arXiv subjects

Hoang Ky Nguyen

Publications and source records attributed to Hoang Ky Nguyen.

24 records · Page 2Linked to original sources

arXiv2023

Traversable Morris-Thorne-Buchdahl wormholes in quadratic gravity

The special Buchdahl-inspired metric obtained in a recent paper [Phys. Rev. D 107, 104008 (2023)] describes asymptotically flat spacetimes in pure $\mathcal{R}^{2}$ gravity. The metric depends on a new (Buchdahl) parameter $\tilde{k}$ of higher-derivative characteristic, and recovers the Schwarzschild metric when $\tilde{k}=0$. It is shown that the special Buchdahl-inspired metric supports a two-way traversable Morris-Thorne wormhole for $\tilde{k}\in(-1,0)$ in which case the Weak Energy Condition is formally violated, a naked singularity for $\tilde{k}\in(-\infty,-1)\cup(0,+\infty)$, and a non-Schwarzschild structure for $\tilde{k}=-1$.

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arXiv2023

Buchdahl-inspired spacetimes and wormholes: Unearthing Hans Buchdahl's other 'hidden' treasure trove

Circa 1962 Hans A. Buchdahl pioneered a program -- and made significant progress -- seeking vacuo configurations in pure $\mathcal{R}^{2}$ gravity [H. A. Buchdahl, Nuovo Cimento 23, 141 (1962)]. Unfortunately, he deemed the final step in his calculations impassable and prematurely suspended his pursuit. Since then, his achievements on this front have faded into dormancy. Unbeknownst to Buchdahl himself, the $\mathcal{R}^{2}$ vacua that he sought were within $\textit{his}$ striking distance. In our recent three-paper body of work published in Phys. Rev. D, we broke this six-decades-old impasse and accomplished his goal: A novel class of metrics, describing non-Schwarzschild spacetimes in quadratic gravity and carrying a hallmark of higher-derivative characteristic. Intriguing properties of Buchdahl-inspired spacetimes and their associated Morris-Thorne-Buchdahl wormholes -- summarized herein -- embody a new branch of phenomenology that transcends the Einstein-Hilbert paradigm.

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arXiv2023

Beyond Schwarzschild-de Sitter spacetimes: II. An exact non-Schwarzschild metric in pure $R^{2}$ gravity and new anomalous properties of $R^{2}$ spacetimes

In our recent publication (Phys. Rev. D 106, 104004 (2022)), we advanced a program that Buchdahl originated but prematurely abandoned circa 1962 (Nuovo Cimento 23, 141 (1962)). Therein we obtained an exhaustive class of metrics that constitute the branch of non-trivial solutions to the pure $R^{2}$ field equation in vacuo. The Buchdahl-inspired metrics in general possess non-constant scalar curvature, thereby defeating the generalized Lichnerowicz theorem previously advocated for quadratic gravity. We found that the said theorem makes an overly strong assumption on the asymptotic falloff in the spatial derivatives of the Ricci scalar, rendering it violable against the Buchdahl-inspired metrics. In this paper, we shall further extend our work mentioned above by showing that, within the class of Buchdahl-inspired metrics, the asymptotically flat member takes on an exact closed analytical expression. The new metric is characterized by a horizon radius $r_{\text{s}}$ and the Buchdahl parameter $k$, the latter of which arises via the higher-derivative nature of $R^{2}$ gravity. For $k=0$, the new metric recovers the classic Schwarzschild metric. Equipped with the exact expression of the new metric, we shall analytically construct the Kruskal-Szekeres diagram for pure $R^{2}$ spacetime. We find that the Buchdahl parameter $k$ fundamentally modifies the properties of $R^{2}$ spacetime structures in a variety of ways.

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arXiv2023

Beyond Schwarzschild-de Sitter spacetimes: III. A perturbative vacuum with non-constant scalar curvature in $R+R^2$ gravity

In violation of the generalized Lichnerowicz theorem advocated by Nelson and others, quadratic gravity admits vacua with non-constant scalar curvature. In a recent publication [Phys. Rev. D 106, 104004 (2022)], we revitalized a program that Buchdahl originated but prematurely abandoned circa 1962 [Nuovo Cimento 23, 141 (1962)], and uncovered a novel exhaustive class of static spherically symmetric vacua for pure $R^2$ gravity. The Buchdahl-inspired metrics we obtained therein are exact solutions which exhibit non-constant scalar curvature. A product of fourth-order gravity, the metrics entail a new (Buchdahl) parameter $k$ which allows the Ricci scalar to vary on the manifold. The metrics are able to defeat the generalized Lichnerowicz theorem by evading an overly strong restriction on the asymptotic falloff in the Ricci scalar as assumed in the theorem. The Buchdahl parameter $k$ is a new characteristic of pure $R^2$ gravity, a higher-derivative theory. By venturing that the Buchdahl parameter should be a universal hallmark of higher-derivative gravity at large, in this paper we seek to extend the concept to the quadratic action $R^2+γ\,(R-2Λ)$. We are able to determine that the quadratic field equation admits a perturbative vacuo that is valid up to the order $O(k^2)$. Conforming with our guiding intuition, the Ricci scalar is non-constant, including the asymptotically flat case, as long as $k\neq0$ and $γ\neq0$. The existence of such an asymptotically flat vacuo with non-constant scalar curvature defeats the generalized Lichnerowicz theorem in its entirety. Our finding thus warrants restoring the $R^2$ term in the full quadratic action, $γ\,R+β\,R^2-α\,C^{μνρσ}C_{μνρσ}$, when applying the Lü-Perkins-Pope-Stelle ansatz. Implications to the Lü-Perkins-Pope-Stelle solution are discussed herein.

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arXiv2022

Beyond Schwarzschild-de Sitter spacetimes: I. A new exhaustive class of metrics inspired by Buchdahl for pure $R^2$ gravity in a compact form

Some sixty years ago Buchdahl pioneered a program in search of static spherically symmetric vacua for pure $R^{2}$ gravity (Nuovo Cimento, Vol 23, No 1, pp 141-157 (1962); [https://link.springer.com/article/10.1007/BF02733549]). Surpassing several obstacles, his work culminated in a non-linear second-order ordinary differential equation (ODE) which required being solved. However Buchdahl deemed the ODE intractable and prematurely abandoned his pursuit for an analytical solution. We have finally managed to break this six-decades-old impasse and accomplish his goal. Reformulating the Buchdahl ODE, we obtain a novel exhaustive class of metrics (which we shall call the Buchdahl-inspired metrics hereafter) in a compact form. We are able to verify ex post, via direct inspection, that the metric obtained herein satisfies the $R^{2}$ vacuo field equation, hence establishing its validity. We show why the Buchdahl-inspired metrics, which exhibit non-constant scalar curvature, defeat a Lichnerowicz-type no-go theorem, previously proved for quadratic gravity, by evading the overly strong restriction on the asymptotic falloff of the metric at spatial infinity. Our novel solution thereby completes Buchdahl's six-decades-old program. We also explore the mathematical properties of the Buchdahl-inspired metrics in the limit of small k and in the region around the coordinate origin.

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arXiv2013

Toward a theory of curvature-scaling gravity

A salient feature of Horava gravity is the anisotropic time variable. We propose an alternative construction of the spacetime manifold which naturally enables time anisotropy. We promote the role of curvature: the Ricci scalar R at a given point sets the length scales for physical processes - including gravity - in the local inertial frames enclosing that point. The manifold is a patchwork of local regions; each region is Lorentz invariant and adopts a local scale a_R defined as a_R = 1/sqrt|R|. In each local patch, the length scales of physical processes are measured relatively to a_R, and only their dimensionless ratios partake in the dynamics of physical processes. Time anisotropy arises by requiring that the form - but not necessarily the parameters - of physical laws be unchanged under variations of the local a_R as one moves on the manifold. The time scaling is found to be dt ~ a_R^(3/2) whereas the spatial part scales as dx ~ a_R. We show how to conjoin the local patches of the manifold in a way which respects causality and special relativity, as well as the equivalence and general covariance principles. All of Einstein's insights are preserved but the parameters of physical laws are only valid locally and become functions of the prevailing Ricci scalar. This alternative construction of the manifold permits a unique choice for the Lagrangian of gravity coupled with matter. Curvature is actively involved in the dynamics of physical processes by setting the scale for them. In vacuo our theory takes the form of R^2 gravity and adopts a larger set of solutions superseding those of Einstein-Hilbert action R. We provide two solutions: one solution connects our work to Mannheim's theory of galactic rotation curves; the other leads to novel properties for Schwarzschild black holes. We apply the theory to address problems in cosmology and discuss its implications in quantum gravity.

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