Hi! My name is Yen-Kheng Lim (he/him). My hometown is Ipoh, Malaysia. I obtained my PhD in physics from the National University of Singapore (NUS) in 2015. I have also worked as an Teaching Assistant and subsequently an Instructor at NUS from 2010-2018. I am currently an Assistant Professor at Xiamen University Malaysia. I also occasionally write fiction, particularly short stories across various genres.

I mostly work in black holes and general relativity. Particularly, I seek exact solutions in various gravity theories like Einstein, Einstein-Maxwell theory, and others. I also tend to work on the mechanics and dynamics of relativistic test particle motion in gravity, as well as test charges in electromagnetic field in curved spacetimes (i.e., solutions of Einstein-Maxwell gravity). Recently I have also been exploring mathematical concepts like algebraic geometry and tropical geometry, and applying these ideas in solving problems in statistical mechanics, quantum mechanics, and gravity.

My list of publications in Google Scholar or Inspire HEP

Archive of curvature components | Notes
Over the years I have calculated the Riemann and Ricci tensors of various spacetimes. I've collected most of it here. 

Gravitational thermodynamics | Notes
Brief notes on black hole/gravitational thermodynamics. Of course these can never replace the original texts and papers. These are a quick review and fills in some calculational steps which are often skipped by research papers because experts already know them.

Harrison transformations | Notes | Curvature tensor calculations (handwritten) | Field equations (handwritten)
Brief notes on the simplified version of the Harrison transformation. This is a procedure taking a known solution to the Einstein-Maxwell equation to generate new solutions. The notes contain an explicit derivation of the Melvin and Ernst spacetimes.

Geodesics and notes on lensing by Schwarzschild black holes | Geodesics notes | Schwarzschild Lensing Notes
Notes on geodesic motion. Includes the derivation of the geodesic equation from parallel transport, and a rederivation from an action principle. The second is a brief note on computations of Schwarzschild null geodesics and the Virbhadra-Ellis strong lensing. The bending angle is given exactly in terms of elliptic functions.

Fulling-Davies-Unruh Effect | Notes
Brief, highly condensed notes summarising the derivation of the Unruh effect.

Basic concepts of differential geometry, forms, and Lie groups | Notes
Brief notes on differential geometry, p-forms, and some results on Lie derivatives, Lie groups, and Lie algebra.

PHY101 Mechanics | Lecture notes
This course teaches the fundamentals of mechanics. Topics include kinematics, Newton’s laws of motion, conservation of energy and momentum, rigid body rotation, gravitation, waves, oscillations and an introduction to special relativity.

PHY103 Electromagnetism | Lecture notes
This course teaches the fundamentals of electricity, magnetism and electrodynamics. Topics include Coulomb’s law and Gauss law, electric potential, capacitance and dielectrics, direct current circuits, magnetic fields and magnetic force, ampere’s law, electromagnetic induction, alternating current and electromagnetic waves.

PHY107 Ordinary Differential Equations | Lecture notes
This course introduces students to basics techniques in solving ordinary differential equations. Topics covered include: direction fields, first order linear equations, separable equations, exact equations, integrating factors, existence and uniqueness theorem, second order linear equations, homogeneous equations, inhomogeneous equations, method of underdetermined coefficients, variations of parameters, higher order linear equations, series solutions, Laplace transforms, Laplace transform methods in solving ordinary differential equations, systems of first order linear equations.

PHY108 Calculus I | Lecture notes
This course introduces students to calculus. Topics covered include: functions, limits, continuity, derivatives, partial derivatives, mean value theorem for derivative, indefinite integral, definite integral, fundamental theorem of calculus, applications of derivatives, maximum and minimum, rate of change, mean value theorem for integrals, pplications of integrals, techniques of integration, improper integrals, sequences, series, and power series.

PHY109 Calculus II | Lecture notes
This course introduces students to advanced methods in calculus. In Part I, we cover parametric equations, geometry of space, and vector functions. In Part II we study multivariable functions, partial derivatives and multiple integrations, line and surface integrals. Important theorems related to multivariable integrations are then covered, such as Green's Theorem, Stokes' Theorem and the divergence theorem.

PHY201 Theoretical Mechanics | Lecture notes
This course teaches intermediate to advanced methods of classical mechanics. Topics include a brief review of Newtonian mechanics, N-body problems, non-inertial frames, rotating rigid bodies, and variational principles of mechanics.

PHY202 Quantum Mechanics I | Lecture notes
This course teaches quantum mechanics at the 2nd year undergraduate level. Topics include Hilbert space and the bra-ket notation, two-state systems, the harmonic oscillator, angular momentum and hydrogen-like atoms, and introduction to entanglement and quantum teleportation.

PHY203 Mathematical Methods in Physics I | Lecture notes
This course covers mathematical techniques relevant to physics. The first part consists of elementary complex analysis, including complex functions and derivatives, Taylor and Laurent series, and contour integrations. The second part of the course involves methods solving partial differential equations. The topics are boundary conditions, the wave, heat, and Laplace equations, separation of variables, and special functions.

PHY311 Mathematical Methods in Physics II | Lecture notes
This course covers advanced mathematical methods in physics, primarily aimed at applications in theoretical physics. Concepts of group theory and vector spaces are introduced. Followed by an introduction to manifolds and differential forms. In the final chapter, basic ideas of Lie groups and Lie algebra are briefly discussed.

PHY405 Relativity | Lecture notes
This course is an introduction to General Relativity. We start with a review of Special Relativity along with an introduction of tensor calculus and tensor notation. Subsequently the relevant notions of differential geometry such as geodesics, Riemann and Ricci curvatures are covered. This is followed by a relativistic formulation of the stress-energy tensor. The notion of stress-energy causing curvature is given by the Einstein equations. Consequences and solutions of the Einstein equations are then discussed, particularly the Schwarzschild solution and FLRW cosmology.