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We build a self-consistent relativistic scalar theory of gravitation on a flat Minkowski spacetime from a general field Lagrangian. It is shown that, for parameters that satisfy the equivalence principle, this theory predicts the same outcome as general relativity (GR) for every classical solar-system test. This theory also admits gravitational waves that propagate at the speed of light, and the gravitational radiation energy loss in a binary system is shown to be very similar to the GR prediction. We then analyze the strong gravity regime of the theory for a spherically symmetric configuration and find that there is an effective 'singularity' near the Schwarzschild radius. The main goal of this work is to show that, contrary to what is commonly believed, there are relativistic scalar theories of gravitation defined on a Minkowski spacetime that are not ruled out by the classical solar system tests of GR. [ABSTRACT FROM AUTHOR]

Gauge invariant, Hamiltonian formulation of field dynamics within a compact region Σ with boundary ∂Σ is given for the gravitational field linearized over a Kottler metric. The boundary conditions which make the system autonomous are discussed. The corresponding Hamiltonian functional uniquely describes the energy carried by the (linearized) gravitational field. It is shown that, under specific boundary conditions, the quasi-local Hawking mass reduces to in the weak field approximation. This observation is a quasi-local version of the classical Brill–Deser result (Brill and Deser 1968 Ann.Phys.(N.Y.) 50 3) and enables us to declare Hawking mass as the correct expression (at least up to quadratic terms in the Taylor expansion) for the quasi-local mass, which correctly describes energy carried by the gravitational field. [ABSTRACT FROM AUTHOR]

In the present work, we explore several gravitational aspects such as energy extraction (via the Penrose process and superradiance), particle collisions around a , U(1)2 rotating dyonic black hole (BH) in the gauged supergravity model. The influence of the rotation parameter (a) and the gauge coupling constant (g) on the behavior of the horizon and ergoregion of the BH is investigated. In comparison to the extremal Kerr BH, the gauge coupling constant, under certain constraints, can interestingly enhance the maximum efficiency of energy extraction through the Penrose process by almost twice. Under the same constraints, we can extract approximately 60.75% of the initial mass-energy from the BH which is noticeably higher and far different from that of the Kerr BH. The limit of energy extraction in terms of the local speeds of the fragments is also determined with the help of the Wald inequality. We discover an upper limit on the gauge coupling constant up to which superradiance is likely to occur. Finally, we estimate the center-of-mass energy (ECM) of two particles with the same rest mass moving in the equatorial plane of the BH. Our study also aims to sensitize ECM to the parameters a and g for both extremal and nonextremal spacetime. Especially, for the extremal case, an infinitely large amount of ECM can be achieved closer to the event horizon confirming a basic point of view that an extreme supergravity BH with dyons could serve as ultimate particle accelerators as compared to Kerr and any other generalized BHs in this family and other alternative theories of gravity. However, ECM for the nonextremal spacetime is shown to be finite and has an upper bound. [ABSTRACT FROM AUTHOR]

We construct, for the first time, the time-domain gravitational wave strain waveform from the collapse of a strongly gravitating Abelian Higgs cosmic string loop in full general relativity. We show that the strain exhibits a large memory effect during merger, ending with a burst and the characteristic ringdown as a black hole is formed. Furthermore, we investigate the waveform and energy emitted as a function of string width, loop radius and string tension Gμ. We find that the mass normalized gravitational wave energy displays a strong dependence on the inverse of the string tension EGW/M0 ∝ 1/Gμ, with at the percent level, for the regime where Gμ ≳ 10−3. Conversely, we show that the efficiency is only weakly dependent on the initial string width and initial loop radii. Using these results, we argue that gravitational wave production is dominated by kinematical instead of geometrical considerations. [ABSTRACT FROM AUTHOR]

Influence of gravity on the quantum vacuum of a massless minimally coupled scalar field under Robin boundary conditions on parallel plates is investigated. We introduce the detailed calculation of the volume energy for the case the gravitational background is weak in its most general form for a static spacetime. It founds that the quantum vacuum usually reacts to the gravitational field by decreasing the Casimir energy. In addition, we find sufficient conditions under which the Casimir force increases. Interestingly, the first order perturbation corrections, are present in the obtained formula for the volume energy. We show that for some specific choices of parameters, the energy is independent of Robin coefficients. Consistency with the literature is shown in some limiting cases and well-known examples are presented for both an increase or decrease in the volume energy. [ABSTRACT FROM AUTHOR]

In recent work we constructed completely general conservation laws for energy (McGrath et�al 2012 Class. Quantum Grav.29 215012) and linear and angular momentum (Epp et�al 2013 Class. Quantum Grav.30 195019) of extended systems in general relativity based on the notion of a rigid quasilocal frame (RQF). We argued at a fundamental level that these RQF conservation laws are superior to conservation laws based on the local stress–energy–momentum tensor of matter because (1) they do not rely on spacetime symmetries and (2) they properly account for both matter and gravitational effects. Moreover, they provide simple, exact, operational expressions for fluxes of gravitational energy and linear and angular momentum. In this paper we derive the form of these laws in a general first post-Newtonian (1PN) approximation, and then apply these approximate laws to the problem of gravitational tidal interactions. We obtain formulas for tidal heating and tidal torque that agree with the literature, but without resorting to the use of pseudotensors. We describe the physical mechanism of these tidal interactions not in the traditional terms of a Newtonian gravitational force, but in terms of a much simpler and universal mechanism that is an exact, quasilocal manifestation of the equivalence principle in general relativity. As concrete examples, we look at the tidal heating of Jupiter’s moon Io and angular momentum transfer in the Earth–Moon system that causes a gradual spin-down of the Earth and recession of the Moon. In both examples we find agreement with observation. [ABSTRACT FROM AUTHOR]

The Bakry--Émery generalized Ricci tensor arises in scalar-tensor gravitation theories in the conformal gauge known as the Jordan frame. Recent results from the mathematics literature show that standard singularity and splitting theorems that hold when an energy condition is applied in general relativity also hold when that energy condition is applied to the Bakry--Émery tensor. We show here that a direct consequence is that the Hawking-Penrose singularity theorem and the timelike splitting theorem hold for scalar-tensor theory in the Jordan frame. As examples, we consider dilaton gravity (including totally anti-symmetric torsion) and the Brans-Dicke family of scalar-tensor theories. For Brans-Dicke theory the theorems do not extend to cover the entire space of values of the Brans-Dicke family parameter ω, and so may fail to hold for ω < -1. Observations show that this range of values does not describe our Universe, but the result is in accord with examples in the literature of Brans--Dicke spacetimes that have no singularity in the Jordan frame and do not split as a Riemannian product. [ABSTRACT FROM AUTHOR]

Viewing gravitational energy-momentum pµG as equal by observation, but different in essence from inertial energy-momentum pµ1 naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner Minkowski space M . The generalized asymptotic free scalar, Dirac and gauge fields in that theory are canonically quantized, the Fock spaces of stationary states are constructed and the gravitational limit--mapping the gravitational energy--momentum onto the inertial energy--momentum to account for their observed equality--is introduced. Next the S-matrix in quantum gravity is defined as the gravitational limit of the transition amplitudes of asymptotic into out-states in the gauge theory of volume-preserving diffeomorphisms. The so-defined S-matrix relates in- and out-states of observable particles carrying gravitational equal to inertial energy--momentum. Finally, generalized Lehmann-Symanzik-Zimmermann reduction formulae for scalar, Dirac and gauge fields are established which allow us to express S-matrix elements as the gravitational limit of truncated Fourier-transformed vacuum expectation values of time-ordered products of field operators of the interacting theory. Together with the generating functional of the latter established in Wiesendanger (2011 arXiv:1103.1012) any transition amplitude can in principle be computed consistently to any order in perturbative quantum gravity. [ABSTRACT FROM AUTHOR]

The problem of quasilocal energy has been extensively studied mainly in four dimensions. Here we report results regarding the quasilocal energy in spacetime dimension . After generalising three distinct quasilocal energy definitions to higher dimensions under appropriate assumptions, we evaluate their small sphere limits along lightcone cuts shrinking towards the lightcone vertex. The results in vacuum are conveniently represented in terms of the electromagnetic decompositions of the Weyl tensor. We find that the limits at presence of matter yield the stress tensor as expected, but the vacuum limits are in general not proportional to the Bel–Robinson superenergy Q in dimensions n  >  4. The result defies the role of the Bel–Robinson superenergy as characterising the gravitational energy in higher dimensions, albeit the fact that it uniquely generalises. Surprisingly, the Hawking energy and the Brown–York energy exactly agree upon the small sphere limits across all dimensions. The ‘new’ vacuum limit , however, cannot be interpreted as a gravitational energy because of its non-positivity. Furthermore, we also give the small sphere limits of the Kijowski–Epp–Liu–Yau type energy in higher dimensions, and again we see in place of Q. Our work extends earlier investigations of the small sphere limits (Horowitz and Schmidt 1982 Proc. R. Soc. A 381 215–24; Bergqvist 1994 Class. Quantum Grav. 11 3013–23; Brown et al 1999 Phys. Rev. D 59 064028; Yu 2007 (arXiv:0706.1081)), and also complements (Miao et al 2017 J. Geom. Anal. 27 1323–54). [ABSTRACT FROM AUTHOR]

The first calculation of the frequency spectrum of gravitational wave mass quadrupole radiation for binaries on hyperbolic orbits was performed in De Vittori et al (2012 Phys. Rev. D 86 044017). Some shortcomings of their derivation were pointed out, but there are still inaccuracies and supplements that we believe are worthwhile to communicate. In this note we provide a consistent and straightforward exposition of the frequency spectrum in the case of hyperbolic encounters and explicitly determine the parabolic limit, which was not possible with the previous treatments. [ABSTRACT FROM AUTHOR]

The energy content of cylindrical gravitational wave spacetimes is analyzed by considering two local descriptions of energy associated with the gravitational field, namely those based on the C-energy and the Bel–Robinson super-energy tensor. A Poynting–Robertson-like effect on the motion of massive test particles, beyond the geodesic approximation, is discussed, allowing them to interact with the background field through an external force which accounts for the exchange of energy and momentum between particles and waves. In addition, the relative strains exerted on a bunch of particles displaced orthogonally to the direction of propagation of the wave are examined, providing invariant information on spacetime curvature effects caused by the passage of the wave. The explicit examples of monochromatic waves with either a single or two polarization states as well as pulses of gravitational radiation are discussed. [ABSTRACT FROM AUTHOR]

A proposal for the gravitational energy–momentum tensor, known in the literature as the square root of Bel–Robinson tensor (SQBR), is analyzed in detail. Being constructed exclusively from the Weyl part of the Riemann tensor, such tensor encapsulates the geometric properties of free gravitational fields in terms of optical scalars of null congruences: making use of the general decomposition of any energy–momentum tensor, we explore the thermodynamic interpretation of such geometric quantities. While the matter energy–momentum is identically conserved due to Einstein’s field equations, the SQBR is not necessarily conserved and dissipative terms could arise in its vacuum continuity equation. We discuss the possible physical interpretations of such mathematical properties. [ABSTRACT FROM AUTHOR]

The first law of causal diamonds relates the area deficit of a small ball relative to flat space to the matter energy density it contains. At second order in the Riemann normal coordinate expansion, this energy density should receive contributions from the gravitational field itself. In this work, we study the second-order area deficit of the ball in the absence of matter and analyze its relation to possible notions of gravitational energy. In the small ball limit, a reasonable expectation for any proposed gravitational energy functional is that it evaluate to the Bel–Robinson energy density W in vacuum spacetimes. A direct calculation of the area deficit reveals a result that is not simply proportional to W. We discuss how the deviation from W is related to ambiguities in defining the shape of the ball in curved space, and provide several proposals for fixing these shape ambiguities. [ABSTRACT FROM AUTHOR]

The post-Newtonian approximation is useful to discuss gravitational waveforms for binary inspirals. In this note, for retrograde circular orbits in the equatorial plane, we discuss the region of validity of the post-Newtonian approximation by using the gravitational energy flux derived numerically and analytically in the black hole perturbation approach. It is found that the edge of the allowable region behaves quite intricately, including prograde orbits even if we treat higher post-Newtonian orders. [ABSTRACT FROM AUTHOR]

We investigate the energy configuration of a charged black hole in the teleparallel framework of general relativity. We obtain the energy–momentum tensor of the gravitational field in a stationary frame, and we calculate its contribution to the total energy of the system. We study the same gravitational field measured by an accelerated frame and we analyze how the energy–momentum tensor is transformed. We found that in the accelerated frame, a Poynting-like flux appears for the gravitational field but not for the electromagnetic field. [ABSTRACT FROM AUTHOR]

We obtain an energy inequality on null surfaces u = const in the Bondi–Sachs formalism. We show that for a sufficiently regular event horizon H there is an affine radial coordinate which is constant on H. Then the energy inequality can be prolongated to the horizon giving an estimation which is closely related to the Penrose inequality. We test it for the Kerr solution written in Fletcher-Lun coordinates. [ABSTRACT FROM AUTHOR]

We study the Schrödinger–Newton (SN) system of equations with the addition of gravitational field energy sourcing—such additional nonlinearity is to be expected from a theory of gravity (like general relativity (GR)), and its appearance in this simplified scalar setting (one of Einstein's precursors to GR) leads to significant changes in the spectrum of the self-gravitating theory. Using an iterative technique, we compare the mass dependence of the ground state energies of both SN and the new, self-sourced system and find that they are dramatically different. The Bohr method approach from old quantization provides a qualitative description of the difference, which comes from the additional nonlinearity introduced in the self-sourced case. In addition to comparison of ground state energies, we calculate the transition energy between the ground state and first excited state to compare emission frequencies between SN and the self-coupled scalar case. [ABSTRACT FROM AUTHOR]

We study the properties of gravitational systems in finite regions bounded by gravitational screens. We present a detailed construction of the total energy of such regions and of the energy and momentum balance equations due to the flow of matter and gravitational radiation through the screen. We establish that the gravitational screen possesses analogs of surface tension, internal energy, and viscous stress tensor, while the conservations are analogs of nonequilibrium balance equations for a viscous system. This gives a precise correspondence between gravity in finite regions and nonequilibrium thermodynamics. [ABSTRACT FROM AUTHOR]

A straightforward prescription for computing the D-dimensional potential energy of gravitational models, which is strongly based on the Feynman path integral, is built up. Using this method, the static potential energy for the interaction of two masses is found in the context of D-dimensional higher-derivative gravity models, and its behavior is analyzed afterwards in both ultraviolet and infrared regimes. As a consequence, two new gravity systems in which the potential energy is finite at the origin, respectively, in D = 5 and D = 6, are found. Since the aforementioned prescription is equivalent to that based on the marriage between quantum mechanics (to leading order, i.e., in the first Born approximation) and the nonrelativistic limit of quantum field theory, and bearing in mind that the latter relies basically on the calculation of the nonrelativistic Feynman amplitude (), a trivial expression for computing is obtained from our prescription as an added bonus. [ABSTRACT FROM AUTHOR]

We investigate some cosmological consequences of a vector–tensor theory where an Abelian symmetry in the vector sector is slightly broken by a mass term and by ghost-free derivative self-interactions. When studying cosmological expansion in the presence of large bare cosmological constant Λcc, we find that the theory admits branches of de Sitter solutions in which the scale of the Hubble parameter is inversely proportional to a power of Λcc. Hence, a large value of Λcc leads to a small size for the Hubble scale. In an appropriate limit, in which the symmetry breaking parameters are small, the theory recovers the Abelian symmetry plus an additional Galileon symmetry acting on the longitudinal vector polarization. The approximate Galileon symmetry can make the structure of this theory stable at the energy scales we are interested in. We also analyze the dynamics of linearized cosmological fluctuations around the de Sitter solutions, showing that no manifest instabilities arise, and that the transverse vector polarizations become massless around these configurations. [ABSTRACT FROM AUTHOR]

We apply the method of images to the exact initial data for cosmological models that contain a number of regularly arranged discrete masses. This allows us to join cosmological regions together by throats, and to construct wormholes in the initial data. These wormholes allow for the removal of the asymptotically flat ‘flange’ regions that would otherwise exist on the far side of black holes. The method of images also provides us with a way to investigate the definition of mass is cosmology, and the cosmological consequences of the gravitational interaction energies between massive objects. We find evidence that the interaction energies within clusters of massive objects do indeed appear to contribute to the total energy budget in the cosmological regions of the space–time. [ABSTRACT FROM AUTHOR]

We extend a previous analysis on the derivation of the dilaton Wess–Zumino (WZ) action in d = 4, based on the method of Weyl gauging, to six dimensions. As in the previous case, we discuss the structure of the same action in dimensional regularization using six-dimensional Weyl invariants, extracting the dilaton interactions in the most general scheme, with the inclusion of the local anomaly terms. As an application, we present the WZ action for the (2,0) tensor multiplet, which has been investigated in the past in the context of the AdS7/CFT6 holographic anomaly matching. We then extend to d = 6 the investigation of fully traced correlation functions of energy–momentum tensor’s, formerly presented in d = 4, showing that their hierarchy is functionally related only to the first six correlators. We give the explicit expressions of these in the most general scheme, up to rank-4. [ABSTRACT FROM AUTHOR]

We give an elementary proof of positivity of total gravitational energy in space-times containing complete smooth light-cones. [ABSTRACT FROM AUTHOR]