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Statements about relativistic effects are often subtle. In this essay we will demonstrate that the three classical tests of general relativity, namely perihelion precession, deflection of light and gravitational redshift, are passed…
We provide irreducible expressions for the metric variations of the gravitational action terms constructed from the 17 curvature invariants of order six in derivatives of the metric tensor i.e. from the geometrical terms appearing in the…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
We explore alternative formulations of the analogy between viable Horndeski gravity and Eckart's first-order thermodynamics. We single out a class of identifications for the effective stress-energy tensor of the scalar field fluid that,…
We construct new classes of modified theories in which the matter sector couples with the Einstein tensor, namely we consider direct couplings of the latter to the energy-momentum tensor, and to the derivatives of its trace. We extract the…
How does one measure the gravitational field? We give explicit answers to this fundamental question and show how all components of the curvature tensor, which represents the gravitational field in Einstein's theory of General Relativity,…
We take a Dirac field non-minimally coupled to the gravitational field within the framework of the Poincar\'e gauge theory of gravity with torsion and curvature. We study the subcase of "weak" gravity, that is, the gravitational Lagrangian…
We generalize the $f(R)$ type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the matter Lagrangian $L_m$. We obtain the gravitational field equations in the…
The mantra about gravitation as curvature is a misnomer. The curvature tensor for a standard of rest does not describe acceleration in a gravitational field but the \underline{gradient} of the acceleration (e.g. geodesic deviation). The…
We study the non-relativistic Newton-Cartan limit of higher-order gravity theories in arbitrary dimensions. We first study it at the level of the action by introducing an additional 1-form gauge field and coupling it appropriately to the…
In the context of a gauge theory for the translation group, we have obtained, for a spinless particle, a gravitational analog of the Lorentz force. Then, we have shown that this force equation can be rewritten in terms of magnitudes related…
In this work, we systematically derive the Einstein field equations in general relativity and $f(\mathcal{R})$ gravity, the Tolman-Oppenheimer-Volkoff (TOV) equation, and the expressions for axial and polar Tidal Love Numbers (TLNs) for…
The Sommerfeld boundary conditions, applied to an asymptotically weak gravitational field, are shown to imply that the 1/r part of the curvature tensor of a space-time, satisfying the Einstein equations, is of type null in the Petrov…
It has been known for some time that there is a deep connection between thermodynamics and gravity, with perhaps the most dramatic implication that the Einstein equations can be viewed as a thermodynamic equation of state. Recently Verlinde…
In the context of mathematical cosmology, the study of necessary and sufficient conditions for a semi-Riemannian manifold to be a (generalised) Robertson-Walker space-time is important. In particular, it is a requirement for the development…
We present a gauge formulation of the special affine algebra extended to include an antisymmetric tensorial generator belonging to the tensor representation of the special linear group. We then obtain a Maxwell modified metric affine…
We present a new approach to quantum gravity starting from Feynman's formulation for the simplest example, that of a scalar field as the representative matter. We show that we extend his treatment to a calculable framework using resummation…
In the work (arXiv:1109.3846 [gr-qc]), to obtain a simple and economic formulation of field equations for generalised theories of gravity described by the Lagrangian $\sqrt{-g}L\big(g^{\alpha\beta},R_{\mu\nu\rho\sigma}\big)$, the key…
We present a novel derivation of the spacetime metric generated by matter, without invoking Einstein's field equations. For static sources, the metric arises from a relativistic formulation of D'Alembert's principle, where the inertial…
We show that "Gravity at cosmological distances: Explaining the accelerating expansion without dark energy" recently proposed by J. Harada [6] is equivalent to the Einstein equation extended by the presence of an arbitrary conformal Killing…