Related papers: Junction Conditions for Signature Change
In this article we obtain a new anisotropic solution for Einstein's field equation of embedding class one metric. The solution is representing the realistic objects such as $Her~X-1$ and $RXJ~1856-37$. We perform detailed investigation of…
Measure contraction properties are generalizations of the notion of Ricci curvature lower bounds in Riemannian geometry to more general metric measure spaces. In this paper, we give sufficient conditions for a Sasakian manifold equipped…
In Eddington gravity, the action principle involves only the symmetric parts of the connection and the Ricci tensor, with a metric that emerges proportionally to the latter. Here, we relax this symmetric character, prolong the action with…
A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in…
Spherically symmetric spacetimes are ambient spaces for models of stellar collapse and inhomogeneous cosmology. We obtain results for the Weyl tensor and the covariant form of the Ricci tensor on general doubly warped (DW) spacetimes. In a…
Junction conditions play a crucial role in constructing new gravity solutions. In this paper, we derive the junction condition for gluing together an arbitrary number of spacetimes along a common interface. We develop a geometric technique…
The Jacobi-Maupertuis metric allows one to reformulate Newton's equations as geodesic equations for a Riemannian metric which degenerates at the Hill boundary. We prove that a JM geodesic which comes sufficiently close to a regular point of…
This paper aims to classify the holonomy of the conformal Tractor connection, and relate these holonomies to the geometry of the underlying manifold. The conformally Einstein case is dealt with through the construction of metric cones,…
We discuss cosmological perturbation theory at third order, deriving the gauge transformation rules for metric and matter perturbations, and constructing third order gauge invariant quantities. We present the Einstein tensor components, the…
When pressure is not negligible in comparison with energy density, the external gravitational field and the motion of particles in it are modified. For spherically symmetric body two effective mass parameters determine the external…
We consider a little known aspect of signature change, where the overall sign of the metric is allowed to change, with physical implications. We show how, in different formulations of general relativity, this type of classical signature…
In Einstein theory of gravity the initial configuration of metric field and its time derivative are related to matter configuration by four equations called constraints. We use the method of conformal metrics (York Method) to solve…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
We introduce a generalization of relative entropy derived from the Wigner-Yanase-Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint convexity of relative entropy, and for the map…
In this brief note, we consider the variation of the entanglement entropy of a region as the shape of the entangling surface is changed. We show that the variation satisfies a Wess-Zumino like integrability condition in field theories which…
Einstein equations are addressed with the energy-momentum tensor that appears if the equations under discussion are required to possess conformal invariance. It is proved that thus derived equations (equations of conformally invariant…
We derive the Klein--Gordon equation for a single scalar field coupled to gravity at second order in perturbation theory and leading order in slow-roll. This is done in two ways: we derive the Klein--Gordon equation first using the Einstein…
I discuss geometry and normal forms for pseudo-Riemannian metrics with parallel spinor fields in some interesting dimensions. I also discuss the interaction of these conditions for parallel spinor fields with the condition that the Ricci…
Two distinct non-singular interior models that describe anisotropic spherical configurations are presented in this work. We develop the Einstein field equations and the associated mass function in accordance with a static spherical…
This paper proposes a toy model where, in the Einstein equations, the right-hand side is modified by the addition of a term proportional to the symmetrized partial contraction of the Ricci tensor with the energy-momentum tensor, while the…