The Classical Solutions of Two-dimensional Gravity

The solutions of two-dimensional gravityfollowing from a non-linear Lagrangian =f(R)g are classified, and their symmetry andsingularity properties are described. Then a conformaltransformation is applied to rewrite these solutions as analogoussolutions of two-dimensional Einstein-dilaton gravityand vice versa.     

On Naked Black Holes

The recently proposed criteria for naked blackholes are conveniently rephrased. It is shown that twosolutions of dilaton-Maxwell gravity, satisfying weakenergy conditions, represent naked blackholes.     

Finding the Hamiltonian for Cosmological Models in Fourth-Order Gravity Theories Without Resorting to the Ostrogradski or Dirac Formalism

The Hamilton formalism of cosmological models in fourth-order theories of gravity is considered. An approach to constructing the Hamilton function is presented which starts by replacing the second order derivatives of configuration space coordinates by functions depending on these coordinates, its first order derivatives, and additional variables playing the role of configuration space coordinates. This formalism, which does not resort to the Ostrogradski or Dirac formalism, is elucidated and applied to examples. For a special class of Lagrange functions, it is demonstrated that the canonical coordinates of the considered formalism and of the Ostrogradski formalism are related via a canonical transformation. The canonical transformation is a transformation of the configuration space coordinates and a transformation of momentum components induced by the transformation of the configuration space coordinates for a special element of the class of Lagrange functions mentioned. The Wheeler-DeWitt equations belonging to this Lagrange function are related via minisuperspace coordinate transformations.     

Charged Gravitational Instantons in Five-Dimensional Einstein-Gauss-Bonnet-Maxwell Theory

We study a solution of the Einstein-Gauss-Bonnet theory coupled to a Maxwell field in five dimensions, whose euclidean continuation gives rise to an instanton describing black hole pair production. We also discuss the dual theory with a 3-form field coupled to gravity.     

A New Duality Transformation for Fourth-order Gravity

We prove that for non-linear L = L(R), G = dL/dR 0 the Lagrangians L and ^L(^R) with ^L = 2R/G³ - 3L/G⁴, ^g_ij = G² g_ij and ^R = 3R/G² - 4L/G³ give conformally equivalent fourth-order field equations being dual to each other. The proof represents a new application of the fact that the operator - R/6 is conformally invariant.     

Recovering the Effective Cosmological Constant in Extended Gravity Theories

In the framework of extended gravity theories, we discuss the meaning of a time-dependent cosmological constant and give a set of conditions to recover an asymptotic de Sitter behaviour for a class of cosmological models independently of initial data. To this purpose we introduce a time-dependent (effective) quantity which asymptotically becomes the true cosmological constant. We will deal with scalar-tensor, fourth and higher than fourth-order theories.     

Metric for an Oblate Earth

In linearized general relativity the metric ofa body is described by a scalar potential and athree-vector potential. We here present a simpletransformation derivation of the linearized metric interms of these potentials, and calculate the exactscalar and vector potentials for a field with oblatespheroidal symmetry. The results for the externalpotentials do not depend on details of the densitydistribution inside the earth; both the scalar and vectorpotentials are fully determined by the total mass, thetotal angular momentum, and a radial parameter, all ofwhich are accurately known from observation. The scalar potential is accurate to roughly10^-6 and the vector potential, which hasnever been accurately measured, should be accurate toabout 10^-5. Applications include an accuratetreatmen t of the details of the motion of satellites, and theprecession of a gyroscope in earth orbit.     

Possible Tests of Curvature Effects in Weak Gravitational Fields

The possibility of performing in proximity of the Earth experiments to test the predictions of general relativity for the trajectories of particles and photons in weak gravitational fields is studied. Three experiments are analyzed, all based on optical detection methods. The first experiment would allow to detect the tidal acceleration using a freely-falling Michelson interferometer. In a second experiment, based on laser-ranging methods, the relativistic correction to the classical gravity acceleration could be detected. Finally, the possibility of detecting light deflection induced by space curvature in an optical cavity with high-reflectivity mirrors is discussed.     

Are the Singularities Stable?

The spacetime singularities play a useful role in gravitational theories by distinguishing physical solutions from non-physical ones. The problem, we are studying in this paper is whether these singularities are stable. To answer this question, we have analyzed the general problem of stability of the family of the static spherically symmetric solutions of the standard Einstein-Maxwell model coupled to an extra free massless scalar field. We have obtained the equations for the axial and polar perturbations. The stability against axial perturbations has been proven.     

Sinh-Gordon Matter Field and a Solvable Model in Two-Dimensional Gravity

The two-dimensional gravity model with a coupling constant k = 4 and a vanishing cosmological constant coupled to a sinh-Gordon matter field is investigated. We find that the classical equations of motion are exactly solvable, and analytically obtain the static solutions of induced metric and scalar curvature. These solutions have some new features and may be used to describe the naked singularities at the horizons.