Scalar-tensor Field Equations Research Articles

Observational constraints on the regularized 4D Einstein-Gauss-Bonnet theory of gravity

In this paper we study the observational constraints that can be imposed on the coupling parameter, $\hat \alpha$, of the regularized version of the 4-dimensional Einstein-Gauss-Bonnet theory of gravity. We use the scalar-tensor field equations of this theory to perform a thorough investigation of its slow-motion and weak-field limit, and apply our results to observations of a wide array of physical systems that admit such a description. We find that the LAGEOS satellites are the most constraining, requiring $| \hat \alpha | \lesssim 10^{10} \,{\rm m}^2$. This constraint suggests that the possibility of large deviations from general relativity is small in all systems except the very early universe ($t<10^{-3}\, {\rm s}$), or the immediate vicinity of stellar-mass black holes ($M\lesssim100\, M_{\odot}$). We then consider constraints that can be imposed on this theory from cosmology, black hole systems, and table-top experiments. It is found that early universe inflation prohibits all but the smallest negative values of $\hat \alpha$, while observations of binary black hole systems are likely to offer the tightest constraints on positive values, leading to overall bounds $0 \lesssim \hat \alpha \lesssim 10^8 \, {\rm m}^2$.

Quasilocal energy in modified gravity

A new generalization of the Hawking–Hayward quasilocal energy to scalar–tensor gravity is proposed without assuming symmetries, asymptotic flatness, or special spacetime metrics. The procedure followed is simple but powerful and consists of writing the scalar–tensor field equations as effective Einstein equations and then applying the standard definition of quasilocal mass. An alternative procedure using the Einstein frame representation leads to the same result in vacuo.

Compact binary systems in scalar-tensor gravity. III. Scalar waves and energy flux

We derive the scalar waveform generated by a binary of nonspinning compact objects (black holes or neutron stars) in a general class of scalar-tensor theories of gravity. The waveform is accurate to 1.5 post-Newtonian order [$O((v/c)^3)$] beyond the leading-order tensor gravitational waves (the "Newtonian quadrupole"). To solve the scalar-tensor field equations, we adapt the direct integration of the relaxed Einstein equations formalism developed by Will, Wiseman, and Pati. The internal gravity of the compact objects is treated with an approach developed by Eardley. We find that the scalar waves are described by the same small set of parameters which describes the equations of motion and tensor waves. For black hole--black hole binaries, the scalar waveform vanishes, as expected from previous results which show that these systems in scalar-tensor theory are indistinguishable from their general relativistic counterparts. For black hole--neutron star binaries, the scalar waveform simplifies considerably from the generic case, essentially depending on only a single parameter up to first post-Newtonian order. With both the tensor and scalar waveforms in hand, we calculate the total energy flux carried by the outgoing waves. This quantity is computed to first post-Newtonian order relative to the "quadrupole formula" and agrees with previous, lower order calculations.

LRS Bianchi type-II dark energy model in a scalar–tensor theory of gravitation

A locally rotationally symmetric Bianchi type-II (LRS B-II) space-time with variable equation of state (EoS) parameter and constant deceleration parameter have been investigated in the scalar-tensor theory proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986). The scalar-tensor field equations have been solved by applying variation law for generalized Hubble’s parameter given by Bermann (Nuovo Cimento 74:182, 1983). The physical and kinematical properties of the model are also discussed.

Quasinormal modes, bifurcations, and nonuniqueness of charged scalar-tensor black holes

In the present paper we study the scalar sector of the quasinormal modes of charged general relativistic, static and spherically symmetric black holes coupled to nonlinear electrodynamics and embedded in a class of scalar-tensor theories. We find that for certain domain of the parametric space there exist unstable quasinormal modes. The presence of instabilities implies the existence of scalar-tensor black holes with primary hair that bifurcate from the embedded general relativistic black-hole solutions at critical values of the parameters corresponding to the static zero-modes. We prove that such scalar-tensor black holes really exist by solving the full system of scalar-tensor field equations for the static, spherically symmetric case. The obtained solutions for the hairy black holes are non-unique and they are in one to one correspondence with the bounded states of the potential governing the linear perturbations of the scalar field. The stability of the non-unique hairy black holes is also examined and we find that the solutions for which the scalar field has zeros are unstable against radial perturbations. The paper ends with a discussion on possible formulations of a new classification conjecture.

GRAVITATIONAL MEMORY OF NATURAL WORMHOLES

A traversable wormhole solution of general scalar–tensor field equations is presented. We have shown, after a numerical analysis for the behavior of the scalar field of Brans–Dicke theory, that the solution is completely singularity-free. Furthermore, the analysis of more general scalar field dependent coupling constants indicates that the gravitational memory phenomenon may play an important role for the fate of natural wormholes.

Second-order scalar-tensor field equations in a four-dimensional space

Lagrange scalar densities which are concomitants of a pseudo-Riemannian metric-tensor, a scalar field and their derivatives of arbitrary order are considered. The most general second-order Euler-Lagrange tensors derivable from such a Lagrangian in a four-dimensional space are constructed, and it is shown that these Euler-Lagrange tensors may be obtained from a Lagrangian which is at most of second order in the derivatives of the field functions.

The tests of general relativity and scalar fields

Conditions are found under which a space-time will give results in agreement with the Schwarzschild values for the three classical tests of general relativity and the radar reflection experiment. These conditions lead to the introduction of a scalar field and a set of scalartensor field equations. The solutions of these field equations are shown to be conformai to the solutions of the Brans-Dicke field equations. The field equations in the presence of matter are also discussed.

Type N solutions of the vacuum scalar-tensor field equations

All solutions of the vacuum relativistic scalar-tensor field equations Rμυ=−φ,μφ,υ are given in the case where the Weyl tensor is of Petrov-Penrose type N. These eight solutions are listed according to the Petrov-Plebanski classification of their trace-free Ricci tensor components and belong to the three classes[T−3S][1−1] (R,N), [3T−S][1−1](R,N) and [4N][2](O,N).