arXiv subjects

Hoang Ky Nguyen

Publications and source records attributed to Hoang Ky Nguyen.

At least 19 recordsLinked to original sources

arXiv2026

Progenitor age-bias-corrected Type Ia supernovae favor a logarithmic luminosity-distance relation

Type Ia supernovae provide one of the principal observational probes of late-time cosmic acceleration. Recently, Son et al. [MNRAS 544, 975 (2025)] proposed that correlations between SNe Ia luminosity and progenitor age could introduce a systematic bias in the inferred luminosities, leading to revised distance moduli in the Pantheon+ and DES-SN5YR compilations. Motivated by this possibility, we test whether the age-bias-corrected SNe Ia Hubble diagrams comply with the luminosity-distance relation $d_L=c/H_0\,(1+z)\ln(1+z)$. We find that this one-parameter logarithmic relation provides a high-quality description of both datasets, with the Hubble constant $H_0$ as its sole free parameter. For Pantheon+ and DES separately, the relation yields lower $χ^2$ values than the two-parameter flat $Λ$CDM, with $Δχ^2=12.0$ and $2.1$, respectively. A joint likelihood analysis of both datasets yields $Δχ^2=17.1$, corresponding to $(Δ\text{AIC},Δ\text{BIC})=(19.1,25.2)$ in favor of the logarithmic relation. We further find that, after the age-bias correction, neither dataset requires higher-order corrections to the relation, whereas the Einstein-de Sitter cosmology is firmly rejected. These results indicate that the closed-form relation $d_L=c/H_0\,(1+z)\ln(1+z)$ provides a viable one-parameter description of progenitor age-bias-corrected SNe Ia Hubble diagrams. Its asymptotic behavior $d_L\propto z\,\ln z$ naturally accounts for the excess distance moduli observed at high redshift. Should the progenitor age-bias correction be confirmed, the logarithmic relation can be stringently tested using larger samples of SNe Ia within $1\lesssim z\lesssim2$, where it already departs markedly from flat $Λ$CDM.

astro-ph.CO↗

arXiv2026

An intrinsic kinematic relation $\boldsymbol{c=\frac{c_{0}}{H_{0}}\,\dot{a}}\,$ inferred from Type Ia supernovae

Based on the Hubble diagram of SNeIa, we present empirical evidence for a kinematic relation between the speed of light and the late-time cosmic expansion rate. To infer this relation, we employ the Dolgov-Barrow cosmology, described by Dolgov's power-law expansion $a=(t/t_0)^μ$ and Barrow's varying-speed-of-light (VSL) $c=c_0\,a^{-ζ}$. In this cosmology, light propagating through an expanding cosmic background undergoes an additional refraction induced by the variation of $c$ along its path, resulting in a modified Lemaître redshift relation $1+z=a^{-(1+ζ)}$. The model yields a high-quality fit to the Pantheon SNeIa Hubble diagram and exhibits a remarkably tight posterior degeneracy along the locus $(1+ζ)\,μ=1$. In particular, the case ${μ=2/3,ζ=1/2}$, referred to as the VSL-Einstein-de Sitter case, is favored over flat $Λ$CDM by $Δχ^2=2.8$, i.e. at 68% confidence level, despite having the same number of free parameters. The empirical relation $(1+ζ)\,μ=1$ entails that the speed of light is exactly proportional to the cosmic expansion rate, $c=c_0H_0^{-1}\,\dot a$, during late times, a synchronous behavior absent in the standard $Λ$CDM model. Although the empirical relation $(1+ζ)\,μ=1$ is inferred using the Dolgov-Barrow parameterization, the resulting expression $c=c_0H_0^{-1}\,\dot a$ is an intrinsic relation because it relates two physical quantities of the same dimension: speed of light and cosmic expansion rate. It is therefore independent of arbitrary choices of units or parameterization and encodes a purely kinematic correspondence between $c$ and $\dot a$. If confirmed by independent probes, this relation may point toward a more general kinematic principle governing late-time cosmic evolution. We discuss implications of this relation for late-time cosmology, including an alternative interpretation of cosmic acceleration.

astro-ph.CO↗

arXiv2025

A mechanism to generate varying speed of light via Higgs-dilaton coupling: Theory and cosmological applications

We allow the Higgs field $Φ$ to interact with a dilaton field $χ$ of the background spacetime via the coupling $χ^2\,Φ^\daggerΦ$. Upon spontaneous gauge symmetry breaking, the Higgs VEV becomes proportional to $χ$. While traditionally this linkage is employed to make the Planck mass and particle masses dependent on $χ$, we present an $\textit alternative$ mechanism: the Higgs VEV will be used to construct Planck's constant $\hbar$ and speed of light $c$. Specifically, each open set vicinity of a given point $x^*$ on the spacetime manifold is equipped with a replica of the Glashow-Weinberg-Salam action operating with its own effective values of $\hbar_*$ and $c_*$ per $\hbar_*\proptoχ^{-1/2}(x^*)$ and $c_*\proptoχ^{1/2}(x^*)$, causing these ``fundamental constants'' to vary alongside the dynamical field $χ$. Moreover, in each open set around $x^*$, the prevailing value $χ(x^*)$ determines the length and time scales for physical processes occurring in this region as $l\proptoχ^{-1}(x^*)$ and $τ\proptoχ^{-3/2}(x^*)$. This leads to an $\textit anisotropic$ relation $τ^{-1}\propto l^{-3/2}$ between the rate of clocks and the length of rods, resulting in a distinct set of novel physical phenomena. For late-time cosmology, the variation of $c$ along the trajectory of light waves from distant supernovae towards the Earth-based observer necessitates modifications to the Lemaître redshift relation and the Hubble law. These modifications are capable of: (1) Accounting for the Pantheon Catalog of SNeIa $\textit{through a declining speed of light in an expanding Einstein--de Sitter universe}$, thus avoiding the need for dark energy; (2) Revitalizing Blanchard-Douspis-Rowan-Robinson-Sarkar's CMB power spectrum analysis that bypassed dark energy [A&A 412, 35 (2003)]; and (3) Resolving the $H_0$ tension without requiring a dynamical dark energy component.

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arXiv2025

New analysis of SNeIa Pantheon Catalog: Variable speed of light as an alternative to dark energy

In A&A 412, 35 (2003) Blanchard, Douspis, Rowan-Robinson, and Sarkar (BDRS) slightly modified the primordial fluctuation spectrum and produced an excellent fit to WMAP's CMB power spectrum for an Einstein-de Sitter (EdS) universe, bypassing dark energy. Curiously, they obtained a Hubble value of $H_0\approx46$, in sharp conflict with the canonical range $H_0\sim67-73$. However, we will demonstrate that the reduced value of $H_0\approx46$ achieved by BDRS is fully compatible with the use of variable speed of light in analyzing the late-time cosmic acceleration observed in Type Ia supernovae (SNeIa). In Phys. Lett. B 862, 139357 (2025) we uncovered a hidden aspect in a generic class of scale-invariant actions: the dynamics of the dilaton can induce a variation in the speed of light as $c\proptoχ^{1/2}$, causing $c$ to vary alongside $χ$ across spacetime. For an EdS universe with varying $c$, besides the effects of cosmic expansion, light waves emitted from distant SNeIa are further subject to a refraction effect, which alters the Lemaitre redshift relation to $1+z=a^{-3/2}$. Based on this new formula, we achieve a fit to the SNeIa Pantheon Catalog exceeding the quality of the $Λ$CDM model. Crucially, our approach does not require dark energy and produces $H_0=47.2$ in strong alignment with the BDRS finding of $H_0\approx46$. Hence, BDRS's analysis of the (early-time) CMB power spectrum and our variable-$c$ analysis of the (late-time) Hubble diagram of SNeIa fully agree on two counts: (i) the dark energy hypothesis is avoided, and (ii) $H_0$ is reduced to $\sim47$, which also yields an age $t_0=2/(3H_0)=13.8$ Gy for an EdS universe, without requiring dark energy. Most importantly, we will demonstrate that the late-time acceleration can be attributed to the declining speed of light in an expanding EdS universe, rather than to a dark energy component.

astro-ph.CO↗

arXiv2025

Dilaton-induced variations in Planck constant and speed of light: An alternative to Dark Energy

We reveal a novel aspect of scale-invariant actions that allow matter to couple with a dilaton field: $\,$The dynamics of the dilaton can induce variations in the Planck constant $\hbar$ and speed of light $c$. $\,$Our mechanism for generating variable $\hbar$ and $c$ in $\textit{curved}$ spacetimes via the dilaton offers a viable alternative account for late-time cosmic acceleration, bypassing the need for dark energy.

gr-qc↗

arXiv2024

New exact solution and $\mathcal{O}\,(1/\sqrtω)$ anomaly in Brans-Dicke gravity with trace-carrying matter

We present an exact static spherisymmetric solution for the Brans-Dicke action sourced by a self-gravitating massless Klein-Gordon helicity-0 field. In contrast to the Maxwell electromagnetic field, a Klein-Gordon field possesses an energy-momentum tensor with $\textit{non-vanishing trace}$. Upon a Weyl mapping into the Einstein frame, the transformed Brans-Dicke scalar field takes on the role of a "dilaton" coupled with the Klein-Gordon field. Despite this dilatonic coupling, the field equations of the resulting Einstein-Klein-Gordon-dilaton action are fully soluble when employing the harmonic radial coordinate. The exact solution derived herein can serve as a prototype for future Brans-Dicke gravity studies involving trace-carrying matter fields. Notably, in the limit of infinite $ω$, the Brans-Dicke scalar field exhibits an anomalous behavior of ${\cal O}\,(1/\sqrtω)$ as opposed to ${\cal O}\,(1/ω)$. As a consequence, the solution converges to a spacetime configuration of General Relativity sourced by the original Klein-Gordon field and a free scalar field, the latter of which is the ${\cal O}\,(1/\sqrtω)$ "remnant" of the Brans-Dicke scalar field. Furthermore, we provide a formal mathematical proof substantiating these two conclusions. Although the ${\cal O}\,(1/\sqrtω)$ anomaly has been previously discovered for Brans-Dicke vacuum and Brans-Dicke-Maxwell electrovacuum, our findings establish its prevalence in Brans-Dicke gravity $\textit{regardless}$ of the trace of the energy-momentum tensor of the source. Taken together, the ${\cal O}\,(1/\sqrtω)$ anomaly challenges the conventional belief in the ${\cal O}\,(1/ω)$ signature commonly associated with Brans-Dicke gravity. In particular, it may have implications in improving the relativistic corrections to Newtonian gravity beyond the weak-field parametrized post-Newtonian formalism.

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arXiv2024

Revisiting Weak Energy Condition and wormholes in Brans-Dicke gravity

It is known that the formation of a wormhole typically involves a violation of the Weak Energy Condition (WEC), but the reverse is not necessarily true. In the context of Brans-Dicke gravity, the $\textit{generalized}$ Campanelli-Lousto solution, which we shall unveil in this paper, demonstrates a WEC violation that coincides with the appearance of $\textit{unbounded}$ sheets of spacetime within the "interior" section. The emergence of a wormhole in the "exterior" section is thus only an indirect consequence of the WEC violation. Additionally, we use the generalized Campanelli-Lousto solution to construct a Kruskal-Szekeres diagram, which exhibits a "gulf" sandwiched between the four quadrants in the diagram, a novel feature in Brans-Dicke gravity. Overall, our findings shed new light onto a complex interplay between the WEC and wormholes in the Brans-Dicke theory.

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arXiv2024

Observational test of ${\cal R}^{2}$ spacetimes with the S2 star in the Milky Way galactic center

A novel class of vacuum metrics expressible in analytical form was recently found for pure $\mathcal R^2$ gravity, based on a groundwork put forth by Buchdahl in 1962. These Buchdahl-inspired solutions offer a practical framework for testing ${\cal R}^2$ gravity through empirical observations. Within a subclass of asymptotically flat Buchdahl-inspired vacuum spacetimes, we identified a parameter $ε$ measuring the deviation from the classic Schwarzschild metric, which corresponds to $ε=0$. In this paper, we employ observational data from the S2 star's orbit around Sgr A* in the Milky Way galactic center and perform Monte Carlo Markov Chain simulations to probe the effects of the new metrics on the orbit of the S2 star. Our analysis presented herein reports a range at 95\% confidence level on the deviation parameter as $ε\in(-0.6690,\ 0.4452)$. While no decisive evidence either in favor or in disfavor of the asymptotically flat Buchdahl-inspired spacetimes has been achieved, the obtained bound is compatible with the tighter results using other data of different nature as recently reported in Eur.\,Phys.\,J.\,C $\bf 84$, 330 (2024). As a meaningful test probing into a strong-field regime, our present study calls for further observations with prolonged period and improved accuracy in order to tighten the bound for $ε$ using the S2 star orbit.

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arXiv2024

Violation of $γ$ in Brans-Dicke gravity

The Brans Class I solution in Brans-Dicke gravity is a staple in the study of gravitational theories beyond General Relativity. Discovered in 1961, it describes the exterior vacuum of a spherical Brans-Dicke star and is characterized by two adjustable parameters. Surprisingly, the relationship between these parameters and the properties of the star has not been rigorously established. In this Proceeding, we bridge this gap by deriving $\textit{the}$ complete exterior solution of Brans Class I, expressed in terms of the total energy and total pressure of the spherisymmetric gravity source. The solution allows for the $\textit{exact}$ derivation of $\textit{all}$ post-Newtonian parameters in Brans-Dicke gravity for far field regions of a spherical source. Particularly for the $γ$ parameter, instead of the conventional result $γ_{\,\text{PPN}}=\frac{ω+1}{ω+2}$, we obtain the analytical expression $γ_{\,\text{exact}}=\frac{ω+1+(ω+2)\,Θ}{ω+2+(ω+1)\,Θ}$ where $Θ$ is the ratio of the total pressure $P_{\parallel}^{*}+2P_{\perp}^{*}$ and total energy $E^{*}$ contained within the mass source. Our $\textit{non-perturbative}$ $γ$ formula is valid for all field strengths and types of matter comprising the mass source. Consequently, observational constraints on $γ$ thus set $\textit{joint}$ bounds on $ω$ and $\varTheta$, with the latter representing a global characteristic of the mass source. More broadly, our formula highlights the importance of pressure (when $\varTheta\neq0$) in spherical Brans-Dicke stars, and potentially in stars within other modified theories of gravitation.

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arXiv2024

Time-reversed information flow through a wormhole in scalar-tensor gravity

This Letter aims to advance unexplored properties of a new class of Closed Timelike Curves recently discovered in scalar-tensor gravity, reported in Universe 9, 467 (2023) and Eur.$\,$Phys.$\,$J.$\,$C 83, 626 (2023). Therein, it was shown that when the Weak Energy Condition is violated, the topology of spacetime in scalar-tensor gravity is altered, enabling the formation of two-way traversable wormholes. Furthermore, each of these wormholes acts a gateway between two $\textit{time-mirrored}$ worlds, where the two asymptotically flat sheets in the Kruskal-Szekeres diagram are glued antipodally along $\textit{three}$ directions -- time $t$ and the polar and azimuth angles $(θ,\,φ)$ of the 2-sphere -- to form a wormhole throat. This contrasts with the standard embedding diagram which typically glues the sheets only along the $θ$ and $φ$ directions. Crucially, due to the `gluing' along the $t$ direction, the wormhole becomes a portal connecting the two spacetime sheets with $\textit{opposite}$ physical time flows, enabling the emergence of closed timelike loops which straddle the throat. We shall point out that this portal $\textit{mathematically}$ permits the possibility of backward propagation of information $\textit{against}$ time. This feature is ubiquitous for wormholes in scalar-tensor theories. In addition, we formulate the Feynman sum for transition amplitudes of microscopic particles in the proximity of a wormhole throat in which we account for timelike paths that experience time reversal.

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arXiv2024

Impact of Star Pressure on $γ$ in Modified Gravity beyond Post-Newtonian Approach

We provide a concrete example exhibiting marked deviation from the PPN approximation in a modified theory of gravity. Specifically, we derive the exact formula for the Robertson parameter $γ$ in Brans-Dicke gravity for compact mass sources, explicitly incorporating the pressure content of these sources. We achieve this by exploiting the $\textit integrability$ of the 00-component of the Brans-Dicke field equation. In place of the conventional PPN result $γ_{PPN}=\frac{ω+1}{ω+2}$, we obtain the analytical expression $γ_{\,exact}=\frac{ω+1+(ω+2)\varTheta}{ω+2+(ω+1)\varTheta}$ where $\varTheta$ is the ratio of the total pressure $P_\parallel^*+2P_\perp^*$ and total energy $E^*$ contained within the mass source. Our $\textit non\text{-}perturbative$ formula is valid for all field strengths and types of matter comprising the mass source. We draw four key conclusions: (1) The usual $γ_{PPN}$ formula is violated in the presence of pressure, viz. when $\varTheta\neq0$, revealing a limitation of the PPN approximation in Brans-Dicke gravity. (2) The PPN result mainly stems from the assumption of pressureless matter. Even in the weak-field star case, non-zero pressure leads to a violation of the PPN $γ$ formula. Conversely, the PPN result is a good approximation for low-pressure matter, i.e. when $\varTheta\approx0$, for all field strengths. (3) Observational constraints on $γ$ set $\textit joint$ bounds on $ω$ and $\varTheta$, with the latter representing a global characteristic of a mass source. If the equation of state of matter in the mass source approaches the ultra-relativistic form, entailing $\varTheta\simeq1$, $γ_{\,exact}$ converges to 1 $\textit irrespective$ of $ω$. (4) In a broader context, our findings indicate the latent significance of considering the interior structure of stars in observational astronomy.

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arXiv2024

The complete exterior spacetime of spherical Brans-Dicke stars

We derive the complete expression for the Brans Class I exterior spacetime explicitly in terms of the energy and pressures profiles of a stationary spherisymmetric gravity source. This novel and generic expression is achieved in a parsimonious manner, requiring only a subset of the Brans-Dicke field equation and the scalar equation. For distant orbiting test particles, this expression promptly provides a simple, closed and exact formula of the [textgreek] \textgreek{g} Eddington parameter, which reads γ_{exact}=((ω+1+(ω+2)Θ)/(ω+2+(ω+1)Θ)), where Θ is the ratio of the star's "total pressure" integral over its energy integral. This non-perturbative result reproduces the usual Post-Newtonian ((ω+1)/(ω+2)) expression in the case of a "Newtonian star", in which the pressure is negligible with respect to the energy density. Furthermore, it converges to the General Relativity value (γ_{GR}=1) as the star's equation of state approaches that of ultra-relativistic matter (in which case Θ approaches 1), a behavior consistent with broader studies on scalar-tensor gravity. Our derivation underscores the essence of these results involving (1) the key relevant portion of the Brans-Dicke field equations, (2) the uniqueness of the Brans Class I vacuum solution for the non-phantom action, viz. ω>-3/2, and (3) the involvement of only two free parameters in this solution, hence requiring two quantities (energy and pressure integrals) of the mass source to fully characterize the solution. From a practical standpoint, it elucidates how a given stellar interior structure model determines the star's exterior gravitational field and impacts the motions of light objects (such as planets and accretion disks) orbiting it.

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arXiv2024

Non-triviality of asymptotically flat Buchdahl-inspired metrics in pure $R^2$ gravity

In Phys. Rev. D $\textbf{107}$, 104008 (2023) we reported a novel exact closed-form solution which describes asymptotically flat spacetimes in pure $R^2$ gravity. The solution is Ricci scalar flat, viz. $R\equiv0$ everywhere. Whereas any metric with a null Ricci scalar would $\textit{trivially}$ satisfy the $R^2$ vacuo field equation, $R\left(R_{μν}-\frac{1}{4}g_{μν}\,R\right)+g_{μν}\,\square\,R-\nabla_μ\nabla_νR=0$, in this article, we shall show that our solution satisfies a "stronger" version of the $R^2$ vacuo field equation, viz. $R_{μν}-\frac{1}{4}g_{μν}\,R+R^{-1}\left(g_{μν}\,\square\,R-\nabla_μ\nabla_νR\right)=0$, despite the term $R^{-1}$ being $\textit{singular}$. Even though $R$ identically vanishes, for our solution, the combinations $\,R^{-1}\,\nabla_μ\nabla_νR\,$ and $\,R^{-1}\,\square\,R\,$ are $\textit{free of singularity}$. This exceptional property sets our solution apart from the set of null-Ricci-scalar metrics and makes it a genuinely $\textit{non-trivial}$ solution. We further demonstrate that, as a member of a larger class of asymptotically de Sitter metrics, our solution is resilient against perturbations in the scalar curvature at largest distances, making it relevant for physical situations where the background deviates from asymptotic flatness.

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arXiv2024

Analyzing Pantheon SNeIa data in the context of Barrow's variable speed of light

We analyze the Combined Pantheon Sample of Type Ia supernovae while allowing the velocity of light to vary as a function of the scale factor $c\propto a^{-ζ}$, as initiated by Barrow [Phys. Rev. D 59, 043515 (1999)]. The variation in the velocity of light creates an effect akin to the refraction phenomenon which occurs for a wave traveling in a medium with varying speed of wave. We elucidate the role of the local scale of gravitationally-bound regions in assisting the refraction effect to manifest. The refraction effect alters the redshift formulae (Lemaitre, distance-vs-z, luminosity distance-vs-z) and warrants a new analysis of the Pantheon dataset. Upon a reformulation of the distance-redshift relations, we achieve a high-quality fit of the Pantheon dataset to the variable light speed approach; the fit is as robust as that obtained in the standard $ΛCDM$ model. We find that the Pantheon dataset is consistent with the variable light speed of the functional form: $a\propto t^μ$ and $c\propto a^{1-1/μ}$ with (i) the cosmic age $t_{0}\approx 13.9$ Gy as a free parameter, while $μ$ is unspecified; and (ii) a monotonic variation in the local scale for gravitationally-bound objects (applicable to the emission sources and the Solar System-based apparatus/observer). Due to the agent in (ii), the high-z portion of the Pantheon dataset would produce an "effective" $H_{0}$ estimate which is 10 percent lower than the $H_{0}$ estimate obtained from the low-z portion of the dataset. We offer an alternative interpretation of the accelerating expansion by way of variable speed of light, and as a by-product of the agent uncovered in (ii), a tentative suggestion toward "resolving" the ongoing tension in the Hubble constant estimates.

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arXiv2024

Observational tests of asymptotically flat ${\cal R}^{2}$ spacetimes

A novel class of Buchdahl-inspired metrics with closed-form expressions was recently obtained based on Buchdahl's seminal work on searching for static, spherically symmetric metrics in ${\cal R}^{2}$ gravity in vacuo. Buchdahl-inspired spacetimes provide an interesting framework for testing predictions of ${\cal R}^{2}$ gravity models against observations. To test these Buchdahl-inspired spacetimes, we consider observational constraints imposed on the deviation parameter, which characterizes the deviation of the asymptotically flat Buchdahl-inspired metric from the Schwarzschild spacetime. We utilize several recent solar system experiments and observations of the S2 star in the Galactic center and the black hole shadow. By calculating the effects of Buchdahl-inspired spacetimes on astronomical observations both within and outside of the solar system, including the deflection angle of light by the Sun, gravitational time delay, perihelion advance, shadow, and geodetic precession, we determine observational constraints on the corresponding deviation parameters by comparing theoretical predictions with the most recent observations. Among these constraints, we find that the tightest one comes from the Cassini mission's measurement of gravitational time delay.

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arXiv2023

A stationary axisymmetric vacuum solution for pure $R^2$ gravity

The closed-form expression for pure $\mathcal{R}^{2}$ vacuum solution obtained in Phys. Rev. D \textbf{107}, 104008 (2023) lends itself to a generalization to axisymmetric setup via the modified Newman--Janis algorithm. We adopt the procedure put forth in Phys. Rev. D \textbf{90}, 064041 (2014) bypassing the complexification of the radial coordinate. The procedure presumes the existence of Boyer-Lindquist coordinates. Using the Event Horizon Telescope Collaboration results, we model the central black hole M87{*} by the thus obtained exact rotating metric, depending on the mass, rotation parameter and a third dimensionless parameter. The latter is constrained upon investigating the shadow angular size assuming mass and rotation parameters are those of M87{*}. Stability is investigated.

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arXiv2023

Closed Timelike Curves Induced by a Buchdahl-inspired Vacuum Spacetime in $R^2$ Gravity

The recently obtained $\textit{special}$ Buchdahl-inspired metric [Phys. Rev. D 107, 104008 (2023)] describes asymptotically flat spacetimes in pure Ricci-squared gravity. The metric depends on a new (Buchdahl) parameter $\tilde{k}$ of higher-derivative characteristic, and reduces to the Schwarzschild metric, for $\tilde{k}=0$. For the case $\tilde{k}\in(-1,0)$, it was shown that it describes a traversable Morris-Thorne-Buchdahl (MTB) wormhole [Eur. Phys. J. C 83, 626 (2023)], where the weak energy condition is formally violated. In this paper, we briefly review the $\textit{special}$ Buchdahl-inspired metric, with focuses on the construction of $ζ-$Kruskal-Szekeres (KS) diagram and the situation for a wormhole to emerge. Interestingly, the MTB wormhole structure appears to permit the formation of closed timelike curves (CTCs). More specifically, a CTC straddles the throat, comprising of two segments positioned in opposite quadrants of the $ζ-$KS diagram. The closed timelike loop thus passes through the wormhole throat twice, causing $\textit{two}$ reversals in the time direction experienced by the (timelike) traveller on the CTC. The key to constructing a CTC lies in identifying any given pair of antipodal points $(T,X)$ and $(-T,-X)$ $\textit{on the wormhole throat}$ in the $ζ-$KS diagram as corresponding to the same spacetime event. It is interesting to note that the Campanelli-Lousto metric in Brans-Dicke gravity is known to support two-way traversable wormholes, and the formation of the CTCs presented herein is equally applicable to the Campanelli-Lousto solution.

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arXiv2023

Emerging Newtonian potential in pure $R^2$ gravity on a de Sitter background

In Fortsch. Phys. $\textbf{64}$, 176 (2016), Alvarez-Gaume et al established that pure $R^2$ theory propagates $\textit{massless}$ spin-2 graviton on a de Sitter (dS) background but $\textit{not}$ on a locally flat background. We build on this insight to derive a Newtonian limit for the theory. Unlike most previous works that linearized the metric around a locally flat background, we explicitly employ the dS background to start with. We directly solve the field equation of the action $(2κ)^{-1}\int d^{4}x\sqrt{-g}\,R^2$ coupled with the stress-energy tensor of normal matter in the form $T_{μν}=Mc^2\,δ(\vec{r})\,δ_μ^0\,δ_ν^0$. We obtain the following Schwarzschild-de Sitter metric $ds^{2}=-\Bigl(1-\fracΛ{3}r^{2}-\frac{κc^{2}}{48πΛ}\frac{M}{r}\Bigr)c^2dt^2+\Bigl(1-\fracΛ{3}r^2-\frac{κc^2}{48πΛ}\frac{M}{r}\Bigr)^{-1}dr^2+r^2dΩ^2$ which features a potential $V(r)=-\frac{κc^4}{96πΛ}\frac{M}{r}$ with the correct Newtonian tail. The parameter $Λ$ plays a dual role: (i) it sets the scalar curvature for the background dS metric, and (ii) it partakes in the Newtonian potential $V(r)$. We reach two key findings. Firstly, the Newtonian limit only emerges owing to the de Sitter background. Most existing studies of the Newtonian limit in modified gravity chose to linearize the metric around a locally flat background. However, this is a $\textit{false}$ vacuum to start with for pure $R^2$ gravity. These studies unknowingly omitted the information about $Λ$ of the de Sitter background, hence incapable of attaining a Newtonian behavior in pure $R^2$ gravity. Secondly, as $Λ$ appears in $V(r)$ in a $\textit{singular}$ manner, viz. $V(r)\proptoΛ^{-1}$, the Newtonian limit for pure $R^2$ gravity cannot be obtained by any perturbative approach treating $Λ$ as a small parameter.

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