New Coordinate Vacuum Solution in Cosmological General Theory of Relativity

In the general relativity theory, we discover new vacuum solution by Einstein’s gravity field equation. We investigate the new coordinate in cosmological general theory of relativity (CGTR).

Darmois matching and C3 matching

We apply the Darmois and the $C^3$ matching conditions to three different spherically symmetric spacetimes. The exterior spacetime is described by the Schwarzschild vacuum solution whereas for the interior counterpart we choose different perfect fluid solutions with the same symmetry. We show that Darmois matching conditions are satisfied in all the three cases whereas the $C^3$ conditions are not fulfilled. We argue that this difference is due to a non-physical behavior of the pressure on the matching surface.

Phase Transitions in the Co–Al–Nb–Mo System

Phase transitions in the Co-rich part of the Co–Al–Nb–Mo phase diagram are studied by energy dispersive spectroscopy (EDS), X-ray analysis, transmission electron microscopy (TEM), and differential scanning calorimetry (DSC) measurements. The obtained results were compared with the results for alloys of the binary Co–Al and ternary Co–Al–Nb, and Co–Al–Mo systems. Formation of the intermetallic phase with the L12 structure was found in a range of alloys with 10 at.% Al, 2–9 at.% Nb, and 3–7 at.% Mo. Intermetallic compound Co2Nb, Laves phase with the different chemical composition and crystal structure (C14 and C36) was detected in the Co–Al–Nb and Co–Al–Nb–Mo samples after vacuum solution treating at 1250 °C for 30 h.

Schwarzschild–Droste solution

The spherically symmetric vacuum solution to the Einstein field equation (Schwarzschild-Droste solution) is derived and associated physical phenomena derived and explained. It is shown how to obtain the Christoffel symbols by the Euler-Lagrange method, and hence the metric for the general spherically symmetric vacuum. Equations for general orbits are presented, and their solution for radial motion and for circular motion. Geodetic (de Sitter) precession is calculated exactly for circular orbits. The null geodesics (photon worldlines) are obtained, and the gravitational redshift. Emission from an accretion disc is calculated.

Holographic JT gravity with quartic couplings

We construct the most general theory of 2D Einstein-dilaton gravity coupled with U(1) gauge fields that contains all the 2-derivative and the 4-derivative interactions allowed by the diffeomorphism invariance. We renormalise the 2D action and obtain the vacuum solution as well as the black hole solution. The vacuum solution in the UV is dominated by Lifshitz2 with dynamical exponent (z = $$ \frac{7}{3} $$ 7 3 ) while on the other hand, the spacetime curvature diverges as we move towards the deep IR limit. We calculate the holographic stress tensor and the central charge for the boundary theory. Our analysis shows that the central charge goes as the inverse power of the coupling associated to 4-derivative interactions. We also compute the Wald entropy for 2D black holes and interpret its near horizon divergence in terms of the density of states. We compare the Wald entropy with the Cardy formula and obtain the eigen value of Virasoro operator (L0) for our model. Finally, we explore the near horizon structure of 2D black holes and calculate the central charge corresponding to the CFT near horizon. We further show that the near horizon CFT may be recast as a 2D Liouville theory with higher derivative corrections. We study the Weyl invariance of this generalised Liouville theory and identify the Weyl anomaly associated to it. We also comment on the classical vacuum structure of the theory.

Universal renormalization procedure for higher curvature gravities in D ≤ 5

We implement a universal method for renormalizing AdS gravity actions applicable to arbitrary higher curvature theories in up to five dimensions. The renormalization procedure considers the extrinsic counterterm for Einstein-AdS gravity given by the Kounterterms scheme, but with a theory-dependent coupling constant that is fixed by the requirement of renormalization for the vacuum solution. This method is shown to work for a generic higher curvature gravity with arbitrary couplings except for a zero measure subset, which includes well-known examples where the asymptotic behavior is modified and the AdS vacua are degenerate, such as Chern-Simons gravity in 5D, Conformal Gravity in 4D and New Massive Gravity in 3D. In order to show the universality of the scheme, we perform a decomposition of the equations of motion into their normal and tangential components with respect to the Poincare coordinate and study the Fefferman-Graham expansion of the metric. We verify the cancellation of divergences of the on-shell action and the well-posedness of the variational principle.

Zipoy-Voorhees Gravitational Object as a Source of High-Energy Relativistic Particles

The Zipoy-Voorhees solution is known as the γ-metric and/or q-metric being static and axisymmetric vacuum solution of Einstein field equations which becomes strong curvature naked singularity. The metric is characterized by two parameters, namely, the mass M and the dimensionless deformation parameter γ. It is shown that the velocity of test particle orbiting around the central γ-object can reach the speed of light, consequently, the total energy of the particle will be very high for a specific value the deformation parameter of the spacetime. It is also shown that causality problem arises in the interior region of the physical singularity for the specific value of the deformation parameter when test particles can move with superluminal velocity being greater than the speed of light that might be an additional tool for explaining the existence of tachyons for γ>1/2 which are invisible for an observer.

Observational constraints in metric-affine gravity

We derive the main classical gravitational tests for a recently found vacuum solution with spin and dilation charges in the framework of Metric-Affine gauge theory of gravity. Using the results of the perihelion precession of the star S2 by the GRAVITY collaboration and the gravitational redshift of Sirius B white dwarf we constrain the corrections provided by the torsion and nonmetricity fields for these effects.

Geometric properties of the Bertotti–Kasner space-time

PurposeThe purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.Design/methodology/approachThis paper is based on the features of λ-tensor and the technique of six-dimensional formalism introduced by Pirani and followed by W. Borgiel, Z. Ahsan et al. and H.M. Manjunatha et al. This technique helps to describe both the geometric properties and the nature of the gravitational field of the space-times in the Segre characteristic.FindingsThe Gaussian curvature quantities specify the curvature of Bertotti–Kasner space-time. They are expressed in terms of invariants of the curvature tensor. The Petrov canonical form and the Weyl invariants have also been obtained.Originality/valueThe findings are revealed to be both physically and geometrically interesting for the description of the gravitational field of the cylindrical universe of Bertotti–Kasner type as far as the literature is concerned. Given the technique of six-dimensional formalism, the authors have defined the Weyl conformal λW-tensor and discussed the canonical form of the Weyl tensor and the Petrov scalars. To the best of the literature survey, this idea is found to be modern. The results deliver new insight into the geometry of the nonstatic cylindrical vacuum solution of Einstein's field equations.

Strange star with Krori–Barua potential in the presence of anisotropy

In this paper, a well-behaved new model of anisotropic compact star in (3+1)-dimensional spacetime has been investigated in the background of Einstein’s general theory of relativity. The model has been developed by choosing [Formula: see text] component as Krori–Barua (KB) ansatz [Krori and Barua in J. Phys. A, Math. Gen. 8 (1975) 508]. The field equations have been solved by a proper choice of the anisotropy factor which is physically reasonable and well behaved inside the stellar interior. Interior spacetime has been matched smoothly to the exterior Schwarzschild vacuum solution and it has also been depicted graphically. Model is free from all types of singularities and is in static equilibrium under different forces acting on the system. The stability of the model has been tested with the help of various conditions available in literature. The solution is compatible with observed masses and radii of a few compact stars like Vela X-1, 4U [Formula: see text], PSR J[Formula: see text], LMC X [Formula: see text], EXO [Formula: see text].