Using the energy momentum complex given by Møller in 1978 based on the absolute parallelism, the energy distribution in Kerr spacetime is evaluated. The energy with this spacetime is found to be the same as it was earlier evaluated using different definitions mainly based on the metric tensor.

We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two ‘ingredient theories’ (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction (Section 1), we briefly review the conceptual problems of the ingredie...

The quantum fluctuations of the stress tensor of a quantum field are discussed , as are the resulting spacetime metric fluctuations. Passive quantum gravity is an approximation in which gravity is not directly quantized, but fluctuations of the spacetime geometry are driven by stress tensor fluctuations. We discuss a decomposition of the stress tensor correlation function into three parts, and ...

In the second set of supplementary notes — Gravity, Metrics and Coordinates — we introduced the idea that matter induces spacetime curvature, and we argued that this curvature is fully described by the metric. In the case of a static, spherically symmetric mass distribution, we presented the Einstein Field Equations whose solution gives the metric and therefore the geometry of spacetime. The cu...

In this paper we find the first and second order perturbations of the induced metric and the extrinsic curvature of a non-degenerate hypersurface Σ in a spacetime (M, g), when the metric g is perturbed arbitrarily to second order and the hypersurface itself is allowed to change perturbatively (i.e. to move within spacetime) also to second order. The results are fully general and hold in arbitra...

Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such classical matter fields, quantum mechanics should be formulated without reference to a classical time. If such a new formulation exists, it follows as a conseq...

We study a Hamiltonian realization of the phase space of κ-Poincaré algebra that yields a definition of velocity consistent with the deformed Lorentz symmetry. We are also able to determine the laws of transformation of spacetime coordinates and to define an invariant spacetime metric, and discuss some possible experimental consequences.

Lattices of topological defects, such as Abrikosov lattices and domain wall lattices, often arise as metastable ground states in higher-dimensional field theoretical models. We demonstrate that such lattice states may be described as extra-dimensional “metamaterials” via higher-dimensional effective medium theory. A 4 + 1 dimensional extension of Maxwell electrodynamics with a compactified time...

Causality violating paths are known to exist in many spacetimes satisfying the Einstein field equations, especially those solutions associated with rotating matter or rotating singularities [1–3] (see also Bonnor [4], and references in [5]). However, examples of causality violating geodesics are sparse in the scientific literature. Chandrasekhar and Wright [6] showed that the Gödel spacetime [1...

We characterize a general solution to the vacuum Einstein equations which admits isolated horizons. We show it is a non-linear superposition – in precise sense – of the Schwarzschild metric with a certain free data set propagating tangentially to the horizon. This proves Ashtekar’s conjecture about the structure of spacetime near the isolated horizon. The same superposition method applied to th...