Related papers: Geodesics in the conformally flat Eisenhart metric
We consider a (d+2)-dimensional class of Lorentzian geometries holographically dual to a relativistic fluid flow in (d+1) dimensions. The fluid is defined on a (d+1)-dimensional time-like surface which is embedded in the (d+2)-dimensional…
This paper presents an in-depth exploration of timelike free geodesics in spatially curved Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime. A unified approach for these geodesics encompassing both radial and non-radial trajectories…
We establish a one-to-one correspondence between static spacetimes and Riemannian manifolds that maps causal geodesics to geodesics, as suggested by L. C. Epstein. We then explore constant curvature spacetimes - such as the de Sitter and…
An imperfect cosmic fluid with energy flux is analyzed. Even though its energy density $\rho$ is positive, the pressure $p = -\rho$ due to the fact that the metric is asymptotically de Sitter. The kinematical quantities for a nongeodesic…
We show that the standard Heisenberg algebra of quantum mechanics admits a noncommutative differential calculus $\Omega^1$ depending on the Hamiltonian $p^2/2m + V(x)$, and a flat quantum connection $\nabla$ with torsion such that a…
Bearing the thermodynamic arguments together with the two definitions of mass in mind, we try to find metrics with spherical symmetry. We consider the adiabatic condition along with the Gong-Wang mass, and evaluate the $g_{rr}$ element…
This paper studies various properties of the Pomeransky-Sen'kov doubly-spinning black ring spacetime. I discuss the structure of the ergoregion, and then go on to demonstrate the separability of the Hamilton-Jacobi equation for null, zero…
We investigate anisotropic and homogeneous cosmological models in the scalar-tensor theory of gravity with non-minimal kinetic coupling of a scalar field to the curvature given by the function $\eta\cdot(\phi/2)\cdot G_{\mu\nu}\,\nabla^\mu…
The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwell equations in flat space-time(Mandel'stam L.I., Tamm I.E.) taken in an effective media the properties of which are determined by metrical…
An expansion is developed for the Weil-Petersson Riemann curvature tensor in the thin region of the Teichm\"{u}ller and moduli spaces. The tensor is evaluated on the gradients of geodesic-lengths for disjoint geodesics. A precise lower…
We construct novel solutions to the effective Einstein equation with four dimensional cosmological constant on a 3-brane in Randall-Sundrum II scenario. The charged solution is obtained by assuming the existence of localized Maxwell fields…
The kinematics on spatially flat FLRW space-times is presented for the first time in co-moving local charts with physical coordinates, i. e. the cosmic time and Painlev\' e-type Cartesian space coordinates. It is shown that there exists a…
We investigate gravitational waves in the $f(Q)$ gravity, i.e., a geometric theory of gravity described by a non-metric compatible connection, free from torsion and curvature, known as symmetric-teleparallel gravity. We show that $f(Q)$…
We study the properties of the null geodesics of four-dimensional Einstein-Gauss-Bonnet black holes surrounded by quintessence matter. Due to the quintessence correction, we discuss the radial and non-radial geodesics. For the case of…
We study the kinematics of timelike geodesic congruences in two and four dimensions in spacetime geometries representing stringy black holes. The Raychaudhuri equations for the kinematical quantities (namely, expansion, shear and rotation)…
The geodesic properties of the extraordinary vacuum string solution in (4+1) dimensions are analyzed by using Hamilton-Jacobi method. The geodesic motions show distinct properties from those of the static one. Especially, any freely falling…
We study the integrability of the conformal geodesic flow (also known as the conformal circle flow) on the $SO(3)$--invariant gravitational instantons. On a hyper--K\"ahler four--manifold the conformal geodesic equations reduce to geodesic…
A new covariant generalization of Einstein's general relativity is developed which allows the existence of a term proportional to $T_{\alpha\beta}T^{\alpha\beta}$ in the action functional of the theory ($T_{\alpha\beta}$ is the…
The field equations of a special class of teleparallel theory of gravitation and electromagnetic fields have been applied to tetrad space having cylindrical symmetry with four unknown functions of radial coordinate $r$ and azimuth angle…
We revisit conformal time $\eta$ in a spatially flat Friedmann--Robertson--Walker universe and use a $1+1$-dimensional setting as a technically transparent pedagogical arena. Our purpose is to clarify the relation among cosmic time $t$,…