We use the 1
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1
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2 covariant approach to clarify a number of aspects of spherically symmetric solutions of non-minimally coupled scalar tensor theories. Particular attention is focused on the ...extension of Birkhoff’s theorem and the nature of quasi-local horizons in this context.
This paper introduces a new instance-based algorithm for multiclass classification problems where the classes have a natural order. The proposed algorithm extends the state-of-the-art gravitational ...models by generalizing the scaling behavior of the class-pattern interaction force. Like the other gravitational models, the proposed algorithm classifies new patterns by comparing the magnitude of the force that each class exerts on a given pattern. To address ordinal problems, the algorithm assumes that, given a pattern, the forces associated to each class follow a unimodal distribution. For this reason, a weight matrix that allows to modify the metric in the attributes space and a vector of parameters that allows to modify the force law for each class have been introduced in the model definition. Furthermore, a probabilistic formulation of the error function allows the estimation of the model parameters using global and local optimization procedures toward minimization of the errors and penalization of the non unimodal outputs. One of the strengths of the model is its competitive grade of interpretability which is a requisite in most of real applications. The proposed algorithm is compared to other well-known ordinal regression algorithms on discretized regression datasets and real ordinal regression datasets. Experimental results demonstrate that the proposed algorithm can achieve competitive generalization performance and it is validated using nonparametric statistical tests.
We study adiabatic, radial perturbations of static, self-gravitating perfect fluids within the theory of general relativity employing a new perturbative formalism. We show that by considering a ...radially static observer, the description of the perturbations can be greatly simplified with respect to the standard comoving treatment. The new perturbation equations can be solved to derive analytic solutions to the problem for a general class of equilibrium solutions. We discuss the thermodynamic description of the fluid under isotropic frame transformations, showing how, in the radially static, non-inertial frame, the stress-energy tensor of the fluid must contain momentum transfer terms. As illustrative examples of the new approach, we study perturbations of equilibrium spacetimes characterized by the Buchdahl I, Heintzmann IIa, Patwardhan-Vaidya IIa, and Tolman VII solutions, computing the first oscillation eigenfrequencies and the associated eigenfunctions. We also analyze the properties of the perturbations of cold neutron stars composed of a perfect fluid verifying the Bethe-Johnson model I equation of state, computing the oscillation eigenfrequencies and the \(e\)-folding time.
We present a new system of equations that fully characterizes adiabatic, radial perturbations of perfect fluid stars within the theory of general relativity. The properties of the system are ...discussed, and, provided that the equilibrium spacetime verifies some general regularity conditions, analytical solutions for the perturbation variables are found. As illustrative examples, the results are applied to study perturbations of selected classical exact spacetimes, and the first oscillation eigenfrequencies are computed. Exploiting the new formalism, we derive an upper bound for the maximum compactness of stable, perfect fluid stars, which is equation-of-state-agnostic and significantly smaller than the Buchdahl bound.
We present a framework to describe completely general first-order
perturbations of static, spatially compact, and locally rotationally symmetric
class II spacetimes within the theory of general ...relativity. The perturbation
variables are by construction covariant and identification gauge invariant and
encompass the geometry and the thermodynamics of the fluid sources. The new
equations are then applied to the study of isotropic, adiabatic perturbations.
We discuss how the choice of frame in which perturbations are described can
significantly simplify the mathematical analysis of the problem and show that
it is possible to change frames directly from the linear level equations. We
find explicitly that the case of isotropic, adiabatic perturbations can be
reduced to a singular Sturm-Liouville eigenvalue problem, and lower bounds for
the values of the eigenfrequencies can be derived. These results lay the
theoretical groundwork to analytically describe linear, isotropic, and
adiabatic perturbations of static, spherically symmetric spacetimes.
In this paper, the issue of how to introduce matter in Ho?ava?Lifshitz theories of gravity is addressed. This is a key point in order to complete the proper definition of these theories and, more ...importantly, to study their possible phenomenological implications. As is well known, in Ho?ava?Lifshitz gravity, the breakdown of Lorentz invariance invalidates the usual notion of minimally coupled matter. Two different approaches to bypass this problem are described here. One is based on a Kaluza?Klein reinterpretation of the 3+1 decomposition of the gravity degrees of freedom, which naturally leads to a definition of a U(1) gauge symmetry and, hence, to a new type of minimal coupling. The other approach relies on a midi-superspace formalism and the subsequent parametrization of the matter stress?energy tensor in terms of deep infrared variables. Using the last option, the phase space of Ho?ava?Lifshitz cosmology in the presence of general matter couplings is studied. It is found, in particular, that the equation of state of the effective matter may be very different from the actual matter one, owing to the nonlinear interactions which exist between matter and gravity.
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