solution to the ghost problem in fourth order derivative theories

We present a solution to the ghost problem in fourth order derivative theories. In particular we study the Pais-Uhlenbeck fourth order oscillator model, a model which serves as a prototype for theories which are based on second plus fourth order derivative actions. Via a Dirac constraint method quantization we construct the appropriate quantum-mechanical Hamiltonian and Hilbert space for the system. We find that while the second-quantized Fock space of the general Pais-Uhlenbeck model does indeed contain the negative norm energy eigenstates which are characteristic of higher derivative theories, in the limit in which we switch off the second order action, such ghost states are found to move off shell, with the spectrum of asymptotic in and out S-matrix states of the pure fourth order theory which results being found to be completely devoid of states with either negative energy or negative norm. We confirm these results by quantizing the Pais-Uhlenbeck theory via path integration and by constructing the associated first-quantized wave mechanics, and show that the disappearance of the would-be ghosts from the energy eigenspectrum in the pure fourth order limit is required by a hidden symmetry that the pure fourth order theory is unexpectedly found to possess. The occurrence of on-shell ghosts is thus seen not to be a shortcoming of pure fourth order theories per se, but rather to be one which only arises when fourth and second order theories are coupled to each other.Comment: 36 pages, revtex. Prepared for the proceedings of the 2006 Biennial Meeting of the International Association for Relativistic Dynamics Version 2 contains an expanded discussion of the path integral quantization of the Pais-Uhlenbeck fourth order oscillator theor

Do static sources respond to massive scalar particles from the Hawking radiation as uniformly accelerated ones do in the inertial vacuum?

We revisit the recently found equivalence for the response of a static scalar source interacting with a {\em massless} Klein-Gordon field when the source is (i) static in Schwarzschild spacetime, in the Unruh vacuum associated with the Hawking radiation and (ii) uniformly accelerated in Minkowski spacetime, in the inertial vacuum, provided that the source's proper acceleration is the same in both cases. It is shown that this equivalence is broken when the massless Klein-Gordon field is replaced by a {\em massive} one.Comment: 4 pages, 2 figure

Quantum Gravitational Bremsstrahlung, Massless versus Massive Gravity

The massive spin-2 quantum gauge theory previously developed is applied to calculate gravitational bremsstrahlung. It is shown that this theory is unique and free from defects. In particular, there is no strong coupling if the graviton mass becomes small. The cross sections go over smoothly into the ones of the massless theory in the limit of vanishing graviton mass. The massless cross sections are calculated for the full tensor theory.Comment: 13 pages, 1 figur

Instability of Extremal Relativistic Charged Spheres

With the question, ``Can relativistic charged spheres form extremal black holes?" in mind, we investigate the properties of such spheres from a classical point of view. The investigation is carried out numerically by integrating the Oppenheimer-Volkov equation for relativistic charged fluid spheres and finding interior Reissner-Nordstr\"om solutions for these objects. We consider both constant density and adiabatic equations of state, as well as several possible charge distributions, and examine stability by both a normal mode and an energy analysis. In all cases, the stability limit for these spheres lies between the extremal ($Q = M$) limit and the black hole limit ($R = R_+$). That is, we find that charged spheres undergo gravitational collapse before they reach $Q = M$, suggesting that extremal Reissner-Nordtr\"om black holes produced by collapse are ruled out. A general proof of this statement would support a strong form of the cosmic censorship hypothesis, excluding not only stable naked singularities, but stable extremal black holes. The numerical results also indicate that although the interior mass-energy $m(R)$ obeys the usual $m/R < 4/9$ stability limit for the Schwarzschild interior solution, the gravitational mass $M$ does not. Indeed, the stability limit approaches $R_+$ as $Q \to M$. In the Appendix we also argue that Hawking radiation will not lead to an extremal Reissner-Nordstr\"om black hole. All our results are consistent with the third law of black hole dynamics, as currently understood

Quantum Stability of Accelerated Black Holes

We study quantum aspects of the accelerated black holes in some detail. Explicitly shown is the fact that a uniform acceleration stabilizes certain charged black holes against the well-known thermal evaporation. Furthermore, a close inspection of the geometry reveals that this is possible only for near-extremal black holes and that most nonextremal varieties continue to evaporate with a modified spectrum under the acceleration. We also introduce a two-dimensional toy model where the energy-momentum flow is easily obtained for general accelerations, and find the behavior to be in accordance with the four-dimensional results. After a brief comparison to the classical system of a uniformly accelerated charge, we close by pointing out the importance of this result in the WKB expansion of the black hole pair-creation rate.Comment: LaTeX, 22 pages, 5 uuencoded figures (minor errors corrected, more discussions on the case with black holes formed by gravitational collapse.