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In this study, we investigate black hole solutions with toroidal horizons in scalar hair and dilaton gravity. First, we obtain the field equations in n-dimensions. Then, we propose different models (ansatz) and find the exact solutions for these types of ansatzs. These solutions are not asymptotically (anti) de Sitter or flat, except in one special case. We also show that the BTZand BTZ-like solutions emerge from some of these solutions as a special case. We also show that when the event horizon radius increases, the temperature will be the same in various dimensions. The only difference is noticeable near the origin (this statement is clear from the figures). For these solutions, we obtained a new version of the Smarr formula. In addition, we show that the presence of the scalar field makes the black holes more stable near the origin, except for the BTZ case. In general, the presence of a scalar field is an important factor in black hole stability investigations. In the critical behavior analysis, we find that there is no evidence to show the existence of P-V criticality. Here, we present a class of interior solutions corresponding to the solution in a scalar hair gravity exterior. The solution obtained in the linear case was regular and well-behaved at the stellar interior.

We obtain three models for geodesic flows and three models for non-geodesic flows of Weyssenhoff fluid considering it as the source of gravitation and spin in the Einstein–Cartan field equations. Influence of spin on the pressure, density, equation of state, and the kinematical parameters is observed in both geodesic and non-geodesic models.

We study the Maxwell equation and the spin-2 field equation in Bondi–Sachs coordinates associated with an asymptotically flat Lorentzian metric. We consider the mixed boundary/initial value problem, where the initial data are imposed on a null hypersurface and a boundary value is prescribed on a timelike hypersurface. We establish Sobolev [Formula: see text] space-time estimates for solutions and their asymptotic expansions at the null infinity.

We show that the scalar curvature of a Riemannian manifold $M$ is constant if it satisfies (i) the concircular field equation and $M$ is compact, (ii) the special concircular field equation. Finally, we show that, if a complete connected Riemannian manifold admits a concircular non-isometric vector field leaving the scalar curvature invariant, and the conformal function is special concircular, then the scalar curvature is a constant.

The exact non-static accelerating solutions of Einstein field equations in vacuum, with an indefinite non-degenerate metric in cylindrical coordinates, are found. The considered spacetime is not conformally flat and the gravitational field is of Petrov type I . The classical symmetry method is used for the symmetry reductions and for obtaining the invariant solutions in terms of arbitrary function. The graphical representations of obtained solutions, are also shown.

We solve field equations in the theory of 5-dimensional Brans-Dicke gravity coupled with SO(3) scalar fields and find a spherically symmetric static solution with warp factor. We discuss its implications for the galactic dark matter.

Recently, a novel four-dimensional Einstein-Gauss-Bonnet (EGB) theory was presented to bypass the Lovelock's theorem and to give nontrivial effects on the four-dimensional local gravity. The main mechanism is to introduce a redefinition $\alpha\rightarrow\alpha/(D-4)$ and to take the limit $D\rightarrow4$. However, this theory does not have standard four-dimensional field equations. Some regularization procedures are then proposed to address this problem [arXiv:2003.11552, arXiv:2003.12771, arXiv:2004.08362, arXiv:2004.09472, arXiv:2004.10716]. The resultant regularized four-dimensional EGB theory has the same on-shell action as the original theory. Thus it is expected that the novel four-dimensional EGB theory is equivalent to its regularized version. However, the equivalence of these two theories is symmetry-dependent. In this paper, we test the equivalence in a cylindrically symmetric spacetime. The well-defined field equations of the two theories are obtained, with which our follow-up analysis shows that they are equivalent in such spacetime. Cylindrical cosmic strings are then considered as specific examples of the metric. Three sets of solutions are obtained and the corresponding string mass densities are evaluated. The results reveal how the Gauss-Bonnet term in four dimensions contributes to the string geometry in the new theory., Comment: 20 pages, 9 figures, published version

Employing the unified first law of thermodynamics and the field equations of the generalized Rastall theory, we get the generalized Misner-Sharp mass of spacetimes for which $g_{tt}=-g^{rr}=-f(r)$. The obtained result differs from those of the Einstein and Rastall theories. Moreover, using the first law of thermodynamics, the obtained generalized Misner-Sharp mass and the field equations, the entropy of the static spherically symmetric horizons is also addressed in the framework of the generalized Rastall theory. In addition, by generalizing the study to the flat FRW universe, the apparent horizon entropy is also calculated. Considering the effects of applying the Newtonian limit to the field equations on the coupling coefficients of the generalized Rastall theory, our study indicates $i$) the obtained entropy-area relation is the same as that of the Rastall theory, and $ii$) the Bekenstein entropy is recovered when the generalized Rastall theory reduces to the Einstein theory. The validity of the second law of thermodynamics is also investigated in the flat FRW universe., Comment: 4 pages, accepted by Can. J. Phys (2019)

In this paper, we present the cylindrically symmetric solutions in a well-known modified theory, namely f(R, G) gravity. After driving the complete system of field equations, six different families of exact solutions using a viable f(R, G) gravity model have been discussed. Moreover, we have investigated the well-known Levi–Civita solution in modified gravity for the model f(R, G) = R2 + αGn for some suitable values of model parameters n and α. Null energy conditions are also calculated for all the obtained solutions. Some regions are observed where the null energy condition is violated, indicating the existence of cylindrical wormholes.

We have presented tilted Bianchi type-VI0 cosmological models in general theory of relativity. To solve Einstein’s field equation, we have used the stiff fluid $$ \tilde{p}_{r} = \tilde{\rho } $$ , considering time varying radial velocity $$ \omega = T^{\alpha } $$ and uniform radial velocity $$ \omega = \omega_{0} $$ , where $$ \alpha,\,\omega_{0} $$ are constant. We have also investigated the behaviors of some physical parameters.

In this work we try to understand the late time acceleration of the universe by assuming some modification in the geometry of the space and using dynamical system analysis. This technique allows to understand the behavior of the universe without analytically solving the field equations. We study the acceleration phase of the universe and stability properties of the critical points which could be compared with observational results. We consider an asymptotic behavior of two particular models $f(R) = R - \mu R_{c} \frac{(R/R_c)^{2n}}{(R/R_c)^{2n} + 1}$ and $f(R) = R - \mu R_{c} \left[ 1 - (1 + R^2/R_{c}^2)^{-n} \right]$ with $n,\mu, R_c >0$ for the study. As a first case we fix the value of $\mu$ and analyzed for all $n$. Later as second case, we fix the value of $n$ and calculation are done for all $\mu$. At the end all the calculations for the generalized case have been shown and results have been discussed in detail., Comment: 17 pages

Recently, it has been claimed by J. Harada [Phys. Rev. D 103, L121502 (2021) that the Cotton tensor can describe the effects of gravity beyond general relativity. In this short comment, we show that the Cotton tensor is already present in general relativity. Moreover, we show that Harada’s proposal is equivalent to general relativity concerning the equation of motion both for the sources and for the trace-free part of the curvature. In essence, what remains completely free in Harada’s theory are the field equations relating the part of the curvature which is locally determined by the energy-momentum distribution. The author is funded by the Beatriz Galindo Contract No. BEAGAL 18/00207 (Spain).

Recently, P. Bargue\~no has commented in Phys. Rev. D 104, DHK1021 (2021) that the field equations obtained in the original paper [J. Harada, Phys. Rev. D 103, L121502 (2021)] have less information than those of general relativity. This reply provides clarification. The field equations obtained in the original paper have information on gravity that cannot be obtained from general relativity. For instance, the effective potential of gravity has a term that is linearly proportional to the distance. It implies that the magnitude of gravity can be stronger than that of Newton's law of gravitation at large distances.

The solutions for the field equations of $f(R)$ gravity are investigated in static cylindrically symmetric space-time. Conserved quantities of the system, as well as unknown functions, can be determined with the help of the Noether symmetry method. In this article, some unknown values of the equations of state parameter (EoS) have emerged as a result of the constraints obtained by analyzing the Noether symmetry equations for the $f(R)=f_0 R$ case. Consequently, several new exact solutions have been found for cases of General Relativity in static cylindrically symmetrical space-time for the non-dust matter., Comment: 6 pages, 4 figures, version accepted for publication in European Physical Journal C

We construct three-dimensional, N=1 off-shell supersymmetric massive Yang-Mills (YM) theory whose YM equation is “third-way” consistent. This means that the field equations of this model do not come from variation of a local action without additional fields, yet the gauge-covariant divergence of the YM equation still vanishes on shell. To achieve this, we modify the massive Majorana spinor equation so that its supersymmetry variation gives a modified YM equation whose bosonic part coincides with the third-way consistent pure massive YM model.

The bosonic large-$N$ master field of the IIB matrix model can, in principle, give rise to an emergent classical spacetime. The task is then to calculate this master field as a solution of the bosonic master-field equation. We consider a simplified version of the algebraic bosonic master-field equation and take dimensionality $D=2$ and matrix size $N=6$. For an explicit realization of the pseudorandom constants entering this simplified algebraic equation, we establish the existence of a solution and find, after diagonalization of one of the two obtained matrices, a band-diagonal structure of the other matrix., 20 pages, v6: published version

We point out that field equations of general relativity are implied by a maximal force given by c4/4G, analogous to the way that special relativity is implied by a maximal speed given by c. We present some of the arguments for this equivalence. The maxi-mal force naturally plays the role of an elastic constant for space-time. Implications of the maximal force for gravitational wave measurements, cosmology and black holes are highlighted. Quantum aspects of the maximal force are discussed.

We study the $f(R,T)$ cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the Field Equations (FE) admit exact self-similar solutions through the matter collineation approach. We study two models: the case$\ f(R,T)=f_{1}(R)+f_{2}(T)$ and the case $f(R,T)=f_{1}(R)+f_{2} (R)f_{3}(T)$. In each case, we state general theorems which determine completely the form of the unknown functions $f_{i}$ such that the field equations admit self-similar solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous self-similar metric$.$ In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models., accepted to IJGMMP. Matches the published version. arXiv admin note: text overlap with arXiv:1407.2013 by other authors

The weak-field Schwarzschild and NUT solutions of general relativity are gravitoelectromagnetically dual to each other, except on the positive $z$-axis. The presence of non-locality weakens this duality and violates it within a smeared region around the positive $z$-axis, whose typical transverse size is given by the scale of non-locality. We restore an exact non-local gravitoelectromagnetic duality everywhere via a manifestly dual modification of the linearized non-local field equations. In the limit of vanishing non-locality we recover the well-known results from weak-field general relativity., 8 pages, comments welcome!

We revisit the Schr\"{o}dinger equation of a quantum particle that is confined on a curved surface. Inspired by the novel work of R. C. T. da Costa [1] we find the field equation in a more convenient notation. The contribution of the principal curvatures in the effective binding potential on the surface is emphasized. Furthermore, using the so-called Monge-Gauge we construct the approximate Schr\"{o}dinger equation for a flat surface with small fluctuations. Finally, the resulting Schr\"{o}dinger equation is solved for some specific surfaces. In particular, we give exact solutions for a particle confined on a Catenary surface and a paraboloid of revolution., Comment: 15 pages 17 figures

Massless field equations are fundamental in particle physics. In Clifford analysis, the Euclidean version of these equations has been dealt with but it is not clear, even in dimension 4, what should be the right analogue of massless field equations for fields with values in a general irreducible Spin(4)-module. The main aim of the paper is to explain that a good possibility is to take the so-called generalized Cauchy-Riemann equations proposed a long time ago by E. Stein and G. Weiss. For this choice of the equations, we show that their polynomial solutions form different irreducible Spin(4)-modules. This is an important step in developing the corrresponding function theory.

An important characteristic of the dilaton cosmological model is the Gasperini–Veneziano duality transformation which follows from the existence of the $$O\left( d,d\right) $$ symmetry. In this study, we consider the equivalent dilaton theory in teleparallel dark energy with the $$O\left( d,d\right) $$ symmetry, while the equivalent teleparallel-duality transformation is presented. The classical solution of the field equations is derived. Finally, the Wheeler–DeWitt equation of quantum cosmology is discussed.

In this paper, the notion of semi-symmetric connections provides us a good apparatus to establish a unified field theory. The field equations are derived from an action principle which is formed naturally by the scalar curvature of the semi-symmetric connection. The derived equations contain the Einstein and Maxwell equations in vacuum, simultaneously.

This paper deals with the existence of wormhole solutions in F ( T , T G ) gravity with the assumption that the matter density profile satisfy the Gaussian and Lorentzian distributions. Further, for the solutions of field equations in F ( T , T G ) gravity, we have used two different models of F ( T , T G ) gravity. For these specific models of F ( T , T G ) gravity, we have calculated the feasible solutions for existence of wormholes by using conformal Killing vectors approach. In the presence of Lorentzian and Gaussian distributions with conformal Killing vectors, it has been shown that stable wormhole solutions would exist for particular values of parameters.

We argue that it is possible to obtain higher-derivative Einstein’s field equations by means of an extended complexified backward–forward nonlocal extension of the space–time metric, which depends on space–time vectors. Our approach generalizes the notion of the covariant derivative along tangent vectors of a given manifold, and accordingly many of the differential geometrical operators and symbols used in general relativity. Equations of motion are derived and a nonlocal complexified general relativity theory is formulated. A number of illustrations are proposed and discussed accordingly.

By exploiting the null tetrad formalism of Jogia and Griffiths and the technique of differential forms on a non-Riemannian space-time, non-static conformally flat, Petrov-type D, spherically symmetric solutions of the Einstein–Cartan field equations; when Weyssenhoff fluid is the source of curvature and spin, are obtained. In general, the solution is expanding, accelerating, rotating and non-shearing. However, the dynamic solution is expanding and rotating with zero acceleration and shear; whereas the static solution is accelerating and rotating with ‘expansion free and shear free “congruences” ’.

In the present work, we have discussed the four dimensional spherically symmetric steller system in the framework of modified $f(T)$ gravity theory with electro-magnetic field. The field equations have been written for two cases, either $T'=0$ or $f_{TT}=0$. Next we have discussed the charged gravastar model which has three regions: interior region, shell region and exterior region. In the interior region, we have found the solutions of all physical quantities like density, pressure, electro-magnetic field and also the metric coefficients for both the cases. For $T'=0$, gravastar cannot form but it forms only for the case $f_{TT}=0$. In the exterior region, we have obtained the exterior solution for vacuum model. In the shell region, we have assumed that the interior and exterior regions join together at a place, so the intermediate region must be thin shell with the approximation $h\ll 1$. Under this approximation, we have found the analytical solutions. The proper length of the thin shell, entropy and energy content inside the thin shell have been found and they are directly proportional to the proper thickness of the shell $\epsilon$ under the approximation ($\epsilon\ll 1$). According to the Darmois-Israel formalism, we have studied the matching between the surfaces of interior and exterior regions of the gravastar. The energy density, pressure, equation of state parameter on the surface and mass of the thin shell have been obtained., Comment: 8 pages, Comments are welcome

A new exact solution of Einstein’s field equations on the background of paraboloidal space–time using Karmarkar condition is reported. The physical acceptability conditions of the model are investi...

We present an application to cosmological models in $$f({{\mathcal {R}}})$$ theories within the Palatini formalism of a method that combines cosmography and the explicit form of the field equations in the calculation of the redshift drift. The method yields a sequence of constraint equations which lead to limits on the parameter space of a given $$f({{\mathcal {R}}})$$ -model. Two particular families of $$f(\mathcal{R})$$ -cosmologies capable of describing the current dynamics of the universe are explored here: (i) power law theories of the type $$f({{\mathcal {R}}})={{\mathcal {R}}}-\beta /{{\mathcal {R}}}^n$$ , and (ii) theories of the form $$f({{\mathcal {R}}})={{\mathcal {R}}}+\alpha \ln {{{\mathcal {R}}}} -\beta $$ . The constraints on $$(n,\beta )$$ and $$(\alpha ,\beta )$$ , respectively, limit the values to intervals that are narrower than the ones previously obtained. As a byproduct, we show that when applied to General Relativity, the method yields values of the kinematic parameters with much smaller errors that those obtained directly from observations.

Dirac field equations are studied for spinor fields without any external interaction and when they are considered on a background having a tensorial connection with a specific non-vanishing structure some solution can be found in polar form displaying a square-integrable localized behaviour., Comment: 6 pages

We discuss the collapsing and expanding solutions of anisotropic charged cylinder in the context of f(R,T) theory (R represents the Ricci scalar and T denotes the trace of energy-momentum tensor). For this purpose, we take an auxiliary solution of Einstein-Maxwell field equations and evaluate expansion scalar whose negative values lead to collapse and positive values give expansion. For both cases, the behavior of density, pressure, anisotropic parameter, and mass is explored and the effects of charge as well as model parameter on these quantities are examined. The energy conditions are found to be satisfied for both solutions.

The current study deals with investigation of Einstein's vacuum field equation for exploring movable critical points. We employ first the Painleve analysis, and then we use the auto-Backlund transf...

In this paper, we report the existence of transitioning scenario of Bianchi type I universe in the context of f (R,T) gravity with special case f (R,T) = f1(R) + f2(R)f3(T) and its functional forms f1(R) = f2(R) = R and f3(T) = αT with α being constant. The exact solution of the Einstein’s field equations is derived by using the generalized hybrid expansion law that yields the model of transitioning universe from early deceleration phase to current acceleration phase. Under this specification, we obtain the singular as well as non singular solution of Bianchi type I model depending upon the particular choice of the value of problem parameters. We also notice that the validation of weak energy condition and dominant energy condition and violation of strong energy condition occurs for these values of problem parameters. The deceleration parameter is found to be negative at present (z = 0) in the derived model which is supported by recent observations.

We have constructed a model in Lyra manifold and time varying cosmological constant with perfect fluid using LVDP (Linear Varying Deceleration Parameter). Bianchi type-III metric is used as source of investigation. To get a deterministic solution of the field equation the expansion scalar (θ) is considered as proportional to the shear scalar (σ). The cosmological constant is found to be positive which satisfies the result obtained by supernova Type-Ia Observations [1999]. Here we analyse the behaviour of pressure and deceleration parameter by using different form of dark energy(DE). In addition to it, some physical and geometrical properties of the solutions are studied.

Inspired by Schaftingen [ 15 ], we develop a symmetric variational principle for the field equation involving a fractional Laplacians \begin{document}$ \begin{equation*} \left\{ \begin{aligned} (-\Delta)^\alpha u+u& = f(u), x\in\mathbb{R}^N,\\ u(x)&\geq 0. \end{aligned} \right. \end{equation*} $\end{document} As an application, we prove the existence of symmetric ground states in the fractional Sobolev space \begin{document}$ H^\alpha (\mathbb{R}^N) $\end{document} . These results improve some known ones in the literature. An example is also given to illustrate our results.

Guided by the rules of Einstein’s geometrization philosophy, a pure geometric field theory is constructed. The Lagrangian used to derive the field equations of the theory is a curvature scalar of a version of absolute parallelism (AP) geometry known in the literature as the parameterized absolute parallelism (PAP) geometry. The linear connection of this version has simultaneously non-vanishing curvature and torsion. Analysis of the theory obtained shows clearly that it is a pure gravity theory. The theory is a teleparallel one, since the building blocks of both PAP and AP geometries are the same. It is shown analytically that the theory has a trivial version in the AP-geometry, if gravity is attributed to curvature not to torsion. In the case of spherical symmetry, solutions of the field equations give rise to the Schwarzschild exterior field. The theory depends on two principles: covariance and unification. The weak equivalence principle is satisfied under a certain condition. The work preserves Einstein’s main idea that gravity is just space–time curvature, although it is not a metric theory. It is shown that the theory reduces to vacuum general relativity upon taking the parameter of the geometry b = 0.

Exact solutions are obtained for models of general scalar-tensor gravitational theories admitting the existence of privileged coordinate systems in which the eikonal equation can be integrated by the method of complete separation of variables of (2.1) type. Characteristics of radiation and explicit forms of functions of the scalar field entering into the field equations of generalized scalar-tensor gravitational theory are obtained.

Langevin equations for fields have been proposed to describe the dynamics of critical phenomena, or as an alternative method of quantization, which could be useful in cases where ordinary methods lead to difficulties, like in gauge theories. Some of their general properties will be described here. For a number of problems, in particular related to perturbation theory, it is more convenient to work with an action and a field integral than with the equation directly, because standard methods of quantum field theory (QFT) then become available. For this purpose, one can associate a field integral representation, involving a dynamic action to the Langevin equation. The dynamic action can be interpreted as generated by the Langevin equation, considered as a constraint equation. Quite generally, the integral representation of constraint equations, including stochastic equations, leads to an action that has a Slavnov–Taylor (ST) symmetry and, in a different form, has an anticommuting type Becchi–Rouet–Stora–Tyutin (BRST) symmetry, a symmetry that involves anticommuting parameters. This symmetry has no geometric origin, but is merely a consequence of associating a specific form of integral representations to the constraint equations. This symmetry is used in a number of different examples to prove the renormalizability of non-Abelian gauge theories, or to prove the geometric stability of models defined on homogeneous spaces under renormalization. In this chapter, it is used to prove Ward-Takahashi (WT) identities, and to determine how the Langevin equation renormalizes.

Two recently published papers (J.D. Barrow and A. Paliathanasis, Eur. Phys. J. C. (2018, 2019)) claim to have found exact solutions of Einstein's field equations belonging to the class of non-trivial Szekeres models, whose source is a mixture of dust and a homogeneous time-dependent scalar field, where the energy-momentum tensors of both mixture components are independently conserved. We prove that the independent conservation of these two mixture components necessarily leads to solutions belonging to the set of spatially homogeneous subcases of the Szekeres family: Friedmann-Lema\^itre-Robertson-Walker for class I, and Kantowski-Sachs, Bianchi-Behr I or Bianchi-Behr $\mbox{VI}_{\tiny{\mbox{-1}}}$ for class II., Comment: 2 pages. Comment on "Szekeres universes with homogeneous scalar fields" and "Cyclic Szekeres universes" by Barrow and Paliathanasis, Eur. Phys. J. C. (2018, 2019); arXiv:1808.00173 and arXiv:1901.09173

From four-dimensional $N=4$ matter-coupled gauged supergravity, we study smooth time-dependent cosmological solutions interpolating between a $dS_2\times \Sigma_2$ spacetime, with $\Sigma_2 = S^2$ and $H^2$, in the infinite past and a $dS_4$ spacetime in the infinite future. The solutions were obtained by solving the second-order equations of motion from all the ten gauged theories known to admit $dS_4$ solutions, of which there are two types. Type I $dS$ gauged theories can admit both $dS$ solutions as well as supersymmetric $AdS$ solutions while type II $dS$ gauged theories only admit $dS$ solutions. We also study the extent to which the first-order equations that solve the aforementioned second-order field equations fail to admit the $dS_4$ vacua and their associated cosmological solutions., Comment: v1: 38 pages, 7 figures. v2: slight modification of section 7, plus more details and references added; v3: Published version

17 pags., 4 apps., We give a detailed account of the Hamiltonian Gotay-Nester-Hinds (GNH) analysis of the parametrized unimodular extension of the Holst action. The purpose of the paper is to derive, through the clear geometric picture furnished by the GNH method, a simple Hamiltonian formulation for this model and explain why it is difficult to arrive at it in other approaches. We will also show how to take advantage of the field equations to anticipate the simple form of the constraints that we find in the paper., This work has been supported by the Spanish Ministerio de Ciencia Innovación y Universidades-Agencia Estatal de Investigación/FIS2017-84440-C2-2-P grant. B. D. was partially supported by a DGAPA-UNAM postdoctoral fellowship and acknowledges support from the CONEX Plus program funded by Universidad Carlos III de Madrid and the European Union’s Horizon 2020 program under the Marie Skłodowska-Curie Grant Agreement No. 81538. J. M.-B. is supported by the Eberly Research Funds of Penn State, by NSF Grant No. PHY-1806356 and by the Urania Stott fund of Pittsburgh Foundation UN2017-92945.

In this chapter we return to mathematics and study curvature in a Riemann space. Einstein’s general relativistic field equations of gravity follow in an intuitive way from a study of the Riemann tensor and the geometric view of gravity.

We consider a vector gauge theory in 2 + 1 dimensions of the type recently proposed by Radzihovsky and Hermele [1] to describe fracton phases of matter. The theory has U(1)×U(1) vector gauge fields coupled to an additional vector field with a non conventional gauge symmetry. We added to the theory scalar matter in order to break the gauge symmetry. We analyze non trivial configurations by reducing the field equations to first order self dual (BPS) equations which we solved numerically. We have found vortex solutions for the gauge fields which in turn generate for the extra vector field non-trivial configurations that can be associated to magnetic dipoles., Instituto de Física La Plata

We report a new one-parameter family of spherically symmetric, inhomogeneous, and time-dependent solutions of the vacuum Brans-Dicke field equations which are conformal to the Roberts scalar field geometries of Einstein gravity. The new solution is spherical and time-dependent and contains a naked central singularity. We use it as a seed to generate another two-parameter family of solutions using a known symmetry of vacuum Brans-Dicke gravity., 6 pages, no figures. Title changed. Updated to match the published version