arXiv subjects

Yen-Kheng Lim

Publications and source records attributed to Yen-Kheng Lim.

At least 19 recordsLinked to original sources

arXiv2026

Conformal Killing--Yano Ricci solitons: Structure, compatibility, and rigidity

We introduce a geometric structure -- a conformal Killing--Yano Ricci soliton (CKY--RS) -- that couples conformal Ricci soliton (CRS) geometry to conformal Killing--Yano (CKY) 2--forms. The soliton field of the CRS geometry is given by the divergence of the CKY 2--form. We introduce a conserved CKY--Cotton current and derive a compatibility identity relating the Cotton tensor, the CRS obstruction tensor, and the CKY 2--form. In 4--dimensional Lorentzian signature, we show that, under non-degeneracy and closedness assumptions on the CKY form, a CKY--RS structure forces the conformal representative to be locally Kerr--NUT--(A)dS. For a closed non-degenerate CKY on a Kerr--NUT--(A)dS background, the conformal deformation is necessarily trivial. For Einstein backgrounds of arbitrary dimension and signature, the conformal factor satisfies an eigenvalue equation and an Obata--type Hessian equation. If the background is also compact or a CKY orbit is periodic, the conformal factor is an invariant of the CKY--flow and we obtain simple spectral obstructions to non-trivial CKY--RS structures. From the Hessian equation, we obtain obstruction and classification results for the non-trivial conformal sector, including product/Brinkmann geometries and a Weyl--aligned branch. Finally, we give explicit constructions for static spherically symmetric geometries and BTZ backgrounds, including a CKY--RS realization with a time-dependent conformally flat representative. These results provide a geometric framework for studying CRS with hidden symmetry structure, with potential applications to exact geometries in general relativity.

math.DG↗

arXiv2026

Magnetising de Sitter and Anti-de Sitter spacetimes

We attempt to magnetise the de Sitter (dS) and Anti-de Sitter (AdS) spacetimes in spherical symmetry. First, the weak field case is considered where Maxwell's equation is solved to find magnetic fields in fixed dS/AdS backgrounds. For strong magnetic fields we consider Einstein-Maxwell gravity with a gravitating fluid source. With gravitational backreaction of the magnetic field taken into account, the strong fields deform the dS/AdS spacetime, resulting in a dS/AdS-type analogue of the Melvin magnetic universe. This solution is obtained via a Harrison-like transformation, along with appropriate transformations of the fluid energy and pressures. Some of its physical and geometrical properties of the solution are studied.

gr-qc↗

arXiv2026

Probing the Strong Equivalence Principle through the External Field Effect. How Do Two Masses Fall?

Despite compelling evidence, the absence of a confirmed dark matter particle has sustained interest in modified gravity as an alternative explanation for the observed phenomenology. One prominent example is Modified Newtonian Dynamics (MOND), which predicts that the internal dynamics of a system depends on the external gravitational field in which it is embedded. This so-called External Field Effect violates the strong equivalence principle (SEP) and is absent in canonical mechanics, making it a promising avenue for experimental tests of modified gravity. Motivated by this, we investigate the dynamics of two spherical masses arranged such that their symmetry axis is either parallel or orthogonal to the local gravitational field. We derive solutions describing the internal dynamics of such systems in both strong uniform and radial external fields. In particular, for a radial external field, if the non-relativistic gravitational field is free to have non-vanishing curl, we find that the mutual attraction of the masses in the perpendicular configuration is not strictly aligned with their symmetry axis. It acquires a small transverse component, even when the external gravitational field is everywhere balanced by non-gravitational forces. Using these solutions, we determine the spatial and temporal sensitivities required to distinguish the two configurations and systematically assess experimentally relevant effects, including air drag, object size, and surface interactions. As an example, detecting the prediction of the simple MOND interpolating function requires a spatial sensitivity of order 0.1 fm for sub-millimeter masses evolving over approximately 30 minutes. Such times may be achievable with levitated particles or in space-based environments. Experiments operating at lower resolutions are also interesting as independent tests of SEP and place constraints on modified-gravity theories.

gr-qc↗

arXiv2026

Interior marginally outer trapped surfaces in Hayward black holes

We locate interior marginally outer trapped and marginally outer trapped open surfaces (MOTS/MOTOS) in the regular Haward metric with parameter $b$ for which a critical (extremal) value $b=b_c$ demarcates when the spacetime admits no horizon and when it admits inner and outer horizons. We identify self-intersecting MOTS which occur in pairs. For $b$ close to the critical value, there are no self-intersecting MOTS/MOTOS, and one can fine-tune $b$ so that the interior contains only near-spherical MOTS. We also show that in a neighborhood of the inner horizon for certain values of $b$, upon reduction of the problem to a singular Sturm-Liouville problem, the locations of the MOTS are given by hypergeometric functions, the eigenspace of the operator for which is complete, not discrete, and discontinuous.

gr-qc↗

arXiv2026

Weyl-type solutions with multipolar scalar fields

A class of solutions in $d$-dimensional Einstein gravity minimally coupled to a massless scalar field is studied, where the spacetime metric is of a generalized Weyl form with $d-2$ commuting Killing vectors. In addition to the procedure to generate scalar multipolar fields, a $SO(2)$ symmetry can be exploited to generate further solutions. A particular result of this procedure is a solution that contains the scalar counterpart of the Schwarzschild--Melvin and the Fisher--Janis--Newman--Winicour solutions as particular limits. Furthermore, a Harrison-type transformation can also be performed to generate solutions with magnetic fields. Using this transformation we obtain a solution with magnetic and scalar fields present and contains both magnetic and scalar counterparts of Schwarzschild--Melvin as limits.

gr-qc↗

arXiv2025

Properties of the magnetic universe with positive cosmological constant

The properties of the Melvin-type spacetime with a positive cosmological constant $Λ$ in $d$-dimensional Einstein--Maxwell gravity is studied. The solution is parametrised in terms of the `de Sitter radius' $\ell\proptoΛ^{-1/2}$ and the magnetic field parameter $β$, and they are warped products of the form $\mathbb{R}^{1,d-3}\times S^2$, where $\mathbb{R}^{1,d-3}$ is the $(d-2)$-dimensional Minkowski spacetime and $S^2$ is topologically a two-sphere which contains a conical singularity, whose nature depends on the product $β\ell$. In the limit $\ell\rightarrow\infty$, the $S^2$ decompactifies and the $d$-dimensional Melvin universe is recovered. The Freund--Rubin-type flux compactification model is shown to be another particular limit of this solution. We also calculate the flux and geodesics in this spacetime.

gr-qc↗

arXiv2025

Periodic orbits of neutral test particles in Reissner-Nordström naked singularities

We conduct studies on Levin's taxonomy of periodic orbits for neutral test particles around a Reissner-Nordström naked singularity. It was known that naked singularities could harbor two distinct regions of time-like bound orbits and thus we expect periodic orbits to appear in both regions. It is possible for a pair of periodic orbits from both regions to possess the exact same angular momentum $L$ and energy $E$ values. We chart the sets of periodic orbits in $(L,E)$-parameter space and highlight the general distribution pattern of these sets for three possible scenarios. Regions within $(L,E)$-space can be partitioned into multiple domains $\mathcal{D}_k$ based on the roots configuration of the quartic polynomial $P(u)$ where $u$ is the inverse radial coordinate. Consequently, each domain and interestingly enough, portions of certain periodic orbits sets that lie in different $\mathcal{D}_k$ require different analytical solutions to plot the resulting orbit. Furthermore, we uncover physical properties of some hypothetical circular orbits residing in the inner region from analysing the $(L,E)$-space.

gr-qc↗

arXiv2024

Links represented by phases of algebraic curves

The prime motivation behind this paper is to prove that any torus link can be realized as the union of the one-dimensional connected components of the set of critical values of the argument map restricted to a complex algebraic plane curve. Moreover, we give an explicit relation between the Newton polygon of such plane curves, and the number of components of the given torus link. This work aims to represent the starting point for a connection between knot theory, tropical geometry, and (co)amoebas.

math.AG↗

arXiv2024

Black hole thermodynamic free energy as $A$-discriminants

We show that the free energy $\mathcal{F}$ and temperature $T$ of black holes, considered as a thermodynamic system, can be viewed as an $A$-discriminant of an appropriately-defined polynomial. As such, mathematical results about $A$-discriminants may lead to implications about black hole thermodynamics. In particular, for static spacetimes with spherical, planar, or hyperbolic symmetry, the number of distinct thermodynamic phases depend on the number of distinct terms in the metric component $g_{tt}$. We prove that if $g_{tt}$ consists of $N_f$ distinct terms, then the $\mathcal{F}$-$T$ curve consists of $N_f-2$ cusps, which in turn leads to $N_f-1$ distinct thermodynamic phases. This result is applied to explicit examples of the Schwarzschild-AdS, Reissner--Nordström, power-law Maxwell, and Euler--Heisenberg black holes.

gr-qc↗

arXiv2024

Probing Modified Gravity with Entanglement of Microspheres

While a wide variety of astrophysical and cosmological phenomena suggest the presence of Dark Matter, all evidence remains via its gravitational effect on the known matter. As such, it is conceivable that this evidence could be explained by a modification to gravitation and/or concepts of inertia. Various formulations of modified gravity exist, each giving rise to several non-canonical outcomes. This motivates us to propose an experiment searching for departures from (quantum) Newtonian predictions in a bipartite setting with gravitational accelerations $\lesssim 10^{-10}$ m/s$^2$, i.e., where the effective force needs to be stronger than Newtonian to account for the Dark Matter effects. Since quantum particles naturally source weak gravitation, their non-relativistic dynamics offers opportunities to test this small acceleration regime. We show that two nearby mesoscopic quantum masses accumulate significantly larger entanglement in modified gravity models, such as the Modified Newtonian Dynamics. Our calculations include Casimir-Polder forces as well as tidal effects next to the surface of the earth, and confirm that entanglement is observable within the limits imposed by environmental decoherence. We demonstrate how the temperature can be fine-tuned such that modified gravity is certified simply by witnessing the entanglement generated from uncorrelated thermal states, eliminating the need for precise noise characterization. Overall, the required parameters could be realized in a tabletop experiment.

gr-qc↗

arXiv2024

Energies and angular momenta of periodic Schwarzschild geodesics

We consider physical parameters of Levin and Perez-Giz's `periodic table of orbits' around the Schwarzschild black hole, where each periodic orbit is classified according to three integers $(z,w,v)$. In particular, we chart its distribution in terms of its angular momenta $L$ and energy $E$. In the $(L,E)$-parameter space, the set of all periodic orbits can be partitioned into domains according to their whirl number $w$, where the limit of infinite $w$ approaches the branch of unstable circular orbits. Within each domain of a given whirl number $w$, the infinite zoom limit $\lim_{z\rightarrow\infty}(z,w,v)$ converges to the common boundary with the adjacent domain of whirl number $w-1$. The distribution of the periodic orbit branches can also be inferred from perturbing stable circular orbits, using the fact that every stable circular orbit is the zero-eccentricity limit of some periodic orbit, or arbitrarily close to one.

gr-qc↗

arXiv2024

Observing Algebraic Variety of Lee-Yang Zeros in Asymmetrical Systems via a Quantum Probe

Lee-Yang (LY) zeros, points on the complex plane of physical parameters where the partition function goes to zero, have found diverse applications across multiple disciplines like statistical physics, protein folding, percolation, complex networks etc. However, experimental extraction of the complete set of LY zeros for general asymmetrical classical systems remains a crucial challenge to put those applications into practice. Here, we propose a qubit-based method to simulate an asymmetrical classical Ising system, enabling the exploration of LY zeros at arbitrary values of physical parameters like temperature, internal couplings etc. Without assuming system symmetry, the full set of LY zeros forms an algebraic variety in a higher-dimensional complex plane. To determine this variety, we pro ject it into sets representing magnitudes (amoeba ) and phases (coamoeba ) of LY zeros. Our approach uses a probe qubit to initialize the system and to extract LY zeros without assuming any control over the system qubits. This is particularly important as controlling system qubits can get intractable with the increasing complexity of the system. Initializing the system at an amoeba point, coamoeba points are sampled by measuring probe qubit dynamics. Iterative sampling yields the entire algebraic variety. Experimental demonstration of the protocol is achieved through a three-qubit NMR register. This work expands the horizon of quantum simulation to domains where identifying LY zeros in general classical systems is pivotal. Moreover, by extracting abstract mathematical objects like amoeba and coamoeba for a given polynomial, our study integrates pure mathematical concepts into the realm of quantum simulations.

cond-mat.stat-mech↗

arXiv2023

Model for an electrostatic capacitor in Einstein-Maxwell theory

A general relativistic model of a parallel-plate electrostatic capacitor is presented. The spacetime is a solution to the Einstein--Maxwell equations and involves class of solution previously studied by Veselý and Žofka (VŽ). In particular, the parts containing curvature singularities are cut out and the remaining regular section is glued to asymptotically-Minkowski spacetimes. In essence, this results in a curved electro-vacuum VŽ spacetime sandwiched on both sides by exterior spacetimes with vanishing electromagnetic fields. Junction conditions require the presence of charged matter on the boundaries. We interpret this configuration as a parallel-plate capacitor with gravitational effects induced by the strong electric fields. The spherical capacitor is briefly considered.

gr-qc↗

arXiv2022

Motion of charged particles in spacetimes with magnetic fields of spherical and hyperbolic symmetry

The motion of charged particles in spacetimes containing a submanifold of constant positive or negative curvature is considered, with the electromagnetic tensor proportional to the volume two-form form of the submanifold. In the positive curvature case, this describes spherically symmetric spacetimes with a magnetic monopole, while in the negative curvature case, it is a hyperbolic spacetime with magnetic field uniform along hyperbolic surfaces. Constants of motion are found by considering Poisson brackets defined on a phase space with gauge-covariant momenta. In the spherically-symmetric case, we find a correspondence between the trajectories on the Poincaré cone with equatorial geodesics in a conical defect spacetime. In the hyperbolic case, the analogue of the Poincaré cone is defined as a surface in an auxiliary Minkowski spacetime. Explicit examples are solved for the Minkowski, $\mathrm{AdS}_4\times S^2$, and the hyperbolic AdS-Reissner--Nordström spacetimes.

gr-qc↗

arXiv2022

Structure of test magnetic fields and charged particle motion around the Hayward spacetime

A configuration of a test magnetic field in Hayward spacetime is obtained by solving Maxwell's equation with the Hayward metric as the background. The magnetic field lines show a dipole loop-like configuration in the regular Hayward interior, and tends to an asymptotically uniform structure away from the cylindrical axis. The motion of charged particles is then studied in this spacetime. The parameters and stability of circular orbits on the equatorial plane are studied. Aspects of non-equatorial motion are also studied.

gr-qc↗

arXiv2021

Properties of the magnetised Kaluza-Klein bubble

In this paper we study a Kaluza-Klein bubble-type spacetime with a magnetic field first obtained by Sarbach and Lehner in 2005. It is shown that this solution can be derived via a Harrison transformation of a vacuum Kaluza-Klein bubble, and its physical and geometrical quantities are determined. For certain ranges of the magnetic field parameter, this solution carries negative mass. Furthermore, for a given value of magnetic flux, there exist two branches of solutions, and the branch with lower mass is thermodynamically favoured. In light of these properties we interpret the spacetime as another analogue to the Anti-de Sitter-Melvin solution.

gr-qc↗

arXiv2021

Retrolensing by a spherically symmetric naked singularity

Considering a strong field limit, we investigate the retrolensing phenomenon in the vicinity of a Janis-Newman-Winicour (JNW) naked singularity embedded in a scalar field. We assume that the light rays from a nearby source are reflected by the photon sphere of the naked singularity, acting as a lens, to create a pair of images. The analytic expressions of the lensing coefficients $\bar{a}$ and $\bar{b}$ are obtained, which are scalar dependent and discordant with \cite{Bozza:2002b}. Moreover, considering the powerful supermassive black hole candidates Sgr A* and M87*, we examined the influence of the scalar field on the apparent brightness and angular positions of the parity images. Our results are highlighted in correspondence with a non-scalar field gravity, specifically the Schwarzschild gravity. We have found that the brightness increases in the presence of the scalar field, while, the lensing coefficients $\bar{a}$, $\bar{b}$, the angular positions and the angular separation of the relativistic images experience a reverse effect.

gr-qc↗

arXiv2021

Solenoid configurations and gravitational free energy of the AdS--Melvin spacetime

In this paper we explore a solenoid configuration involving a magnetic universe solution embedded in an empty Anti-de Sitter (AdS) spacetime. This requires a non-trivial surface current at the interface between the two spacetimes which can be provided by a charged scalar field. When the interface is taken to the AdS boundary, we recover the full AdS--Melvin spacetime. The stability of the AdS--Melvin solution is also studied by computing the gravitational free energy from the Euclidean action.

gr-qc↗