Related papers: Why is the metric invertible?
It is well-known that the trace-free Einstein tensor of a pseudo-Riemannian metric cannot arise by variation of a local diffeomorphism-invariant action functional with the (inverse) metric as field variable. We show that this statement…
In this short note is on the equivalence between non-Newtonian metric (particularly multiplicative metric) and metric. We present a different proof the fact that the notion of a non-Newtonian metric space is not more general than that of a…
In a recently proposed theory, the cosmological constant (CC) does not curve spacetime in our universe, but instead gets absorbed into another universe endowed with its own dynamical metric, nonlocally coupled to ours. Thus, one achieves a…
A possible way out of the conundrum of quantum gravity is the proposal that general relativity (GR) is not a fundamental theory but emerges from an underlying microscopic description. Despite recent interest in the emergent gravity program…
A unified description of all interactions could be based on a higher-dimensional theory involving only spinor fields. The metric arises as a composite object and the gravitational field equations contain torsion-corrections as compared to…
The Einstein field equations have no known and acceptable interior solution that can be matched to an exterior Kerr field. In particular, there are no interior solutions that could represent objects like the Earth or other rigidly rotating…
Emergent modified gravity presents a new set of generally covariant gravitational theories in which the space-time metric is not directly given by one of the fundamental fields. A metric compatible with the modified dynamics of gravity is…
Attention is drawn to the fact that the well-known expression for the red-shift of spectral lines due to a gravitational field may be derived with no recourse to the theory of general relativity. This raises grave doubts over the inclusion…
Let M be a complete metric space. It is proved that if the space or scalar-valued bounded continuous functions on M admits an isometric shift, then M is separable.
We extend the results of antecedent literature on quadratic Metric-Affine Gravity by studying a new quadratic gravity action in vacuum which, besides the usual (non-Riemannian) Einstein-Hilbert contribution, involves all the parity even…
We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible…
We construct a general relativity formula for the law of gravity for material bodies. The formula contains three numeric parameters that are to be determined experimentally. If they are chosen from symmetry considerations, then the theory…
The field inside a Casimir cavity has an effective negative mass, which acts as a buoyancy force in a gravitational field. Can this render the total mass of the cavity negative, making it "float" in the vacuum ? Recent theoretical arguments…
An earlier paper [1] presented a gravity theory based on the optics of de Broglie waves rather than curved space-time. While the universe's geometry is flat, it agrees with the standard tests of general relativity. A second paper [2] showed…
The rotational metric provides an exact solution to Einstein's clock-rate problem in curved spacetime, specifically, whether time flows more slowly at the equator of a compact object such as a neutron star than at its poles. It features a…
The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the…
In the general framework of Metric-Affine theories of gravity, where the metric and the connection are independent variables, we consider actions quadratic in the Ricci scalar curvature and the Holst invariant (the contraction of the…
The huge amounts of undetected and exotic dark matter and dark energy needed to make general relativity work on large scales argue that we should investigate modifications of gravity. The only stable, metric-based and invariant alternative…
Quantum vacuum and matter immersed in it interact through electromagnetic, strong and weak interactions. However, we have zero knowledge of the gravitational properties of the quantum vacuum. As an illustration of possible fundamental…
The closed system of Hamilton equations is derived for all tensor components of the free gravitational field $g_{\alpha\beta}$ and corresponding momenta $\pi^{\gamma\delta}$ in the metric General Relativity. The Hamilton-Jacobi equation for…